From 65d1bdcce4613c54efabf926e038e4ad2403f8df Mon Sep 17 00:00:00 2001 From: mb706 Date: Fri, 6 Sep 2024 13:59:20 +0200 Subject: [PATCH 01/87] colroles tests respect new colroles constraints --- tests/testthat/test_pipeop_colroles.R | 10 ++++++---- 1 file changed, 6 insertions(+), 4 deletions(-) diff --git a/tests/testthat/test_pipeop_colroles.R b/tests/testthat/test_pipeop_colroles.R index 88de51627..500f5f0b3 100644 --- a/tests/testthat/test_pipeop_colroles.R +++ b/tests/testthat/test_pipeop_colroles.R @@ -18,7 +18,8 @@ test_that("PipeOpColRoles - assertion works", { test_that("PipeOpColRoles - name checking works", { task = mlr_tasks$get("iris") - op = PipeOpColRoles$new(param_vals = list(new_role = list(Petal.Length = "name", wrong = "feature"))) + task$cbind(data.table(rn = sprintf("%03d", 1:150))) + op = PipeOpColRoles$new(param_vals = list(new_role = list(rn = "name", wrong = "feature"))) expect_error(train_pipeop(op, inputs = list(task)), regexp = "subset") }) @@ -30,15 +31,16 @@ test_that("PipeOpColRoles - changing the role of a target fails", { test_that("PipeOpColRoles - functionality works", { task = mlr_tasks$get("iris") - op = PipeOpColRoles$new(param_vals = list(new_role = list(Petal.Length = c("name", "order"), Petal.Width = character(0)))) + task$cbind(data.table(rn = sprintf("%03d", 1:150))) + op = PipeOpColRoles$new(param_vals = list(new_role = list(rn = "name", Petal.Length = "order", Petal.Width = character(0)))) train_out = train_pipeop(op, inputs = list(task))$output col_roles_actual = train_out$col_roles col_roles_expected = list( - feature = c("Sepal.Length", "Sepal.Width"), target = "Species", name = "Petal.Length", + feature = c("Sepal.Length", "Sepal.Width"), target = "Species", name = "rn", order = "Petal.Length", stratum = character(0), group = character(0), weight = character(0)) if ("weights_learner" %in% names(task)) names(col_roles_expected)[names(col_roles_expected) == "weight"] = "weights_learner" expect_equal(train_out$col_roles[names(col_roles_expected)], col_roles_expected) - expect_equal(train_out$row_names$row_name, task$data(cols = "Petal.Length")[[1L]]) + expect_equal(train_out$row_names$row_name, task$data(cols = "rn")[[1L]]) expect_true("Petal.Width" %nin% colnames(train_out$data())) predict_out = predict_pipeop(op, inputs = list(task))$output expect_equal(train_out, predict_out) From d419f1400c672c316a6cffb1382f9e90775212b4 Mon Sep 17 00:00:00 2001 From: mb706 Date: Fri, 6 Sep 2024 22:57:01 +0200 Subject: [PATCH 02/87] logical expressions as CNF --- R/CnfFormula.R | 366 +++++++++++++++++++++++++++++++++++++++++++++++ R/GraphLearner.R | 27 +++- 2 files changed, 386 insertions(+), 7 deletions(-) create mode 100644 R/CnfFormula.R diff --git a/R/CnfFormula.R b/R/CnfFormula.R new file mode 100644 index 000000000..9c3b6163c --- /dev/null +++ b/R/CnfFormula.R @@ -0,0 +1,366 @@ + +### CNF representation of branch activation conditions +### Where doing it man. Where making this hapen +# For every position in a Graph, we want to express which PipeOpBranch needs +# to have which output active in order to activate this PipeOp. +# If a normal PipeOp has multipel inputs, then it is active when all of its inputs are active, +# corresponding to a logical AND. +# If a PipeOpUnbranch has multiple active inputs, then it is active when exactly one of its +# input is active, corresponding to a logical OR. +# We could, strictly speaking, also try to handle cases where a normal PipeOp with +# mixed inputs gives an error, or where a PipeOpUnbranch with multiple active inputs gives +# an error, but that would make things even more complicated than they already are, so +# we are not doing that here. + +# Container object for possible branch conditions. +CnfUniverse = function() structure(new.env(parent = emptyenv()), class = "CnfUniverse") + +# We represent symbols through a name and a pointer to their universe. +# We only allow operations between symbols that are in the same universe. +CnfSymbol = function(universe, name, domain) { + assert_class(universe, "CnfUniverse") + assert_string(name) + assert_character(domain, any.missing = FALSE, min.len = 1) + if (exists(name, universe)) { + stopf("Variable '%s' already exists in the universe.", name) + } + assign(name, domain, universe) + structure( + name, + universe = universe, + class = "CnfSymbol" + ) +} + +# We allow retrieving symbols from the universe by name. +`[[.CnfUniverse` = function(universe, name) { + assert_string(name) + if (!exists(name, universe)) { + stopf("Variable '%s' does not exist in the universe.", name) + } + structure( + name, + universe = universe, + class = "CnfSymbol" + ) +} + +`$.CnfUniverse` = `[[.CnfUniverse` + +# An expression of the form "X %in% {x1, x2, x3}" +CnfAtom = function(symbol, values) { + assert_class(symbol, "CnfSymbol") + domain = get(symbol, attr(symbol, "universe")) + assert_subset(values, domain) + if (test_set_equal(values, domain)) { + structure( + TRUE, + universe = attr(symbol, "universe"), + class = "CnfAtom" + ) + } else if (length(values) == 0) { + structure( + FALSE, + universe = attr(symbol, "universe"), + class = "CnfAtom" + ) + } else { + structure( + list(symbol = c(symbol), values = unique(values)), + universe = attr(symbol, "universe"), + class = "CnfAtom" + ) + } +} + +# A clause is a disjunction of atoms. +CnfClause = function(atoms) { + assert_list(atoms, types = "CnfAtom") + if (!length(atoms)) { + return(structure( + FALSE, + universe = NULL, + class = "CnfClause" + )) + } + entries = list() + universe = attr(atoms[[1]], "universe") + for (a in atoms) { + if (!identical(attr(a, "universe"), universe)) { + stop("All symbols must be in the same universe.") + } + if (isTRUE(a)) { + entries = TRUE + break + } + if (isFALSE(a)) { + next + } + entries[[a$symbol]] = unique(c(entries[[a$symbol]], a$values)) + if (test_set_equal(entries[[a$symbol]], get(a$symbol, universe))) { + entries = TRUE + break + } + } + structure( + if (!length(entries)) FALSE else entries, + universe = universe, + class = "CnfClause" + ) +} + +# A formula is a conjunction of clauses. +CnfFormula = function(clauses) { + assert_list(clauses, types = "CnfClause") + if (!length(clauses)) { + return(structure( + TRUE, + universe = NULL, + class = "CnfFormula" + )) + } + universe = attr(clauses[[1]], "universe") + entries = list() + for (c in clauses) { + if (isFALSE(c)) { + entries = FALSE + break + } + if (isTRUE(c)) { + next + } + if (!identical(attr(c, "universe"), universe)) { + # if clauses[[1]] is FALSE, then it is possible that it has no + # universe; however, in that case we will break before coming here. + stop("All clauses must be in the same universe.") + } + attr(c, "universe") = NULL + entries[[length(entries) + 1]] = c + } + simplify_cnf(entries, universe) +} + +simplify_cnf = function(entries, universe) { + return_false = structure( + FALSE, + universe = universe, + class = "CnfFormula" + ) + + # if we are already TRUE or FALSE no simplification is necessary + can_simplify = !is.logical(entries) + # likewise, if there is only one clause left, no simplification is necessary. + + units = list() + + while (can_simplify && length(entries) > 1) { + # we do the following until we are sure there are no more simplifications to be made. + # this is the case if we have not meaningfully simplified anything in the last iteration. + can_simplify = FALSE + # sort clauses by length, since (1) length-1-clauses are special, and (2) short clauses can only ever subsume longer ones + entries = entries[order(lengths(entries))] + eliminated = logical(length(entries)) + # Let sum(A) be the symbols in clause A, and val(A, s) be the values of symbol s admitted in clause A. + for (i in seq_along(entries)) { + ei = entries[[i]] + # If |sym(A)| == 1, sym(A) == {s} and s is in sym(B), then val(B, s) <- intersect(val(A, s), val(B, s)) ("unit propagation") + # units is a named list of symbols in size-one-clauses, together with their values. + # We iterate over all symbols in ei that are also in units, and intersect their values. + for (unit_symbol in intersect(names(ei), names(units))) { + length_before_ei = length(ei[[unit_symbol]]) + length_before_unit = length(units[[unit_symbol]]) + intersection = intersect(units[[unit_symbol]], ei[[unit_symbol]]) + ei[[unit_symbol]] = intersection + if (length(ei) == 1 && length(intersection) != length_before_unit) { + # we made a unit shorter, this means we need to simplify the entry from which units[[unit_symbol]] came + can_simplify = TRUE + } + if (!length(ei[[unit_symbol]])) { + ei[[unit_symbol]] = NULL + can_simplify = TRUE # could have new subset-relationships now + } + if (!length(ei)) { + return(return_false) + } + if (length(intersection) != length_before_ei) { + # need to store changed ei entry only if its length changed; otherwise we know the intersection did not do anything. + entries[[i]] = ei + } + } + if (length(ei) == 1) { + # even if names(ei) is already in units, at this point ei[[1]] is the intersection of the values + units[[names(ei)]] = ei[[1]] + } + # If sym(A) is a subset of sym(B) and for each s in sym(A), val(A, s) is a subset of val(B, s), then A implies B, so B can be removed ("subsumption elimination"). + for (j in seq_len(i - 1)) { + ej = entries[[j]] + if (all(names(ej) %in% names(ei)) && all(sapply(names(ej), function(s) all(ej[[s]] %in% ei[[s]])))) { + # can't do entries[[i]] = NULL, since we are iterating over entries; the entries[[i]] would break. + eliminated[[i]] = TRUE + } + } + } + entries = entries[!eliminated] + } + structure( + if (!length(entries)) TRUE else entries, + universe = universe, + class = "CnfFormula" + ) +} + +`&.CnfFormula` = function(e1, e2) { + e1 = as.CnfFormula(e1) + e2 = as.CnfFormula(e2) + if (isTRUE(e1)) return(e2) + if (isTRUE(e2)) return(e1) + if (isFALSE(e1)) return(e1) + if (isFALSE(e2)) return(e2) + if (!identical(attr(e1, "universe"), attr(e2, "universe"))) { + stop("Both formulas must be in the same universe.") + } + simplify_cnf(c(e1, e2), attr(e1, "universe")) +} + +`|.CnfFormula` = function(e1, e2) { + e1 = as.CnfFormula(e1) + e2 = as.CnfFormula(e2) + if (isFALSE(e1)) return(e2) + if (isFALSE(e2)) return(e1) + if (isTRUE(e1)) return(e1) + if (isTRUE(e2)) return(e2) + if (!identical(attr(e1, "universe"), attr(e2, "universe"))) { + stop("Both formulas must be in the same universe.") + } + universe = attr(e1, "universe") + if (length(e1) > length(e2)) { + # we want the outer loop to be over the shorter of the two + e1 = e2 + e2 = e1 + } + # distribute || into clauses + distributed = lapply(e1, function(e1_clause) { + for (i2 in seq_along(e2)) { + e2_clause = e2[[i2]] + eliminated = logical(length(e2_clause)) + for (sym in names(e1_clause)) { + # add the symbols from e1_clause to e2_clause + # (if e2_clause does not contain a symbol, it is added) + e2_clause[[sym]] = unique(c(e1_clause[[sym]], e2_clause[[sym]])) + if (test_set_equal(e2_clause[[sym]], get(sym, universe))) { + eliminated[[i2]] = TRUE + break + } + } + e2[[i2]] = e2_clause + } + e2[!eliminated] + }) + simplify_cnf(unlist(distributed, recursive = FALSE), universe) +} + +`&.CnfClause` = function(e1, e2) { + as.CnfFormula(e1) & as.CnfFormula(e2) +} + +`|.CnfClause` = function(e1, e2) { + as.CnfFormula(e1) | as.CnfFormula(e2) +} + +`&.CnfAtom` = function(e1, e2) { + as.CnfFormula(e1) & as.CnfFormula(e2) +} + +`|.CnfAtom` = function(e1, e2) { + as.CnfFormula(e1) | as.CnfFormula(e2) +} + +as.CnfFormula = function(x) { + UseMethod("as.CnfFormula") +} + +chooseOpsMethod.CnfFormula <- function(x, y, mx, my, cl, reverse) TRUE +chooseOpsMethod.CnfClause <- function(x, y, mx, my, cl, reverse) TRUE +chooseOpsMethod.CnfAtom <- function(x, y, mx, my, cl, reverse) TRUE + +as.CnfFormula.logical = function(x) { + assert_flag(x) + return(structure( + x, + universe = NULL, + class = "CnfFormula" + )) +} + +as.CnfFormula.CnfAtom = function(x) { + as.CnfFormula(CnfClause(list(x))) +} + +as.CnfFormula.CnfClause = function(x) { + CnfFormula(list(x)) +} + +as.CnfFormula.CnfFormula = function(x) { + x +} + +as.CnfFormula.default = function(x) { + stop("Cannot convert object to CnfFormula.") +} + +print.CnfUniverse = function(x, ...) { + if (!length(x)) { + cat("CnfUniverse (empty).\n") + return(invisible(x)) + } + cat("CnfUniverse with variables:\n") + for (var in names(x)) { + cat(sprintf(" %s: {%s}\n", var, paste(get(var, x), collapse = ", "))) + } + invisible(x) +} + +print.CnfSymbol = function(x, ...) { + cat(sprintf("CnfSymbol '%s' with domain {%s}.\n", c(x), paste(get(x, attr(x, "universe")), collapse = ", "))) + invisible(x) +} + +print.CnfAtom = function(x, ...) { + if (isTRUE(x)) { + cat("TRUE\n") + } else if (isFALSE(x)) { + cat("FALSE\n") + } else { + cat(sprintf("%s %%in%% {%s}.\n", x$symbol, paste(x$values, collapse = ", "))) + } + invisible(x) +} + +print.CnfClause = function(x, ...) { + if (isTRUE(x)) { + cat("TRUE\n") + } else if (isFALSE(x)) { + cat("FALSE\n") + } else { + cat("CnfClause with entries:\n") + for (sym in names(x)) { + cat(sprintf(" %s %%in%% {%s}\n", sym, paste(x[[sym]], collapse = ", "))) + } + } + invisible(x) +} + +print.CnfFormula = function(x, ...) { + if (isTRUE(x)) { + cat("TRUE\n") + } else if (isFALSE(x)) { + cat("FALSE\n") + } else { + cat("CnfFormula with entries:\n") + for (i in seq_along(x)) { + cat(sprintf(" Clause %d:\n", i)) + print(x[[i]]) + } + } + invisible(x) +} diff --git a/R/GraphLearner.R b/R/GraphLearner.R index b09c0ed0b..3c369e0c6 100644 --- a/R/GraphLearner.R +++ b/R/GraphLearner.R @@ -611,9 +611,14 @@ infer_task_type = function(graph) { # i.e. that gets non-NOP-input in the current hyperparameter configuration of PipeOpBranch ops. # Returns a list, named by PipeOpUnbranch IDs, containing the incoming PipeOp IDs. # PipeOpBranch ops that are connected to overall Graph input get an empty string as predecessor ID. +# Returns a named `list`, named by PipeOpUnbranch IDs, containing the incoming PipeOp ID. +# Typically, there is only one incoming PipeOp ID; only if a `selection` is not set, or a `TuneToken`, +# do we concede that we do not know the exact input; in this case the list entry contains a vector +# of all possible incoming PipeOp IDs. get_po_unbranch_active_input = function(graph) { # query a given PipeOpBranch what its selected output is # Currently, PipeOpBranch 'selection' can be either integer-valued or a string. + # If it is something else (unset, or a TuneToken), we cannot infer the active output. get_po_branch_active_output = function(pipeop) { assertR6(pipeop, "PipeOpBranch") pob_ps = pipeop$param_set @@ -622,12 +627,14 @@ get_po_unbranch_active_input = function(graph) { # is not given or a TuneToken or something like that. if (pob_ps$class[["selection"]] == "ParamInt") { if (!test_int(selection)) { - stopf("Cannot infer active output of PipeOpBranch %s with non-numeric 'selection'.", pipeop$id) + # stopf("Cannot infer active output of PipeOpBranch %s with non-numeric 'selection'.", pipeop$id) + return(pipeop$output$name) } return(pipeop$output$name[[pob_ps$values$selection]]) } else { if (!test_string(selection)) { - stopf("Cannot infer active output of PipeOpBranch %s with non-string 'selection'.", pipeop$id) + # stopf("Cannot infer active output of PipeOpBranch %s with non-string 'selection'.", pipeop$id) + return(pipeop$output$name) } return(pob_ps$values$selection) } @@ -690,11 +697,15 @@ get_po_unbranch_active_input = function(graph) { if (state_current && inherits(pipeop, "PipeOpBranch")) { # PipeOpBranch is only special when it is actually active active_output = get_po_branch_active_output(pipeop) - branch_state_info[src_id == pipeop_id, `:=`(state = src_channel == active_output, - reason = as.list(sprintf("PipeOpBranch '%s' %s output '%s'", - pipeop_id, ifelse(src_channel == active_output, "active", "inactive"), - src_channel)) - )] + if (length(active_output) == 1) { + branch_state_info[src_id == pipeop_id, `:=`(state = src_channel == active_output, + reason = as.list(sprintf("PipeOpBranch '%s' %s output '%s'", + pipeop_id, ifelse(src_channel == active_output, "active", "inactive"), + src_channel)) + )] + } else { + + } } else { branch_state_info[src_id == pipeop_id, `:=`(state = state_current, reason = list(reason_current))] } @@ -702,6 +713,8 @@ get_po_unbranch_active_input = function(graph) { po_unbranch_active_input } + + andpaste = function(x, sep = ", ", lastsep = ", and ") { if (length(x) == 0) return("") if (length(x) == 1) return(x[[1]]) From 4d6279a7854d372b16b6312275a0ed4ab4453f07 Mon Sep 17 00:00:00 2001 From: mb706 Date: Sat, 7 Sep 2024 00:30:17 +0200 Subject: [PATCH 03/87] more autism --- R/CnfFormula.R | 77 ++++++++++++++++++++++++++++++++++++++++++++---- R/GraphLearner.R | 2 -- 2 files changed, 71 insertions(+), 8 deletions(-) diff --git a/R/CnfFormula.R b/R/CnfFormula.R index 9c3b6163c..691939926 100644 --- a/R/CnfFormula.R +++ b/R/CnfFormula.R @@ -7,10 +7,9 @@ # corresponding to a logical AND. # If a PipeOpUnbranch has multiple active inputs, then it is active when exactly one of its # input is active, corresponding to a logical OR. -# We could, strictly speaking, also try to handle cases where a normal PipeOp with -# mixed inputs gives an error, or where a PipeOpUnbranch with multiple active inputs gives -# an error, but that would make things even more complicated than they already are, so -# we are not doing that here. +# We handle cases where a normal PipeOp with mixed inputs gives an error, or where +# a PipeOpUnbranch with multiple active inputs gives an error, by also representing +# the conditions under which an error is thrown. # Container object for possible branch conditions. CnfUniverse = function() structure(new.env(parent = emptyenv()), class = "CnfUniverse") @@ -73,7 +72,11 @@ CnfAtom = function(symbol, values) { } } +# construct CnfAtom with `X %among% c("a", "b", "c")` +`%among%` = CnfAtom + # A clause is a disjunction of atoms. +# X %among% c("a", "b", "c") | Y %among% c("d", "e", "f") CnfClause = function(atoms) { assert_list(atoms, types = "CnfAtom") if (!length(atoms)) { @@ -110,6 +113,7 @@ CnfClause = function(atoms) { } # A formula is a conjunction of clauses. +# (X %among% c("a", "b", "c") | Y %among% c("d", "e", "f")) & (Z %among% c("g", "h", "i")) CnfFormula = function(clauses) { assert_list(clauses, types = "CnfClause") if (!length(clauses)) { @@ -235,14 +239,15 @@ simplify_cnf = function(entries, universe) { universe = attr(e1, "universe") if (length(e1) > length(e2)) { # we want the outer loop to be over the shorter of the two + tmp = e1 e1 = e2 - e2 = e1 + e2 = tmp } # distribute || into clauses distributed = lapply(e1, function(e1_clause) { + eliminated = logical(length(e2)) for (i2 in seq_along(e2)) { e2_clause = e2[[i2]] - eliminated = logical(length(e2_clause)) for (sym in names(e1_clause)) { # add the symbols from e1_clause to e2_clause # (if e2_clause does not contain a symbol, it is added) @@ -275,6 +280,34 @@ simplify_cnf = function(entries, universe) { as.CnfFormula(e1) | as.CnfFormula(e2) } +`!.CnfAtom` = function(x) { + if (is.logical(x)) { + not_x = if (x) FALSE else TRUE # can't use '!' here... + attributes(not_x) = attributes(x) # keep class and universe + return(not_x) + } + structure( + list(symbol = x$symbol, values = setdiff(get(x$symbol, attr(x, "universe")), x$values)), + universe = attr(x, "universe"), + class = "CnfAtom" + ) +} + +`!.CnfClause` = function(x) { + !as.CnfFormula(x) +} + +`!.CnfFormula` = function(x) { + universe = attr(x, "universe") + negated_formulae = lapply(x, function(clause) { + CnfFormula(lapply(names(clause), function(sym) { + CnfClause(list(!CnfAtom(universe[[sym]], clause[[sym]]))) + })) + }) + # can't Reduce(`|`, negated_formulae) here, since for this we'd have to register the `|` S3 method + Reduce(function(x, y) x | y, negated_formulae) +} + as.CnfFormula = function(x) { UseMethod("as.CnfFormula") } @@ -308,6 +341,24 @@ as.CnfFormula.default = function(x) { stop("Cannot convert object to CnfFormula.") } +as.logical.CnfFormula = function(x) { + if (isTRUE(x)) { + return(TRUE) + } + if (isFALSE(x)) { + return(FALSE) + } + return(NA) +} + +as.logical.CnfClause = function(x) { + as.logical(as.CnfFormula(x)) +} + +as.logical.CnfAtom = function(x) { + as.logical(as.CnfFormula(x)) +} + print.CnfUniverse = function(x, ...) { if (!length(x)) { cat("CnfUniverse (empty).\n") @@ -364,3 +415,17 @@ print.CnfFormula = function(x, ...) { } invisible(x) } + + + +## to test: +# subsumption +# unit elimination +# unit elimination makes large clause smaller, leading to additional u.e. +# unit elimination makes large clause smaller, leading to subsumption + +# branch with totune is swallowed by single unbranch +# branch with totune is swallowed by multiple unbranch +# branches with totune can possibly lead to conflicts, but not always (multiple active inputs to unbranch, or mixed inputs to normal pipeops) +# branches with totune always lead to conflicts (multiple active inputs to unbranch, or mixed inputs to normal pipeops, or choice between both) +# can we recognize that a certain choice would lead to a conflict, making only other choices possible? diff --git a/R/GraphLearner.R b/R/GraphLearner.R index 3c369e0c6..d3294defb 100644 --- a/R/GraphLearner.R +++ b/R/GraphLearner.R @@ -713,8 +713,6 @@ get_po_unbranch_active_input = function(graph) { po_unbranch_active_input } - - andpaste = function(x, sep = ", ", lastsep = ", and ") { if (length(x) == 0) return("") if (length(x) == 1) return(x[[1]]) From e3240d0ebda53906eb31be7453a9a6367b6769bd Mon Sep 17 00:00:00 2001 From: mb706 Date: Sat, 7 Sep 2024 00:31:46 +0200 Subject: [PATCH 04/87] enough for today --- R/CnfFormula.R | 1 + 1 file changed, 1 insertion(+) diff --git a/R/CnfFormula.R b/R/CnfFormula.R index 691939926..ecf8f1476 100644 --- a/R/CnfFormula.R +++ b/R/CnfFormula.R @@ -73,6 +73,7 @@ CnfAtom = function(symbol, values) { } # construct CnfAtom with `X %among% c("a", "b", "c")` +# we cannot overload `%in%`, unfortunately `%among%` = CnfAtom # A clause is a disjunction of atoms. From 259c16d59ace2858461a5151aece62ac66a90802 Mon Sep 17 00:00:00 2001 From: mb706 Date: Sat, 7 Sep 2024 04:23:19 +0200 Subject: [PATCH 05/87] incredibly overdoing this --- R/CnfFormula.R | 52 ++++++++++++++++++++++++++++++++++++++++++++++---- 1 file changed, 48 insertions(+), 4 deletions(-) diff --git a/R/CnfFormula.R b/R/CnfFormula.R index ecf8f1476..f584d4a63 100644 --- a/R/CnfFormula.R +++ b/R/CnfFormula.R @@ -152,8 +152,10 @@ simplify_cnf = function(entries, universe) { class = "CnfFormula" ) + # can we do unit elimination? # if we are already TRUE or FALSE no simplification is necessary - can_simplify = !is.logical(entries) + # this only works if there actually are units. + can_simplify = !is.logical(entries) && any(lengths(entries) == 1) # likewise, if there is only one clause left, no simplification is necessary. units = list() @@ -164,7 +166,6 @@ simplify_cnf = function(entries, universe) { can_simplify = FALSE # sort clauses by length, since (1) length-1-clauses are special, and (2) short clauses can only ever subsume longer ones entries = entries[order(lengths(entries))] - eliminated = logical(length(entries)) # Let sum(A) be the symbols in clause A, and val(A, s) be the values of symbol s admitted in clause A. for (i in seq_along(entries)) { ei = entries[[i]] @@ -182,7 +183,6 @@ simplify_cnf = function(entries, universe) { } if (!length(ei[[unit_symbol]])) { ei[[unit_symbol]] = NULL - can_simplify = TRUE # could have new subset-relationships now } if (!length(ei)) { return(return_false) @@ -196,13 +196,49 @@ simplify_cnf = function(entries, universe) { # even if names(ei) is already in units, at this point ei[[1]] is the intersection of the values units[[names(ei)]] = ei[[1]] } + } + } + if (!is.logical(entries) && length(entries) > 1) { + entries = entries[order(lengths(entries))] # removing units may have changed the order + eliminated = logical(length(entries)) + for (i in seq_along(entries)) { + if (eliminated[[i]]) next # can only happen if we do the tautology elimination, which searches forward + ei = entries[[i]] # If sym(A) is a subset of sym(B) and for each s in sym(A), val(A, s) is a subset of val(B, s), then A implies B, so B can be removed ("subsumption elimination"). for (j in seq_len(i - 1)) { + if (eliminated[[j]]) next ej = entries[[j]] - if (all(names(ej) %in% names(ei)) && all(sapply(names(ej), function(s) all(ej[[s]] %in% ei[[s]])))) { + name_overlap = names(ej) %in% names(ei) + if (all(name_overlap) && all(sapply(names(ej), function(s) all(ej[[s]] %in% ei[[s]])))) { # can't do entries[[i]] = NULL, since we are iterating over entries; the entries[[i]] would break. eliminated[[i]] = TRUE } + # simple tautology elimination + # if s is in sym(A) and sym(B), and val(A, s) and val(B, s) are disjoint, then (A - s | B - s) is implied, + # and all superset clauses of (A - s | B - s) can be removed. + # we could also do this for higher order terms, intersection over X of val(X, s) == 0 etc., but this gets more complex. + # tbh, I am not sure if this is actually worth it + if (!eliminated[[i]]) { + which_name_overlap = which(name_overlap) + if (length(which_name_overlap)) cnames = union(names(ei), names(ej)) + for (no in which_name_overlap) { + s = names(ej)[[no]] + # intersection is not 0 --> try next one + if (length(intersect(ej[[s]], ei[[s]]))) next + cnames_s = setdiff(cnames, s) + # loop down from large to small, since then we can break once we find a clause with insufficient entries + for (k in rev(seq_along(entries))) { + if (k == i || k == j) next + ek = entries[[k]] + # all of cnames_s must be in ek, otherwise we can't eliminate + # since we are looping down from large to small ek, we can break once this is not the case + if (length(ek) < length(cnames) - 1) break + if (all(cnames_s %in% names(ek)) && all(sapply(cnames_s, function(s2) all(union(ei[[s2]], ej[[s2]]) %in% ek[[s2]])))) { + eliminated[[k]] = TRUE + } + } + } + } } } entries = entries[!eliminated] @@ -430,3 +466,11 @@ print.CnfFormula = function(x, ...) { # branches with totune can possibly lead to conflicts, but not always (multiple active inputs to unbranch, or mixed inputs to normal pipeops) # branches with totune always lead to conflicts (multiple active inputs to unbranch, or mixed inputs to normal pipeops, or choice between both) # can we recognize that a certain choice would lead to a conflict, making only other choices possible? + +# why does this blow up? +# + +#!!(((u$A %among% "T" | u$B %among% "F") & (u$A %among% "F" | u$C %among% "T") & (u$B %among% "T" | u$C %among% "F"))) + +# This is because we don't eliminate (C | A) & (!C | B) & (B | A) by removing (B | A) +# so, if clause X and clause Y have a symbol in common where the values are disjoint, the disjunction of the rest is implied? From 940efcd215863d01ef13b2340a4137394a316254 Mon Sep 17 00:00:00 2001 From: mb706 Date: Sat, 7 Sep 2024 04:52:44 +0200 Subject: [PATCH 06/87] performance improvement --- R/CnfFormula.R | 20 ++++++++++++++++---- 1 file changed, 16 insertions(+), 4 deletions(-) diff --git a/R/CnfFormula.R b/R/CnfFormula.R index f584d4a63..afc04e9f3 100644 --- a/R/CnfFormula.R +++ b/R/CnfFormula.R @@ -220,7 +220,13 @@ simplify_cnf = function(entries, universe) { # tbh, I am not sure if this is actually worth it if (!eliminated[[i]]) { which_name_overlap = which(name_overlap) - if (length(which_name_overlap)) cnames = union(names(ei), names(ej)) + if (length(which_name_overlap)) { + # build the union of values of overlapping symbols + # in the innerloop we will check that most of this is a subset of any other clause + # "most of" here means: all but the one symbol s where the values are disjoint + cnames = union(names(ei), names(ej)) + cunion = sapply(cnames, function(s2) union(ei[[s2]], ej[[s2]]), simplify = FALSE) + } for (no in which_name_overlap) { s = names(ej)[[no]] # intersection is not 0 --> try next one @@ -233,7 +239,7 @@ simplify_cnf = function(entries, universe) { # all of cnames_s must be in ek, otherwise we can't eliminate # since we are looping down from large to small ek, we can break once this is not the case if (length(ek) < length(cnames) - 1) break - if (all(cnames_s %in% names(ek)) && all(sapply(cnames_s, function(s2) all(union(ei[[s2]], ej[[s2]]) %in% ek[[s2]])))) { + if (all(cnames_s %in% names(ek)) && all(sapply(cnames_s, function(s2) all(cunion[[s2]] %in% ek[[s2]])))) { eliminated[[k]] = TRUE } } @@ -338,7 +344,13 @@ simplify_cnf = function(entries, universe) { universe = attr(x, "universe") negated_formulae = lapply(x, function(clause) { CnfFormula(lapply(names(clause), function(sym) { - CnfClause(list(!CnfAtom(universe[[sym]], clause[[sym]]))) + # !CnfAtom(universe[[sym]], clause[[sym]]) + structure( + list(setdiff(get(sym, universe), clause[[sym]])), + names = sym, + universe = universe, + class = "CnfClause" + ) })) }) # can't Reduce(`|`, negated_formulae) here, since for this we'd have to register the `|` S3 method @@ -470,7 +482,7 @@ print.CnfFormula = function(x, ...) { # why does this blow up? # -#!!(((u$A %among% "T" | u$B %among% "F") & (u$A %among% "F" | u$C %among% "T") & (u$B %among% "T" | u$C %among% "F"))) +# profvis::profvis(replicate(3000, { !!(((u$A %among% "T" | u$B %among% "F") & (u$A %among% "F" | u$C %among% "T") & (u$B %among% "T" | u$C %among% "F"))) ; NULL }) -> ., simplify = FALSE) # This is because we don't eliminate (C | A) & (!C | B) & (B | A) by removing (B | A) # so, if clause X and clause Y have a symbol in common where the values are disjoint, the disjunction of the rest is implied? From deffc737157a88c422ffb307898ddc9b2dee0b85 Mon Sep 17 00:00:00 2001 From: mb706 Date: Sat, 7 Sep 2024 05:11:27 +0200 Subject: [PATCH 07/87] going crazy with optimizations --- R/CnfFormula.R | 20 ++++++++++---------- 1 file changed, 10 insertions(+), 10 deletions(-) diff --git a/R/CnfFormula.R b/R/CnfFormula.R index afc04e9f3..9340fe058 100644 --- a/R/CnfFormula.R +++ b/R/CnfFormula.R @@ -51,7 +51,7 @@ CnfAtom = function(symbol, values) { assert_class(symbol, "CnfSymbol") domain = get(symbol, attr(symbol, "universe")) assert_subset(values, domain) - if (test_set_equal(values, domain)) { + if (all(domain %in% values)) { structure( TRUE, universe = attr(symbol, "universe"), @@ -101,7 +101,7 @@ CnfClause = function(atoms) { next } entries[[a$symbol]] = unique(c(entries[[a$symbol]], a$values)) - if (test_set_equal(entries[[a$symbol]], get(a$symbol, universe))) { + if (all(get(a$symbol, universe) %in% entries[[a$symbol]])) { entries = TRUE break } @@ -220,13 +220,12 @@ simplify_cnf = function(entries, universe) { # tbh, I am not sure if this is actually worth it if (!eliminated[[i]]) { which_name_overlap = which(name_overlap) - if (length(which_name_overlap)) { - # build the union of values of overlapping symbols - # in the innerloop we will check that most of this is a subset of any other clause - # "most of" here means: all but the one symbol s where the values are disjoint - cnames = union(names(ei), names(ej)) - cunion = sapply(cnames, function(s2) union(ei[[s2]], ej[[s2]]), simplify = FALSE) - } + # - build the union of values of overlapping symbols + # - in the innerloop we will check that most of this is a subset of any other clause + # - "most of" here means: all but the one symbol s where the values are disjoint + # - use delayedAssign to avoid computation if there is no overlap with empty intersect + delayedAssign("cnames", union(names(ei), names(ej))) + delayedAssign("cunion", sapply(cnames, function(s2) union(ei[[s2]], ej[[s2]]), simplify = FALSE)) for (no in which_name_overlap) { s = names(ej)[[no]] # intersection is not 0 --> try next one @@ -295,7 +294,8 @@ simplify_cnf = function(entries, universe) { # add the symbols from e1_clause to e2_clause # (if e2_clause does not contain a symbol, it is added) e2_clause[[sym]] = unique(c(e1_clause[[sym]], e2_clause[[sym]])) - if (test_set_equal(e2_clause[[sym]], get(sym, universe))) { + # faster than test_set_equal + if (all(get(sym, universe) %in% e2_clause[[sym]])) { eliminated[[i2]] = TRUE break } From b9b45c332078e25be06edef6255a311c0f8676a1 Mon Sep 17 00:00:00 2001 From: mb706 Date: Sat, 7 Sep 2024 22:51:29 +0200 Subject: [PATCH 08/87] printers --- R/CnfFormula.R | 184 +++++++++++++++++++++++++++++++++++++++++-------- 1 file changed, 157 insertions(+), 27 deletions(-) diff --git a/R/CnfFormula.R b/R/CnfFormula.R index 9340fe058..e7b620146 100644 --- a/R/CnfFormula.R +++ b/R/CnfFormula.R @@ -293,7 +293,7 @@ simplify_cnf = function(entries, universe) { for (sym in names(e1_clause)) { # add the symbols from e1_clause to e2_clause # (if e2_clause does not contain a symbol, it is added) - e2_clause[[sym]] = unique(c(e1_clause[[sym]], e2_clause[[sym]])) + e2_clause[[sym]] = union(e1_clause[[sym]], e2_clause[[sym]]) # faster than test_set_equal if (all(get(sym, universe) %in% e2_clause[[sym]])) { eliminated[[i2]] = TRUE @@ -308,19 +308,73 @@ simplify_cnf = function(entries, universe) { } `&.CnfClause` = function(e1, e2) { - as.CnfFormula(e1) & as.CnfFormula(e2) + if (isFALSE(e1)) return(e1) + if (isFALSE(e2)) return(e2) + if (isTRUE(e1)) return(e2) + if (isTRUE(e2)) return(e1) + if (inherits(e2, "CnfAtom")) { + e2 = CnfClause(list(e2)) + } + if (inherits(e2, "CnfClause")) { + CnfFormula(list(e1, e2)) + } else { + # e2 is anything else -- go the lazy route + as.CnfFormula(e1) & as.CnfFormula(e2) + } } `|.CnfClause` = function(e1, e2) { + if (isFALSE(e1)) return(e2) + if (isFALSE(e2)) return(e1) + if (isTRUE(e1)) return(e1) + if (isTRUE(e2)) return(e2) + if (inherits(e2, "CnfAtom")) { + e2 = CnfClause(list(e2)) + } + if (inherits(e2, "CnfClause")) { + for (sym in names(e2)) { + e1[[sym]] = union(e1[[sym]], e2[[sym]]) + if (all(get(sym, attr(e1, "universe")) %in% e1[[sym]])) { + return(structure( + TRUE, + universe = attr(e1, "universe"), + class = "CnfClause" + )) + } + } + return(e1) + } + # e2 is anything else -- go the lazy route as.CnfFormula(e1) | as.CnfFormula(e2) } `&.CnfAtom` = function(e1, e2) { - as.CnfFormula(e1) & as.CnfFormula(e2) + if (isFALSE(e1)) return(e1) + if (isFALSE(e2)) return(e2) + if (isTRUE(e1)) return(e2) + if (isTRUE(e2)) return(e1) + if (inherits(e2, "CnfAtom")) { + e2 = CnfClause(list(e2)) + } + if (inherits(e2, "CnfClause")) { + CnfFormula(list(CnfClause(list(e1)), e2)) + } else { + # e2 is anything else -- go the lazy route + as.CnfFormula(e1) & as.CnfFormula(e2) + } } `|.CnfAtom` = function(e1, e2) { - as.CnfFormula(e1) | as.CnfFormula(e2) + if (isFALSE(e1)) return(e2) + if (isFALSE(e2)) return(e1) + if (isTRUE(e1)) return(e1) + if (isTRUE(e2)) return(e2) + if (inherits(e2, "CnfAtom")) { + CnfClause(list(e1, e2)) + } else { + # e2 is anything else -- go the lazy route + as.CnfFormula(e1) | as.CnfFormula(e2) + } } `!.CnfAtom` = function(x) { @@ -337,6 +391,9 @@ simplify_cnf = function(entries, universe) { } `!.CnfClause` = function(x) { + if (is.logical(x)) { + return(as.CnfClause(!unclass(x))) + } !as.CnfFormula(x) } @@ -361,6 +418,14 @@ as.CnfFormula = function(x) { UseMethod("as.CnfFormula") } +as.CnfClause = function(x) { + UseMethod("as.CnfClause") +} + +as.CnfAtom = function(x) { + UseMethod("as.CnfAtom") +} + chooseOpsMethod.CnfFormula <- function(x, y, mx, my, cl, reverse) TRUE chooseOpsMethod.CnfClause <- function(x, y, mx, my, cl, reverse) TRUE chooseOpsMethod.CnfAtom <- function(x, y, mx, my, cl, reverse) TRUE @@ -386,26 +451,56 @@ as.CnfFormula.CnfFormula = function(x) { x } +as.CnfAtom.logical = function(x) { + assert_flag(x) + return(structure( + x, + universe = attr(x, "universe"), + class = "CnfAtom" + )) +} + +as.CnfClause.logical = function(x) { + assert_flag(x) + return(structure( + x, + universe = attr(x, "universe"), + class = "CnfClause" + )) +} + +as.CnfFormula.logical = function(x) { + assert_flag(x) + structure( + x, + universe = attr(x, "universe"), + class = "CnfFormula" + ) +} + as.CnfFormula.default = function(x) { stop("Cannot convert object to CnfFormula.") } as.logical.CnfFormula = function(x) { - if (isTRUE(x)) { - return(TRUE) - } - if (isFALSE(x)) { - return(FALSE) + if (is.logical(x)) { + return(unclass(x)) } return(NA) } as.logical.CnfClause = function(x) { - as.logical(as.CnfFormula(x)) + if (is.logical(x)) { + return(unclass(x)) + } + return(NA) } as.logical.CnfAtom = function(x) { - as.logical(as.CnfFormula(x)) + if (is.logical(x)) { + return(unclass(x)) + } + return(NA) } print.CnfUniverse = function(x, ...) { @@ -427,40 +522,75 @@ print.CnfSymbol = function(x, ...) { print.CnfAtom = function(x, ...) { if (isTRUE(x)) { - cat("TRUE\n") + cat("CnfAtom: \n") } else if (isFALSE(x)) { - cat("FALSE\n") + cat("CnfAtom: \n") } else { - cat(sprintf("%s %%in%% {%s}.\n", x$symbol, paste(x$values, collapse = ", "))) + cat(sprintf("CnfAtom: %s \U2208 {%s}.\n", x$symbol, paste(x$values, collapse = ", "))) } invisible(x) } +format.CnfAtom = function(x, ...) { + if (isTRUE(x)) { + return("CnfAtom(FALSE)") + } else if (isFALSE(x)) { + return("CnfAtom(TRUE)") + } else { + return(sprintf("CnfAtom(%s ...)", x$symbol)) + } +} + print.CnfClause = function(x, ...) { if (isTRUE(x)) { - cat("TRUE\n") + cat("CnfClause: TRUE\n") } else if (isFALSE(x)) { - cat("FALSE\n") + cat("CnfClause: FALSE\n") } else { - cat("CnfClause with entries:\n") - for (sym in names(x)) { - cat(sprintf(" %s %%in%% {%s}\n", sym, paste(x[[sym]], collapse = ", "))) - } + cat("CnfClause:\n") + elements = map_chr(names(x), function(sym) { + sprintf("%s \U2208 {%s}", sym, paste(x[[sym]], collapse = ", ")) + }) + cat(strwrap(paste(elements, collapse = " | "), prefix = " "), sep = "\n") } invisible(x) } +format.CnfClause = function(x, ...) { + if (isTRUE(x)) { + return("CnfClause(TRUE)") + } else if (isFALSE(x)) { + return("CnfClause(FALSE)") + } else { + return(sprintf("CnfClause(%s)", str_collapse(names(x), sep = "|", n = 2, ellipsis = ".."))) + } +} + +format.CnfClause = function(x, ...) { + if (isTRUE(x)) { + return("") + } else if (isFALSE(x)) { + return("") + } else { + return("") + } +} + print.CnfFormula = function(x, ...) { if (isTRUE(x)) { - cat("TRUE\n") + cat("CnfFormula: TRUE\n") } else if (isFALSE(x)) { - cat("FALSE\n") + cat("CnfFormula: FALSE\n") } else { - cat("CnfFormula with entries:\n") - for (i in seq_along(x)) { - cat(sprintf(" Clause %d:\n", i)) - print(x[[i]]) - } + cat("CnfFormula:\n (") + clauses = map_chr(x, function(clause) { + elements = map_chr(names(clause), function(sym) { + sprintf("%s \U2208 {%s}", sym, paste(clause[[sym]], collapse = ", ")) + }) + paste(elements, collapse = " | ") + }) + clause_paragraphs = map_chr(strwrap(clauses, exdent = 4, simplify = FALSE), paste, collapse = "\n ") + cat(paste0(paste(clause_paragraphs, collapse = ")\n & ("), ")\n")) } invisible(x) } From e0c6d13be9da4ab8a7584cc57038afade62251eb Mon Sep 17 00:00:00 2001 From: mb706 Date: Sun, 8 Sep 2024 00:11:28 +0200 Subject: [PATCH 09/87] documenting --- DESCRIPTION | 1 + NAMESPACE | 47 ++++++ R/CnfFormula.R | 364 ++++++++++++++++++++++++++++++++++++++++++++- man/CnfAtom.Rd | 92 ++++++++++++ man/CnfClause.Rd | 84 +++++++++++ man/CnfFormula.Rd | 109 ++++++++++++++ man/CnfSymbol.Rd | 53 +++++++ man/CnfUniverse.Rd | 45 ++++++ 8 files changed, 794 insertions(+), 1 deletion(-) create mode 100644 man/CnfAtom.Rd create mode 100644 man/CnfClause.Rd create mode 100644 man/CnfFormula.Rd create mode 100644 man/CnfSymbol.Rd create mode 100644 man/CnfUniverse.Rd diff --git a/DESCRIPTION b/DESCRIPTION index 85253382c..cf7be202d 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -98,6 +98,7 @@ Roxygen: list(markdown = TRUE, r6 = FALSE) RoxygenNote: 7.3.2 VignetteBuilder: knitr Collate: + 'CnfFormula.R' 'Graph.R' 'GraphLearner.R' 'mlr_pipeops.R' diff --git a/NAMESPACE b/NAMESPACE index 6d8c22381..237a4e69d 100644 --- a/NAMESPACE +++ b/NAMESPACE @@ -1,7 +1,35 @@ # Generated by roxygen2: do not edit by hand +S3method("!",CnfAtom) +S3method("!",CnfClause) +S3method("!",CnfFormula) +S3method("$",CnfUniverse) +S3method("%among%",CnfSymbol) +S3method("%among%",default) +S3method("&",CnfAtom) +S3method("&",CnfClause) +S3method("&",CnfFormula) +S3method("[[",CnfUniverse) +S3method("|",CnfAtom) +S3method("|",CnfClause) +S3method("|",CnfFormula) +S3method(as.CnfAtom,CnfAtom) +S3method(as.CnfAtom,default) +S3method(as.CnfAtom,logical) +S3method(as.CnfClause,CnfAtom) +S3method(as.CnfClause,CnfClause) +S3method(as.CnfClause,default) +S3method(as.CnfClause,logical) +S3method(as.CnfFormula,CnfAtom) +S3method(as.CnfFormula,CnfClause) +S3method(as.CnfFormula,CnfFormula) +S3method(as.CnfFormula,default) +S3method(as.CnfFormula,logical) S3method(as.data.table,DictionaryGraph) S3method(as.data.table,DictionaryPipeOp) +S3method(as.logical,CnfAtom) +S3method(as.logical,CnfClause) +S3method(as.logical,CnfFormula) S3method(as_graph,Graph) S3method(as_graph,default) S3method(as_graph,list) @@ -11,6 +39,8 @@ S3method(as_pipeop,Filter) S3method(as_pipeop,Learner) S3method(as_pipeop,PipeOp) S3method(as_pipeop,default) +S3method(format,CnfAtom) +S3method(format,CnfClause) S3method(marshal_model,Multiplicity) S3method(marshal_model,graph_learner_model) S3method(marshal_model,pipeop_impute_learner_state) @@ -25,6 +55,11 @@ S3method(pos,"NULL") S3method(pos,character) S3method(pos,list) S3method(predict,Graph) +S3method(print,CnfAtom) +S3method(print,CnfClause) +S3method(print,CnfFormula) +S3method(print,CnfSymbol) +S3method(print,CnfUniverse) S3method(print,Multiplicity) S3method(print,Selector) S3method(set_validate,GraphLearner) @@ -35,6 +70,12 @@ S3method(unmarshal_model,pipeop_impute_learner_state_marshaled) S3method(unmarshal_model,pipeop_learner_cv_state_marshaled) export("%>>!%") export("%>>%") +export("%among%") +export(CnfAtom) +export(CnfClause) +export(CnfFormula) +export(CnfSymbol) +export(CnfUniverse) export(Graph) export(GraphLearner) export(LearnerClassifAvg) @@ -113,6 +154,9 @@ export(PipeOpUnbranch) export(PipeOpVtreat) export(PipeOpYeoJohnson) export(add_class_hierarchy_cache) +export(as.CnfAtom) +export(as.CnfClause) +export(as.CnfFormula) export(as.Multiplicity) export(as.data.table) export(as_graph) @@ -154,6 +198,9 @@ export(selector_none) export(selector_setdiff) export(selector_type) export(selector_union) +if (getRversion() >= "4.3.0") S3method(chooseOpsMethod,CnfAtom) +if (getRversion() >= "4.3.0") S3method(chooseOpsMethod,CnfClause) +if (getRversion() >= "4.3.0") S3method(chooseOpsMethod,CnfFormula) import(checkmate) import(data.table) import(mlr3) diff --git a/R/CnfFormula.R b/R/CnfFormula.R index e7b620146..e7fc1f715 100644 --- a/R/CnfFormula.R +++ b/R/CnfFormula.R @@ -12,10 +12,77 @@ # the conditions under which an error is thrown. # Container object for possible branch conditions. + + + +#' @title Symbol Table for CNF Formulas +#' +#' @description +#' A symbol table for CNF formulas. The `CnfUniverse` is a by-reference object +#' that stores the domain of each symbol. Symbols are created with [`CnfSymbol()`] +#' and can be retrieved with `[[` or `$`. +#' +#' It is only possible to combine symbols from the same (identical) universe. +#' +#' This is part of the CNF representation tooling, which is currently considered +#' experimental; it is for internal use. +#' +#' @return A new `CnfUniverse` object. +#' @examples +#' u = CnfUniverse() +#' X = CnfSymbol(u, "X", c("a", "b", "c")) +#' Y = CnfSymbol(u, "Y", c("d", "e", "f")) +#' +#' u$X +#' u[["Y"]] +#' +#' X %among% c("a", "d") +#' u$X %among% c("a", "d") +#' Y %among% c("d", "e", "f") +#' Y %among% character(0) +#' +#' u$X %among% "a" | u$Y %among% "d" +#' @family CNF representation objects +#' @keywords internal +#' @export CnfUniverse = function() structure(new.env(parent = emptyenv()), class = "CnfUniverse") # We represent symbols through a name and a pointer to their universe. # We only allow operations between symbols that are in the same universe. +#' @title Symbols for CNF Formulas +#' +#' @description +#' Representation of Symbols used in CNF formulas. Symbols have a name and a +#' domain (a set of possible values), and are stored in a [`CnfUniverse`]. +#' +#' Once created, it is currently not intended to modify or delete symbols. +#' +#' Symbols can be used in CNF formulas by creating [`CnfAtom`] objects, either +#' by using the `%among%` operator or by using the [`CnfAtom()`] constructor +#' explicitly. +#' +#' This is part of the CNF representation tooling, which is currently considered +#' experimental; it is for internal use. +#' +#' @param universe ([`CnfUniverse`]) \cr +#' The universe in which the symbol is defined. +#' @param name (`character(1)`) \cr +#' The name of the symbol. +#' @param domain (`character`) \cr +#' The domain, i.e. the set of possible values for the symbol. +#' Must not be empty. +#' @return A new `CnfSymbol` object. +#' @examples +#' u = CnfUniverse() +#' X = CnfSymbol(u, "X", c("a", "b", "c")) +#' +#' X %among% c("a", "b") +#' X %among% "a" +#' X %among% character(0) +#' X %among% c("a", "b", "c") +#' @family CNF representation objects +#' @keywords internal +#' @export CnfSymbol = function(universe, name, domain) { assert_class(universe, "CnfUniverse") assert_string(name) @@ -32,6 +99,7 @@ CnfSymbol = function(universe, name, domain) { } # We allow retrieving symbols from the universe by name. +#' @export `[[.CnfUniverse` = function(universe, name) { assert_string(name) if (!exists(name, universe)) { @@ -44,9 +112,75 @@ CnfSymbol = function(universe, name, domain) { ) } +#' @export `$.CnfUniverse` = `[[.CnfUniverse` # An expression of the form "X %in% {x1, x2, x3}" +#' @title Atoms for CNF Formulas +#' +#' @description +#' `Atom` objects represent a single statement that is used to build up CNF formulae. +#' They are mostly intermediate, created using the [`%among%`] operator or [`CnfAtom()`] +#' directly, and combined into [`CnfClause`] and [`CnfFormula`] objects. +#' [`CnfClause`] and [`CnfFormula`] do not, however, contain [`Atom`] objects directly, +#' +#' `Atom`s contain an indirect reference to a [`CnfSymbol`] by referencing its name +#' and its [`CnfUniverse`]. They furthermore contain a set of values. An `Atom` +#' represents a statement asserting that the given symbol takes up one of the +#' given values. +#' +#' If the set of values is empty, the `Atom` represents a contradiction (FALSE). +#' If it is the full domain of the symbol, the `Atom` represents a tautology (TRUE). +#' These values can be converted to, and from, `logical(1)` values using `as.logical()` +#' and `as.CnfAtom()`. +#' +#' `Atom` objects can be negated using the `!` operator, which will return the `Atom` +#' representing set membership in the complement of the symbol with respect to its domain. +#' `Atom`s can furthermore be combined using the `|` operator to form a [`CnfClause`], +#' and using the `&` operator to form a [`CnfFormula`]. This happens even if the +#' resulting statement could be represented as a single `Atom`. +#' +#' This is part of the CNF representation tooling, which is currently considered +#' experimental; it is for internal use. +#' +#' @details +#' We would have preferred to overload the `%in%` operator, but this is currently +#' not easily possible in R. We therefore created the `%among%` operator. +#' +#' @param symbol ([`CnfSymbol`]) \cr +#' The symbol to which the atom refers. +#' @param values (`character`) \cr +#' The values that the symbol can take. +#' @param e1 (`CnfSymbol`) \cr +#' Left-hand side of the `%among%` operator. +#' Passed as `symbol` to `CnfAtom()`. +#' @param e2 (`character`) \cr +#' Right-hand side of the `%among%` operator. +#' Passed as `values` to `CnfAtom()`. +#' @param x (any) \cr +#' The object to be coerced to a `CnfAtom` by `as.CnfAtom`. +#' Only `logical(1)` and `CnfAtom` itself are currently supported. +#' @return A new `CnfAtom` object. +#' @examples +#' u = CnfUniverse() +#' X = CnfSymbol(u, "X", c("a", "b", "c")) +#' +#' CnfAtom(X, c("a", "b")) +#' X %among% "a" +#' X %among% character(0) +#' X %among% c("a", "b", "c") +#' +#' as.logical(X %among% character(0)) +#' as.CnfAtom(TRUE) +#' +#' !(X %among% "a") +#' +#' X %among% "a" | X %among% "b" # creates a CnfClause +#' +#' X %among% "a" & X %among% c("a", "b") # creates a CnfFormula +#' @family CNF representation objects +#' @keywords internal +#' @export CnfAtom = function(symbol, values) { assert_class(symbol, "CnfSymbol") domain = get(symbol, attr(symbol, "universe")) @@ -74,10 +208,88 @@ CnfAtom = function(symbol, values) { # construct CnfAtom with `X %among% c("a", "b", "c")` # we cannot overload `%in%`, unfortunately -`%among%` = CnfAtom +#' @export +#' @rdname CnfAtom +`%among%` = function(e1, e2) { + UseMethod("%among%") +} + +#' @export +`%among%.CnfSymbol` = function(e1, e2) { + CnfAtom(e1, e2) +} + +#' @export +`%among%.default` = function(e1, e2) { + stop("%among% operation not defined for LHS. %among% should typically be used with a CnfSymbol.") +} # A clause is a disjunction of atoms. # X %among% c("a", "b", "c") | Y %among% c("d", "e", "f") + +#' @title Clauses in CNF Formulas +#' +#' @description +#' A `CnfClause` is a disjunction of [`CnfAtom`] objects. It represents a statement +#' that is true if at least one of the atoms is true. These are for example of the form +#' ```r +#' X %among% c("a", "b", "c") | Y %among% c("d", "e", "f") | ... +#' ``` +#' +#' `CnfClause` objects can be constructed explicitly, using the `CnfClause()` constructor, +#' or implicitly, by using the `|` operator on [`CnfAtom`]s or other `CnfClause` objects. +#' +#' Upon construction, the `CnfClause` is simplified by (1) removing contradictions, (2) unifying +#' atoms that refer to the same symbol, and (3) evaluating to `TRUE` if any atom is `TRUE`. +#' Note that the order of atoms in a clause is not preserved. +#' +#' If a `CnfClause` contains no atoms, or only `FALSE` atoms, it evaluates to `FALSE`. +#' If it contains at least one atom that is always true, the clause evaluates to `TRUE`. +#' These values can be converted to, and from, `logical(1)` values using `as.logical()` +#' and `as.CnfClause()`. +#' +#' `CnfClause` objects can be negated using the `!` operator, and combined using the +#' `&` operator. Both of these operations return a [`CnfFormula`], even if the result +#' could in principle be represented as a single `CnfClause`. +#' +#' This is part of the CNF representation tooling, which is currently considered +#' experimental; it is for internal use. +#' +#' @param atoms (`list` of [`CnfAtom`]) \cr +#' A list of [`CnfAtom`] objects. The clause represents the disjunction of these atoms. +#' @param x (any) \cr +#' The object to be coerced to a `CnfClause` by `as.CnfClause`. +#' Only `logical(1)`, [`CnfAtom`], and `CnfClause` itself are currently supported. +#' @return A new `CnfClause` object. +#' @examples +#' u = CnfUniverse() +#' X = CnfSymbol(u, "X", c("a", "b", "c")) +#' Y = CnfSymbol(u, "Y", c("d", "e", "f")) +#' +#' CnfClause(list(X %among% c("a", "b"), Y %among% c("d", "e"))) +#' X %among% c("a", "b") | Y %among% c("d", "e") +#' +#' as.CnfClause(X %among% c("a", "b")) +#' +#' # The same symbols are unified +#' X %among% "a" | Y %among% "d" | X %among% "b" +#' +#' # tautology evaluates to TRUE +#' X %among% "a" | X %among% "b" | X %among% "c" +#' +#' # contradictions are removed +#' X %among% "a" | Y %among% character(0) +#' +#' # create CnfFormula: +#' !(X %among% "a" | Y %among% "d") +#' +#' # also a CnfFormula, even if it contains a single clause: +#' !CnfClause(list(X %among% "a")) +#' (X %among% c("a", "c") | Y %among% "d") & +#' (X %among% c("a", "b") | Y %among% "d") +#' @family CNF representation objects +#' @keywords internal +#' @export CnfClause = function(atoms) { assert_list(atoms, types = "CnfAtom") if (!length(atoms)) { @@ -115,6 +327,94 @@ CnfClause = function(atoms) { # A formula is a conjunction of clauses. # (X %among% c("a", "b", "c") | Y %among% c("d", "e", "f")) & (Z %among% c("g", "h", "i")) +#' @title CNF Formulas +#' +#' @description +#' A `CnfFormula` is a conjunction of [`CnfClause`] objects. It represents a statement +#' that is true if all of the clauses are true. These are for example of the form +#' ```r +#' (X %among% "a" | Y %among% "d") & Z %among% "g" +#' ``` +#' +#' `CnfFormula` objects can be constructed explicitly, using the `CnfFormula()` constructor, +#' or implicitly, by using the `&` operator on [`CnfAtom`]s, [`CnfClause`]s, or other `CnfFormula` objects. +#' +#' Upon construction, the `CnfFormula` is simplified by using various heuristics. +#' This includes unit propagation, subsumption elimination, and hidden tautology elimination. +#' Note that the order of clauses in a formula is not preserved. +#' +#' If a `CnfFormula` contains no clauses, or only `TRUE` clauses, it evaluates to `TRUE`. +#' If it contains at least one clause that is always false, the formula evaluates to `FALSE`. +#' These values can be converted to, and from, `logical(1)` values using `as.logical()` +#' and `as.CnfFormula()`. +#' +#' `CnfFormula` objects can be negated using the `!` operator. Beware that this +#' may lead to an exponential blow-up in the number of clauses. +#' +#' This is part of the CNF representation tooling, which is currently considered +#' experimental; it is for internal use. +#' +#' @param clauses (`list` of [`CnfClause`]) \cr +#' A list of [`CnfClause`] objects. The formula represents the conjunction of these clauses. +#' @param x (any) \cr +#' The object to be coerced to a `CnfFormula` by `as.CnfFormula`. +#' Only `logical(1)`, [`CnfAtom`], [`CnfClause`], and `CnfFormula` itself are currently supported. +#' @return A new `CnfFormula` object. +#' @examples +#' u = CnfUniverse() +#' X = CnfSymbol(u, "X", c("a", "b", "c")) +#' Y = CnfSymbol(u, "Y", c("d", "e", "f")) +#' Z = CnfSymbol(u, "Z", c("g", "h", "i")) +#' +#' (X %among% c("a", "b") | Y %among% c("d", "e")) & +#' Z %among% c("g", "h") +#' +#' # Negation of a formula +#' !(X %among% c("a", "b") | Y %among% c("d", "e")) & +#' Z %among% c("g", "h") +#' +#' ## unit propagation +#' # The second clause can not be satisfied when X is "b", so it can be removed +#' # from the first clause. +#' (X %among% c("a", "b") | Y %among% c("d", "e")) & +#' X %among% c("a", "c") +#' +#' ## subsumption elimination +#' # The first clause is a subset of the second clause; whenever the +#' # first clause is satisfied, the second clause is satisfied as well, so it +#' # can be removed. +#' (X %among% "a" | Y %among% c("d", "e")) & +#' (X %among% c("a", "b") | Y %among% c("d", "e") | Z %among% "g") +#' +#' ## hidden tautology elimination +#' # The first two statements can only be satisfied if Y is either "d" or "e", +#' # since when X is "a", Y must be "e", and when X is "b", Y must be "d". +#' # The third statement is therefore implied by the first two, and can be +#' # removed. +#' (X %among% "a" | Y %among% "d") & +#' (X %among% "b" | Y %among% "e") & +#' (Y %among% c("d", "e")) +#' +#' ## Simple contradictions are recognized: +#' (X %among% "a") & (X %among% "b") +#' # Tautologies are preserved +#' (X %among% c("a", "b", "c")) & (Y %among% c("d", "e", "f")) +#' +#' # But not all contradictions are recognized. +#' # Builtin heuristic CnfFormula preprocessing is not a SAT solver. +#' contradiction <- (X %among% "a" | Y %among% "d") & +#' (X %among% "b" | Y %among% "e") & +#' (X %among% "c" | Y %among% "f") +#' contradiction +#' +#' # Negation of a contradiction results in a tautology, which is recognized +#' # and simplified to TRUE. However, note that this operation (1) generally has +#' # exponential complexity in the number of terms and (2) is currently also not +#' # particularly well optimized +#' !contradiction +#' @family CNF representation objects +#' @keywords internal +#' @export CnfFormula = function(clauses) { assert_list(clauses, types = "CnfClause") if (!length(clauses)) { @@ -255,6 +555,7 @@ simplify_cnf = function(entries, universe) { ) } +#' @export `&.CnfFormula` = function(e1, e2) { e1 = as.CnfFormula(e1) e2 = as.CnfFormula(e2) @@ -268,6 +569,7 @@ simplify_cnf = function(entries, universe) { simplify_cnf(c(e1, e2), attr(e1, "universe")) } +#' @export `|.CnfFormula` = function(e1, e2) { e1 = as.CnfFormula(e1) e2 = as.CnfFormula(e2) @@ -307,6 +609,7 @@ simplify_cnf = function(entries, universe) { simplify_cnf(unlist(distributed, recursive = FALSE), universe) } +#' @export `&.CnfClause` = function(e1, e2) { if (isFALSE(e1)) return(e1) if (isFALSE(e2)) return(e2) @@ -323,6 +626,7 @@ simplify_cnf = function(entries, universe) { } } +#' @export `|.CnfClause` = function(e1, e2) { if (isFALSE(e1)) return(e2) if (isFALSE(e2)) return(e1) @@ -348,6 +652,7 @@ simplify_cnf = function(entries, universe) { as.CnfFormula(e1) | as.CnfFormula(e2) } +#' @export `&.CnfAtom` = function(e1, e2) { if (isFALSE(e1)) return(e1) if (isFALSE(e2)) return(e2) @@ -364,6 +669,7 @@ simplify_cnf = function(entries, universe) { } } +#' @export `|.CnfAtom` = function(e1, e2) { if (isFALSE(e1)) return(e2) if (isFALSE(e2)) return(e1) @@ -377,6 +683,7 @@ simplify_cnf = function(entries, universe) { } } +#' @export `!.CnfAtom` = function(x) { if (is.logical(x)) { not_x = if (x) FALSE else TRUE # can't use '!' here... @@ -390,6 +697,7 @@ simplify_cnf = function(entries, universe) { ) } +#' @export `!.CnfClause` = function(x) { if (is.logical(x)) { return(as.CnfClause(!unclass(x))) @@ -397,6 +705,7 @@ simplify_cnf = function(entries, universe) { !as.CnfFormula(x) } +#' @export `!.CnfFormula` = function(x) { universe = attr(x, "universe") negated_formulae = lapply(x, function(clause) { @@ -414,22 +723,32 @@ simplify_cnf = function(entries, universe) { Reduce(function(x, y) x | y, negated_formulae) } +#' @rdname CnfFormula +#' @export as.CnfFormula = function(x) { UseMethod("as.CnfFormula") } +#' @rdname CnfClause +#' @export as.CnfClause = function(x) { UseMethod("as.CnfClause") } +#' @rdname CnfAtom +#' @export as.CnfAtom = function(x) { UseMethod("as.CnfAtom") } +#' @rawNamespace if (getRversion() >= "4.3.0") S3method(chooseOpsMethod,CnfFormula) chooseOpsMethod.CnfFormula <- function(x, y, mx, my, cl, reverse) TRUE +#' @rawNamespace if (getRversion() >= "4.3.0") S3method(chooseOpsMethod,CnfClause) chooseOpsMethod.CnfClause <- function(x, y, mx, my, cl, reverse) TRUE +#' @rawNamespace if (getRversion() >= "4.3.0") S3method(chooseOpsMethod,CnfAtom) chooseOpsMethod.CnfAtom <- function(x, y, mx, my, cl, reverse) TRUE +#' @export as.CnfFormula.logical = function(x) { assert_flag(x) return(structure( @@ -439,18 +758,22 @@ as.CnfFormula.logical = function(x) { )) } +#' @export as.CnfFormula.CnfAtom = function(x) { as.CnfFormula(CnfClause(list(x))) } +#' @export as.CnfFormula.CnfClause = function(x) { CnfFormula(list(x)) } +#' @export as.CnfFormula.CnfFormula = function(x) { x } +#' @export as.CnfAtom.logical = function(x) { assert_flag(x) return(structure( @@ -460,6 +783,12 @@ as.CnfAtom.logical = function(x) { )) } +#' @export +as.CnfAtom.CnfAtom = function(x) { + x +} + +#' @export as.CnfClause.logical = function(x) { assert_flag(x) return(structure( @@ -469,6 +798,17 @@ as.CnfClause.logical = function(x) { )) } +#' @export +as.CnfClause.CnfAtom = function(x) { + CnfClause(list(x)) +} + +#' @export +as.CnfClause.CnfClause = function(x) { + x +} + +#' @export as.CnfFormula.logical = function(x) { assert_flag(x) structure( @@ -478,10 +818,22 @@ as.CnfFormula.logical = function(x) { ) } +#' @export +as.CnfAtom.default = function(x) { + stop("Cannot convert object to CnfAtom.") +} + +#' @export +as.CnfClause.default = function(x) { + stop("Cannot convert object to CnfClause.") +} + +#' @export as.CnfFormula.default = function(x) { stop("Cannot convert object to CnfFormula.") } +#' @export as.logical.CnfFormula = function(x) { if (is.logical(x)) { return(unclass(x)) @@ -489,6 +841,7 @@ as.logical.CnfFormula = function(x) { return(NA) } +#' @export as.logical.CnfClause = function(x) { if (is.logical(x)) { return(unclass(x)) @@ -496,6 +849,7 @@ as.logical.CnfClause = function(x) { return(NA) } +#' @export as.logical.CnfAtom = function(x) { if (is.logical(x)) { return(unclass(x)) @@ -503,6 +857,7 @@ as.logical.CnfAtom = function(x) { return(NA) } +#' @export print.CnfUniverse = function(x, ...) { if (!length(x)) { cat("CnfUniverse (empty).\n") @@ -515,11 +870,13 @@ print.CnfUniverse = function(x, ...) { invisible(x) } +#' @export print.CnfSymbol = function(x, ...) { cat(sprintf("CnfSymbol '%s' with domain {%s}.\n", c(x), paste(get(x, attr(x, "universe")), collapse = ", "))) invisible(x) } +#' @export print.CnfAtom = function(x, ...) { if (isTRUE(x)) { cat("CnfAtom: \n") @@ -531,6 +888,7 @@ print.CnfAtom = function(x, ...) { invisible(x) } +#' @export format.CnfAtom = function(x, ...) { if (isTRUE(x)) { return("CnfAtom(FALSE)") @@ -541,6 +899,7 @@ format.CnfAtom = function(x, ...) { } } +#' @export print.CnfClause = function(x, ...) { if (isTRUE(x)) { cat("CnfClause: TRUE\n") @@ -556,6 +915,7 @@ print.CnfClause = function(x, ...) { invisible(x) } +#' @export format.CnfClause = function(x, ...) { if (isTRUE(x)) { return("CnfClause(TRUE)") @@ -566,6 +926,7 @@ format.CnfClause = function(x, ...) { } } +#' @export format.CnfClause = function(x, ...) { if (isTRUE(x)) { return("") @@ -576,6 +937,7 @@ format.CnfClause = function(x, ...) { } } +#' @export print.CnfFormula = function(x, ...) { if (isTRUE(x)) { cat("CnfFormula: TRUE\n") diff --git a/man/CnfAtom.Rd b/man/CnfAtom.Rd new file mode 100644 index 000000000..11fd8dd07 --- /dev/null +++ b/man/CnfAtom.Rd @@ -0,0 +1,92 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/CnfFormula.R +\name{CnfAtom} +\alias{CnfAtom} +\alias{\%among\%} +\alias{as.CnfAtom} +\title{Atoms for CNF Formulas} +\usage{ +CnfAtom(symbol, values) + +e1 \%among\% e2 + +as.CnfAtom(x) +} +\arguments{ +\item{symbol}{(\code{\link{CnfSymbol}}) \cr +The symbol to which the atom refers.} + +\item{values}{(\code{character}) \cr +The values that the symbol can take.} + +\item{e1}{(\code{CnfSymbol}) \cr +Left-hand side of the \verb{\%among\%} operator. +Passed as \code{symbol} to \code{CnfAtom()}.} + +\item{e2}{(\code{character}) \cr +Right-hand side of the \verb{\%among\%} operator. +Passed as \code{values} to \code{CnfAtom()}.} + +\item{x}{(any) \cr +The object to be coerced to a \code{CnfAtom} by \code{as.CnfAtom}. +Only \code{logical(1)} and \code{CnfAtom} itself are currently supported.} +} +\value{ +A new \code{CnfAtom} object. +} +\description{ +\code{Atom} objects represent a single statement that is used to build up CNF formulae. +They are mostly intermediate, created using the \code{\link{\%among\%}} operator or \code{\link[=CnfAtom]{CnfAtom()}} +directly, and combined into \code{\link{CnfClause}} and \code{\link{CnfFormula}} objects. +\code{\link{CnfClause}} and \code{\link{CnfFormula}} do not, however, contain \code{\link{Atom}} objects directly, + +\code{Atom}s contain an indirect reference to a \code{\link{CnfSymbol}} by referencing its name +and its \code{\link{CnfUniverse}}. They furthermore contain a set of values. An \code{Atom} +represents a statement asserting that the given symbol takes up one of the +given values. + +If the set of values is empty, the \code{Atom} represents a contradiction (FALSE). +If it is the full domain of the symbol, the \code{Atom} represents a tautology (TRUE). +These values can be converted to, and from, \code{logical(1)} values using \code{as.logical()} +and \code{as.CnfAtom()}. + +\code{Atom} objects can be negated using the \code{!} operator, which will return the \code{Atom} +representing set membership in the complement of the symbol with respect to its domain. +\code{Atom}s can furthermore be combined using the \code{|} operator to form a \code{\link{CnfClause}}, +and using the \code{&} operator to form a \code{\link{CnfFormula}}. This happens even if the +resulting statement could be represented as a single \code{Atom}. + +This is part of the CNF representation tooling, which is currently considered +experimental; it is for internal use. +} +\details{ +We would have preferred to overload the \code{\%in\%} operator, but this is currently +not easily possible in R. We therefore created the \verb{\%among\%} operator. +} +\examples{ +u = CnfUniverse() +X = CnfSymbol(u, "X", c("a", "b", "c")) + +CnfAtom(X, c("a", "b")) +X \%among\% "a" +X \%among\% character(0) +X \%among\% c("a", "b", "c") + +as.logical(X \%among\% character(0)) +as.CnfAtom(TRUE) + +!(X \%among\% "a") + +X \%among\% "a" | X \%among\% "b" # creates a CnfClause + +X \%among\% "a" & X \%among\% c("a", "b") # creates a CnfFormula +} +\seealso{ +Other CNF representation objects: +\code{\link{CnfClause}()}, +\code{\link{CnfFormula}()}, +\code{\link{CnfSymbol}()}, +\code{\link{CnfUniverse}()} +} +\concept{CNF representation objects} +\keyword{internal} diff --git a/man/CnfClause.Rd b/man/CnfClause.Rd new file mode 100644 index 000000000..0004ab7db --- /dev/null +++ b/man/CnfClause.Rd @@ -0,0 +1,84 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/CnfFormula.R +\name{CnfClause} +\alias{CnfClause} +\alias{as.CnfClause} +\title{Clauses in CNF Formulas} +\usage{ +CnfClause(atoms) + +as.CnfClause(x) +} +\arguments{ +\item{atoms}{(\code{list} of \code{\link{CnfAtom}}) \cr +A list of \code{\link{CnfAtom}} objects. The clause represents the disjunction of these atoms.} + +\item{x}{(any) \cr +The object to be coerced to a \code{CnfClause} by \code{as.CnfClause}. +Only \code{logical(1)}, \code{\link{CnfAtom}}, and \code{CnfClause} itself are currently supported.} +} +\value{ +A new \code{CnfClause} object. +} +\description{ +A \code{CnfClause} is a disjunction of \code{\link{CnfAtom}} objects. It represents a statement +that is true if at least one of the atoms is true. These are for example of the form + +\if{html}{\out{
}}\preformatted{ X \%among\% c("a", "b", "c") | Y \%among\% c("d", "e", "f") | ... +}\if{html}{\out{
}} + +\code{CnfClause} objects can be constructed explicitly, using the \code{CnfClause()} constructor, +or implicitly, by using the \code{|} operator on \code{\link{CnfAtom}}s or other \code{CnfClause} objects. + +Upon construction, the \code{CnfClause} is simplified by (1) removing contradictions, (2) unifying +atoms that refer to the same symbol, and (3) evaluating to \code{TRUE} if any atom is \code{TRUE}. +Note that the order of atoms in a clause is not preserved. + +If a \code{CnfClause} contains no atoms, or only \code{FALSE} atoms, it evaluates to \code{FALSE}. +If it contains at least one atom that is always true, the clause evaluates to \code{TRUE}. +These values can be converted to, and from, \code{logical(1)} values using \code{as.logical()} +and \code{as.CnfClause()}. + +\code{CnfClause} objects can be negated using the \code{!} operator, and combined using the +\code{&} operator. Both of these operations return a \code{\link{CnfFormula}}, even if the result +could in principle be represented as a single \code{CnfClause}. + +This is part of the CNF representation tooling, which is currently considered +experimental; it is for internal use. +} +\examples{ +u = CnfUniverse() +X = CnfSymbol(u, "X", c("a", "b", "c")) +Y = CnfSymbol(u, "Y", c("d", "e", "f")) + +CnfClause(list(X \%among\% c("a", "b"), Y \%among\% c("d", "e"))) +X \%among\% c("a", "b") | Y \%among\% c("d", "e") + +as.CnfClause(X \%among\% c("a", "b")) + +# The same symbols are unified +X \%among\% "a" | Y \%among\% "d" | X \%among\% "b" + +# tautology evaluates to TRUE +X \%among\% "a" | X \%among\% "b" | X \%among\% "c" + +# contradictions are removed +X \%among\% "a" | Y \%among\% character(0) + +# create CnfFormula: +!(X \%among\% "a" | Y \%among\% "d") + +# also a CnfFormula, even if it contains a single clause: +!CnfClause(list(X \%among\% "a")) +(X \%among\% c("a", "c") | Y \%among\% "d") & + (X \%among\% c("a", "b") | Y \%among\% "d") +} +\seealso{ +Other CNF representation objects: +\code{\link{CnfAtom}()}, +\code{\link{CnfFormula}()}, +\code{\link{CnfSymbol}()}, +\code{\link{CnfUniverse}()} +} +\concept{CNF representation objects} +\keyword{internal} diff --git a/man/CnfFormula.Rd b/man/CnfFormula.Rd new file mode 100644 index 000000000..f80c7237f --- /dev/null +++ b/man/CnfFormula.Rd @@ -0,0 +1,109 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/CnfFormula.R +\name{CnfFormula} +\alias{CnfFormula} +\alias{as.CnfFormula} +\title{CNF Formulas} +\usage{ +CnfFormula(clauses) + +as.CnfFormula(x) +} +\arguments{ +\item{clauses}{(\code{list} of \code{\link{CnfClause}}) \cr +A list of \code{\link{CnfClause}} objects. The formula represents the conjunction of these clauses.} + +\item{x}{(any) \cr +The object to be coerced to a \code{CnfFormula} by \code{as.CnfFormula}. +Only \code{logical(1)}, \code{\link{CnfAtom}}, \code{\link{CnfClause}}, and \code{CnfFormula} itself are currently supported.} +} +\value{ +A new \code{CnfFormula} object. +} +\description{ +A \code{CnfFormula} is a conjunction of \code{\link{CnfClause}} objects. It represents a statement +that is true if all of the clauses are true. These are for example of the form + +\if{html}{\out{
}}\preformatted{ (X \%among\% "a" | Y \%among\% "d") & Z \%among\% "g" +}\if{html}{\out{
}} + +\code{CnfFormula} objects can be constructed explicitly, using the \code{CnfFormula()} constructor, +or implicitly, by using the \code{&} operator on \code{\link{CnfAtom}}s, \code{\link{CnfClause}}s, or other \code{CnfFormula} objects. + +Upon construction, the \code{CnfFormula} is simplified by using various heuristics. +This includes unit propagation, subsumption elimination, and hidden tautology elimination. +Note that the order of clauses in a formula is not preserved. + +If a \code{CnfFormula} contains no clauses, or only \code{TRUE} clauses, it evaluates to \code{TRUE}. +If it contains at least one clause that is always false, the formula evaluates to \code{FALSE}. +These values can be converted to, and from, \code{logical(1)} values using \code{as.logical()} +and \code{as.CnfFormula()}. + +\code{CnfFormula} objects can be negated using the \code{!} operator. Beware that this +may lead to an exponential blow-up in the number of clauses. + +This is part of the CNF representation tooling, which is currently considered +experimental; it is for internal use. +} +\examples{ +u = CnfUniverse() +X = CnfSymbol(u, "X", c("a", "b", "c")) +Y = CnfSymbol(u, "Y", c("d", "e", "f")) +Z = CnfSymbol(u, "Z", c("g", "h", "i")) + +(X \%among\% c("a", "b") | Y \%among\% c("d", "e")) & + Z \%among\% c("g", "h") + +# Negation of a formula +!(X \%among\% c("a", "b") | Y \%among\% c("d", "e")) & + Z \%among\% c("g", "h") + +## unit propagation +# The second clause can not be satisfied when X is "b", so it can be removed +# from the first clause. +(X \%among\% c("a", "b") | Y \%among\% c("d", "e")) & + X \%among\% c("a", "c") + +## subsumption elimination +# The first clause is a subset of the second clause; whenever the +# first clause is satisfied, the second clause is satisfied as well, so it +# can be removed. +(X \%among\% "a" | Y \%among\% c("d", "e")) & + (X \%among\% c("a", "b") | Y \%among\% c("d", "e") | Z \%among\% "g") + +## hidden tautology elimination +# The first two statements can only be satisfied if Y is either "d" or "e", +# since when X is "a", Y must be "e", and when X is "b", Y must be "d". +# The third statement is therefore implied by the first two, and can be +# removed. +(X \%among\% "a" | Y \%among\% "d") & + (X \%among\% "b" | Y \%among\% "e") & + (Y \%among\% c("d", "e")) + +## Simple contradictions are recognized: +(X \%among\% "a") & (X \%among\% "b") +# Tautologies are preserved +(X \%among\% c("a", "b", "c")) & (Y \%among\% c("d", "e", "f")) + +# But not all contradictions are recognized. +# Builtin heuristic CnfFormula preprocessing is not a SAT solver. +contradiction <- (X \%among\% "a" | Y \%among\% "d") & + (X \%among\% "b" | Y \%among\% "e") & + (X \%among\% "c" | Y \%among\% "f") +contradiction + +# Negation of a contradiction results in a tautology, which is recognized +# and simplified to TRUE. However, note that this operation (1) generally has +# exponential complexity in the number of terms and (2) is currently also not +# particularly well optimized +!contradiction +} +\seealso{ +Other CNF representation objects: +\code{\link{CnfAtom}()}, +\code{\link{CnfClause}()}, +\code{\link{CnfSymbol}()}, +\code{\link{CnfUniverse}()} +} +\concept{CNF representation objects} +\keyword{internal} diff --git a/man/CnfSymbol.Rd b/man/CnfSymbol.Rd new file mode 100644 index 000000000..2dccb0d70 --- /dev/null +++ b/man/CnfSymbol.Rd @@ -0,0 +1,53 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/CnfFormula.R +\name{CnfSymbol} +\alias{CnfSymbol} +\title{Symbols for CNF Formulas} +\usage{ +CnfSymbol(universe, name, domain) +} +\arguments{ +\item{universe}{(\code{\link{CnfUniverse}}) \cr +The universe in which the symbol is defined.} + +\item{name}{(\code{character(1)}) \cr +The name of the symbol.} + +\item{domain}{(\code{character}) \cr +The domain, i.e. the set of possible values for the symbol. +Must not be empty.} +} +\value{ +A new \code{CnfSymbol} object. +} +\description{ +Representation of Symbols used in CNF formulas. Symbols have a name and a +domain (a set of possible values), and are stored in a \code{\link{CnfUniverse}}. + +Once created, it is currently not intended to modify or delete symbols. + +Symbols can be used in CNF formulas by creating \code{\link{CnfAtom}} objects, either +by using the \verb{\%among\%} operator or by using the \code{\link[=CnfAtom]{CnfAtom()}} constructor +explicitly. + +This is part of the CNF representation tooling, which is currently considered +experimental; it is for internal use. +} +\examples{ +u = CnfUniverse() +X = CnfSymbol(u, "X", c("a", "b", "c")) + +X \%among\% c("a", "b") +X \%among\% "a" +X \%among\% character(0) +X \%among\% c("a", "b", "c") +} +\seealso{ +Other CNF representation objects: +\code{\link{CnfAtom}()}, +\code{\link{CnfClause}()}, +\code{\link{CnfFormula}()}, +\code{\link{CnfUniverse}()} +} +\concept{CNF representation objects} +\keyword{internal} diff --git a/man/CnfUniverse.Rd b/man/CnfUniverse.Rd new file mode 100644 index 000000000..bb031e699 --- /dev/null +++ b/man/CnfUniverse.Rd @@ -0,0 +1,45 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/CnfFormula.R +\name{CnfUniverse} +\alias{CnfUniverse} +\title{Symbol Table for CNF Formulas} +\usage{ +CnfUniverse() +} +\value{ +A new \code{CnfUniverse} object. +} +\description{ +A symbol table for CNF formulas. The \code{CnfUniverse} is a by-reference object +that stores the domain of each symbol. Symbols are created with \code{\link[=CnfSymbol]{CnfSymbol()}} +and can be retrieved with \code{[[} or \code{$}. + +It is only possible to combine symbols from the same (identical) universe. + +This is part of the CNF representation tooling, which is currently considered +experimental; it is for internal use. +} +\examples{ +u = CnfUniverse() +X = CnfSymbol(u, "X", c("a", "b", "c")) +Y = CnfSymbol(u, "Y", c("d", "e", "f")) + +u$X +u[["Y"]] + +X \%among\% c("a", "d") +u$X \%among\% c("a", "d") +Y \%among\% c("d", "e", "f") +Y \%among\% character(0) + +u$X \%among\% "a" | u$Y \%among\% "d" +} +\seealso{ +Other CNF representation objects: +\code{\link{CnfAtom}()}, +\code{\link{CnfClause}()}, +\code{\link{CnfFormula}()}, +\code{\link{CnfSymbol}()} +} +\concept{CNF representation objects} +\keyword{internal} From 0681ba8564b1c2c2271ab0df340d705dabe3fcf6 Mon Sep 17 00:00:00 2001 From: mb706 Date: Sun, 8 Sep 2024 00:15:56 +0200 Subject: [PATCH 10/87] small doc change --- R/CnfFormula.R | 2 +- man/CnfFormula.Rd | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/R/CnfFormula.R b/R/CnfFormula.R index e7fc1f715..af7a24361 100644 --- a/R/CnfFormula.R +++ b/R/CnfFormula.R @@ -388,7 +388,7 @@ CnfClause = function(atoms) { #' #' ## hidden tautology elimination #' # The first two statements can only be satisfied if Y is either "d" or "e", -#' # since when X is "a", Y must be "e", and when X is "b", Y must be "d". +#' # since when X is "a" then Y must be "e", and when X is "b" then Y must be "d". #' # The third statement is therefore implied by the first two, and can be #' # removed. #' (X %among% "a" | Y %among% "d") & diff --git a/man/CnfFormula.Rd b/man/CnfFormula.Rd index f80c7237f..9e2b431c2 100644 --- a/man/CnfFormula.Rd +++ b/man/CnfFormula.Rd @@ -73,7 +73,7 @@ Z = CnfSymbol(u, "Z", c("g", "h", "i")) ## hidden tautology elimination # The first two statements can only be satisfied if Y is either "d" or "e", -# since when X is "a", Y must be "e", and when X is "b", Y must be "d". +# since when X is "a" then Y must be "e", and when X is "b" then Y must be "d". # The third statement is therefore implied by the first two, and can be # removed. (X \%among\% "a" | Y \%among\% "d") & From 6ec7e1dce1d36004906e02809e7f4f0b8ddcea94 Mon Sep 17 00:00:00 2001 From: mb706 Date: Sun, 8 Sep 2024 00:25:30 +0200 Subject: [PATCH 11/87] documenting --- R/CnfFormula.R | 24 ++++++++++++++++++------ man/CnfFormula.Rd | 14 ++++++++------ 2 files changed, 26 insertions(+), 12 deletions(-) diff --git a/R/CnfFormula.R b/R/CnfFormula.R index af7a24361..7cd60357d 100644 --- a/R/CnfFormula.R +++ b/R/CnfFormula.R @@ -340,11 +340,13 @@ CnfClause = function(atoms) { #' or implicitly, by using the `&` operator on [`CnfAtom`]s, [`CnfClause`]s, or other `CnfFormula` objects. #' #' Upon construction, the `CnfFormula` is simplified by using various heuristics. -#' This includes unit propagation, subsumption elimination, and hidden tautology elimination. +#' This includes unit propagation, subsumption elimination, and hidden tautology elimination +#' (see examples). #' Note that the order of clauses in a formula is not preserved. #' #' If a `CnfFormula` contains no clauses, or only `TRUE` clauses, it evaluates to `TRUE`. -#' If it contains at least one clause that is always false, the formula evaluates to `FALSE`. +#' If it contains at least one clause that is, by itself, always false, the formula evaluates to `FALSE`. +#' Not all contradictions between clauses are recognized, however. #' These values can be converted to, and from, `logical(1)` values using `as.logical()` #' and `as.CnfFormula()`. #' @@ -374,15 +376,15 @@ CnfClause = function(atoms) { #' Z %among% c("g", "h") #' #' ## unit propagation -#' # The second clause can not be satisfied when X is "b", so it can be removed -#' # from the first clause. +#' # The second clause can not be satisfied when X is "b", so "b" it can be +#' # removed from the possibilities in the first clause. #' (X %among% c("a", "b") | Y %among% c("d", "e")) & #' X %among% c("a", "c") #' #' ## subsumption elimination #' # The first clause is a subset of the second clause; whenever the -#' # first clause is satisfied, the second clause is satisfied as well, so it -#' # can be removed. +#' # first clause is satisfied, the second clause is satisfied as well, so the +#' # second clause can be removed. #' (X %among% "a" | Y %among% c("d", "e")) & #' (X %among% c("a", "b") | Y %among% c("d", "e") | Z %among% "g") #' @@ -978,3 +980,13 @@ print.CnfFormula = function(x, ...) { # This is because we don't eliminate (C | A) & (!C | B) & (B | A) by removing (B | A) # so, if clause X and clause Y have a symbol in common where the values are disjoint, the disjunction of the rest is implied? + + +# This is not right + +# !(X %among% c("a", "b") | Y %among% c("d", "e")) & +# Z %among% c("g", "h") +# CnfFormula: +# (X ∈ {c}) +# & (Y ∈ {f}) +# & (Z ∈ {g, h}) diff --git a/man/CnfFormula.Rd b/man/CnfFormula.Rd index 9e2b431c2..e5375be8a 100644 --- a/man/CnfFormula.Rd +++ b/man/CnfFormula.Rd @@ -31,11 +31,13 @@ that is true if all of the clauses are true. These are for example of the form or implicitly, by using the \code{&} operator on \code{\link{CnfAtom}}s, \code{\link{CnfClause}}s, or other \code{CnfFormula} objects. Upon construction, the \code{CnfFormula} is simplified by using various heuristics. -This includes unit propagation, subsumption elimination, and hidden tautology elimination. +This includes unit propagation, subsumption elimination, and hidden tautology elimination +(see examples). Note that the order of clauses in a formula is not preserved. If a \code{CnfFormula} contains no clauses, or only \code{TRUE} clauses, it evaluates to \code{TRUE}. -If it contains at least one clause that is always false, the formula evaluates to \code{FALSE}. +If it contains at least one clause that is, by itself, always false, the formula evaluates to \code{FALSE}. +Not all contradictions between clauses are recognized, however. These values can be converted to, and from, \code{logical(1)} values using \code{as.logical()} and \code{as.CnfFormula()}. @@ -59,15 +61,15 @@ Z = CnfSymbol(u, "Z", c("g", "h", "i")) Z \%among\% c("g", "h") ## unit propagation -# The second clause can not be satisfied when X is "b", so it can be removed -# from the first clause. +# The second clause can not be satisfied when X is "b", so "b" it can be +# removed from the possibilities in the first clause. (X \%among\% c("a", "b") | Y \%among\% c("d", "e")) & X \%among\% c("a", "c") ## subsumption elimination # The first clause is a subset of the second clause; whenever the -# first clause is satisfied, the second clause is satisfied as well, so it -# can be removed. +# first clause is satisfied, the second clause is satisfied as well, so the +# second clause can be removed. (X \%among\% "a" | Y \%among\% c("d", "e")) & (X \%among\% c("a", "b") | Y \%among\% c("d", "e") | Z \%among\% "g") From fe0d9e4e2934bf6ddf76562bf8b95fd75888bf49 Mon Sep 17 00:00:00 2001 From: mb706 Date: Sun, 8 Sep 2024 00:54:59 +0200 Subject: [PATCH 12/87] all.equal for CnfFormula etc --- NAMESPACE | 3 ++ R/CnfFormula.R | 97 +++++++++++++++++++++++++++++++++++++++++------ man/CnfClause.Rd | 2 +- man/CnfFormula.Rd | 5 ++- 4 files changed, 92 insertions(+), 15 deletions(-) diff --git a/NAMESPACE b/NAMESPACE index 237a4e69d..736cd7a51 100644 --- a/NAMESPACE +++ b/NAMESPACE @@ -13,6 +13,9 @@ S3method("[[",CnfUniverse) S3method("|",CnfAtom) S3method("|",CnfClause) S3method("|",CnfFormula) +S3method(all,equal.CnfAtom) +S3method(all,equal.CnfClause) +S3method(all,equal.CnfFormula) S3method(as.CnfAtom,CnfAtom) S3method(as.CnfAtom,default) S3method(as.CnfAtom,logical) diff --git a/R/CnfFormula.R b/R/CnfFormula.R index 7cd60357d..f0fb75372 100644 --- a/R/CnfFormula.R +++ b/R/CnfFormula.R @@ -241,7 +241,7 @@ CnfAtom = function(symbol, values) { #' #' Upon construction, the `CnfClause` is simplified by (1) removing contradictions, (2) unifying #' atoms that refer to the same symbol, and (3) evaluating to `TRUE` if any atom is `TRUE`. -#' Note that the order of atoms in a clause is not preserved. +#' Note that the order of atoms in a clause is not preserved #' #' If a `CnfClause` contains no atoms, or only `FALSE` atoms, it evaluates to `FALSE`. #' If it contains at least one atom that is always true, the clause evaluates to `TRUE`. @@ -372,8 +372,9 @@ CnfClause = function(atoms) { #' Z %among% c("g", "h") #' #' # Negation of a formula -#' !(X %among% c("a", "b") | Y %among% c("d", "e")) & -#' Z %among% c("g", "h") +#' # Note the parentheses, otherwise `!` would be applied to the first clause only. +#' !((X %among% c("a", "b") | Y %among% c("d", "e")) & +#' Z %among% c("g", "h")) #' #' ## unit propagation #' # The second clause can not be satisfied when X is "b", so "b" it can be @@ -442,7 +443,7 @@ CnfFormula = function(clauses) { stop("All clauses must be in the same universe.") } attr(c, "universe") = NULL - entries[[length(entries) + 1]] = c + entries[[length(entries) + 1]] = unclass(c) } simplify_cnf(entries, universe) } @@ -960,6 +961,86 @@ print.CnfFormula = function(x, ...) { } +#' @export +all.equal.CnfAtom = function(target, current, ...) { + if (is.logical(target) && is.logical(current)) { + # compare truth-values directly, even if they disagree on universe + # (since logical atoms sometimes have universe set to NULL) + if (identical(c(target), c(current))) { + return(TRUE) + } + return("target and current are both logicals but not equal") + } + if (is.logical(target) || is.logical(current)) { + return("target and current are not both logicals") + } + if (!inherits(current, "CnfAtom")) { + return("current is not a CnfAtom") + } + target$values = sort(target$values) + current$values = sort(current$values) + all.equal.list(target, current, ...) +} + +#' @export +all.equal.CnfClause = function(target, current, ...) { + if (is.logical(target) && is.logical(current)) { + # compare truth-values directly, even if they disagree on universe + # (since logical atoms sometimes have universe set to NULL) + if (identical(c(target), c(current))) { + return(TRUE) + } + return("target and current are both logicals but not equal") + } + if (is.logical(target) || is.logical(current)) { + return("target and current are not both logicals") + } + if (!inherits(current, "CnfClause")) { + return("current is not a CnfClause") + } + # []-assign to preserve class and attributes + target[] = lapply(target[order(names(target))], sort) + current[] = lapply(current[order(names(current))], sort) + + all.equal.list(target, current, ...) +} + +#' @export +all.equal.CnfFormula = function(target, current, ...) { + if (is.logical(target) && is.logical(current)) { + # compare truth-values directly, even if they disagree on universe + # (since logical atoms sometimes have universe set to NULL) + if (identical(c(target), c(current))) { + return(TRUE) + } + return("target and current are both logicals but not equal") + } + if (is.logical(target) || is.logical(current)) { + return("target and current are not both logicals") + } + if (!inherits(current, "CnfFormula")) { + return("current is not a CnfFormula") + } + + normalize = function(formula) { + formula[] = lapply(formula, function(clause) { + clause[] = lapply(clause[order(names(clause))], sort) + clause + }) + # sort by symbol names, then by hash + # note we had to sort elements internally first before we can do this! + formula[] = formula[order(map_chr(target, function(clause) { + paste0(paste(names(clause), collapse = ".__."), digest::digest(c(clause), algo = "xxhash64")) + }))] + formula + } + target = normalize(target) + current = normalize(current) + + all.equal.list(target, current, ...) +} + + ## to test: # subsumption @@ -982,11 +1063,3 @@ print.CnfFormula = function(x, ...) { # so, if clause X and clause Y have a symbol in common where the values are disjoint, the disjunction of the rest is implied? -# This is not right - -# !(X %among% c("a", "b") | Y %among% c("d", "e")) & -# Z %among% c("g", "h") -# CnfFormula: -# (X ∈ {c}) -# & (Y ∈ {f}) -# & (Z ∈ {g, h}) diff --git a/man/CnfClause.Rd b/man/CnfClause.Rd index 0004ab7db..b586ac881 100644 --- a/man/CnfClause.Rd +++ b/man/CnfClause.Rd @@ -32,7 +32,7 @@ or implicitly, by using the \code{|} operator on \code{\link{CnfAtom}}s or other Upon construction, the \code{CnfClause} is simplified by (1) removing contradictions, (2) unifying atoms that refer to the same symbol, and (3) evaluating to \code{TRUE} if any atom is \code{TRUE}. -Note that the order of atoms in a clause is not preserved. +Note that the order of atoms in a clause is not preserved If a \code{CnfClause} contains no atoms, or only \code{FALSE} atoms, it evaluates to \code{FALSE}. If it contains at least one atom that is always true, the clause evaluates to \code{TRUE}. diff --git a/man/CnfFormula.Rd b/man/CnfFormula.Rd index e5375be8a..1a9b0fda4 100644 --- a/man/CnfFormula.Rd +++ b/man/CnfFormula.Rd @@ -57,8 +57,9 @@ Z = CnfSymbol(u, "Z", c("g", "h", "i")) Z \%among\% c("g", "h") # Negation of a formula -!(X \%among\% c("a", "b") | Y \%among\% c("d", "e")) & - Z \%among\% c("g", "h") +# Note the parentheses, otherwise `!` would be applied to the first clause only. +!((X \%among\% c("a", "b") | Y \%among\% c("d", "e")) & + Z \%among\% c("g", "h")) ## unit propagation # The second clause can not be satisfied when X is "b", so "b" it can be From 967659558f888fe3bb1ed572b60b17f527d3bf30 Mon Sep 17 00:00:00 2001 From: mb706 Date: Mon, 9 Sep 2024 00:19:15 +0200 Subject: [PATCH 13/87] more autism --- R/CnfFormula.R | 241 +++++++++++++++++++++++++++++++++------------- man/CnfClause.Rd | 10 +- man/CnfFormula.Rd | 12 ++- 3 files changed, 190 insertions(+), 73 deletions(-) diff --git a/R/CnfFormula.R b/R/CnfFormula.R index f0fb75372..b85d17ed7 100644 --- a/R/CnfFormula.R +++ b/R/CnfFormula.R @@ -241,7 +241,10 @@ CnfAtom = function(symbol, values) { #' #' Upon construction, the `CnfClause` is simplified by (1) removing contradictions, (2) unifying #' atoms that refer to the same symbol, and (3) evaluating to `TRUE` if any atom is `TRUE`. -#' Note that the order of atoms in a clause is not preserved +#' Note that the order of atoms in a clause is not preserved. +#' +#' Using `CnfClause()` on lists that contain other `CnfClause` objects will create +#' a clause that is the disjunction of all atoms in all clauses. #' #' If a `CnfClause` contains no atoms, or only `FALSE` atoms, it evaluates to `FALSE`. #' If it contains at least one atom that is always true, the clause evaluates to `TRUE`. @@ -255,8 +258,9 @@ CnfAtom = function(symbol, values) { #' This is part of the CNF representation tooling, which is currently considered #' experimental; it is for internal use. #' -#' @param atoms (`list` of [`CnfAtom`]) \cr -#' A list of [`CnfAtom`] objects. The clause represents the disjunction of these atoms. +#' @param atoms (`list` of ([`CnfAtom`] | `CnfClause`)) \cr +#' A list of [`CnfAtom`] or other `CnfClause` objects. +#' The clause represents the disjunction of these atoms. #' @param x (any) \cr #' The object to be coerced to a `CnfClause` by `as.CnfClause`. #' Only `logical(1)`, [`CnfAtom`], and `CnfClause` itself are currently supported. @@ -291,7 +295,7 @@ CnfAtom = function(symbol, values) { #' @keywords internal #' @export CnfClause = function(atoms) { - assert_list(atoms, types = "CnfAtom") + assert_list(atoms, types = c("CnfAtom", "CnfClause")) if (!length(atoms)) { return(structure( FALSE, @@ -312,10 +316,21 @@ CnfClause = function(atoms) { if (isFALSE(a)) { next } - entries[[a$symbol]] = unique(c(entries[[a$symbol]], a$values)) - if (all(get(a$symbol, universe) %in% entries[[a$symbol]])) { - entries = TRUE - break + if (inherits(a, "CnfAtom")) { + entries[[a$symbol]] = union(entries[[a$symbol]], a$values) + if (all(get(a$symbol, universe) %in% entries[[a$symbol]])) { + entries = TRUE + break + } + } else { + # union with another CnfClause objects + for (sym in names(a)) { + entries[[sym]] = union(entries[[sym]], a[[sym]]) + if (all(get(sym, universe) %in% entries[[sym]])) { + entries = TRUE + break + } + } } } structure( @@ -340,10 +355,14 @@ CnfClause = function(atoms) { #' or implicitly, by using the `&` operator on [`CnfAtom`]s, [`CnfClause`]s, or other `CnfFormula` objects. #' #' Upon construction, the `CnfFormula` is simplified by using various heuristics. -#' This includes unit propagation, subsumption elimination, and hidden tautology elimination +#' This includes unit propagation, (self) subsumption elimination, and hidden tautology elimination #' (see examples). #' Note that the order of clauses in a formula is not preserved. #' +#' Using `CnfFormula()` on lists that contain other `CnfFormula` objects will create +#' a formula that is the conjunction of all clauses in all formulas. +#' This may be somewhat more efficient than applying `&` many times in a row. +#' #' If a `CnfFormula` contains no clauses, or only `TRUE` clauses, it evaluates to `TRUE`. #' If it contains at least one clause that is, by itself, always false, the formula evaluates to `FALSE`. #' Not all contradictions between clauses are recognized, however. @@ -389,6 +408,12 @@ CnfClause = function(atoms) { #' (X %among% "a" | Y %among% c("d", "e")) & #' (X %among% c("a", "b") | Y %among% c("d", "e") | Z %among% "g") #' +#' ## self subsumption elimination +#' # If the first clause is satisfied but X is not "a", then Y must be "e". +#' # The `Y %among% "d"` part of the first clause can therefore be removed. +#' (X %among% c("a", "b") | Y %among% "d") & +#' (X %among% "a" | Y %among% "e") +#' #' ## hidden tautology elimination #' # The first two statements can only be satisfied if Y is either "d" or "e", #' # since when X is "a" then Y must be "e", and when X is "b" then Y must be "d". @@ -419,7 +444,7 @@ CnfClause = function(atoms) { #' @keywords internal #' @export CnfFormula = function(clauses) { - assert_list(clauses, types = "CnfClause") + assert_list(clauses, types = c("CnfClause", "CnfFormula")) if (!length(clauses)) { return(structure( TRUE, @@ -429,21 +454,27 @@ CnfFormula = function(clauses) { } universe = attr(clauses[[1]], "universe") entries = list() - for (c in clauses) { - if (isFALSE(c)) { + for (cl in clauses) { + if (isFALSE(cl)) { entries = FALSE break } - if (isTRUE(c)) { + if (isTRUE(cl)) { next } - if (!identical(attr(c, "universe"), universe)) { + if (!identical(attr(cl, "universe"), universe)) { # if clauses[[1]] is FALSE, then it is possible that it has no # universe; however, in that case we will break before coming here. stop("All clauses must be in the same universe.") } - attr(c, "universe") = NULL - entries[[length(entries) + 1]] = unclass(c) + attr(cl, "universe") = NULL + ## don't unclass() here, since we check the class in the next line! + if (inherits(cl, "CnfClause")) { + entries[[length(entries) + 1]] = unclass(cl) + } else { + # union with another CnfFormula object + entries = c(entries, unclass(cl)) + } } simplify_cnf(entries, universe) } @@ -458,7 +489,7 @@ simplify_cnf = function(entries, universe) { # can we do unit elimination? # if we are already TRUE or FALSE no simplification is necessary # this only works if there actually are units. - can_simplify = !is.logical(entries) && any(lengths(entries) == 1) + can_simplify = !is.logical(entries) # likewise, if there is only one clause left, no simplification is necessary. units = list() @@ -470,42 +501,44 @@ simplify_cnf = function(entries, universe) { # sort clauses by length, since (1) length-1-clauses are special, and (2) short clauses can only ever subsume longer ones entries = entries[order(lengths(entries))] # Let sum(A) be the symbols in clause A, and val(A, s) be the values of symbol s admitted in clause A. - for (i in seq_along(entries)) { - ei = entries[[i]] - # If |sym(A)| == 1, sym(A) == {s} and s is in sym(B), then val(B, s) <- intersect(val(A, s), val(B, s)) ("unit propagation") - # units is a named list of symbols in size-one-clauses, together with their values. - # We iterate over all symbols in ei that are also in units, and intersect their values. - for (unit_symbol in intersect(names(ei), names(units))) { - length_before_ei = length(ei[[unit_symbol]]) - length_before_unit = length(units[[unit_symbol]]) - intersection = intersect(units[[unit_symbol]], ei[[unit_symbol]]) - ei[[unit_symbol]] = intersection - if (length(ei) == 1 && length(intersection) != length_before_unit) { - # we made a unit shorter, this means we need to simplify the entry from which units[[unit_symbol]] came - can_simplify = TRUE - } - if (!length(ei[[unit_symbol]])) { - ei[[unit_symbol]] = NULL - } - if (!length(ei)) { - return(return_false) + if (any(lengths(entries) == 1)) { + for (i in seq_along(entries)) { + ei = entries[[i]] + # If |sym(A)| == 1, sym(A) == {s} and s is in sym(B), then val(B, s) <- intersect(val(A, s), val(B, s)) ("unit propagation") + # units is a named list of symbols in size-one-clauses, together with their values. + # We iterate over all symbols in ei that are also in units, and intersect their values. + for (unit_symbol in intersect(names(ei), names(units))) { + length_before_ei = length(ei[[unit_symbol]]) + length_before_unit = length(units[[unit_symbol]]) + intersection = intersect(units[[unit_symbol]], ei[[unit_symbol]]) + ei[[unit_symbol]] = intersection + if (length(ei) == 1 && length(intersection) != length_before_unit) { + # we made a unit shorter, this means we need to simplify the entry from which units[[unit_symbol]] came + can_simplify = TRUE + } + if (!length(ei[[unit_symbol]])) { + ei[[unit_symbol]] = NULL + } + if (!length(ei)) { + return(return_false) + } + if (length(intersection) != length_before_ei) { + # need to store changed ei entry only if its length changed; otherwise we know the intersection did not do anything. + entries[[i]] = ei + } } - if (length(intersection) != length_before_ei) { - # need to store changed ei entry only if its length changed; otherwise we know the intersection did not do anything. - entries[[i]] = ei + if (length(ei) == 1) { + # even if names(ei) is already in units, at this point ei[[1]] is the intersection of the values + units[[names(ei)]] = ei[[1]] } } - if (length(ei) == 1) { - # even if names(ei) is already in units, at this point ei[[1]] is the intersection of the values - units[[names(ei)]] = ei[[1]] - } + if (can_simplify) next } - } - if (!is.logical(entries) && length(entries) > 1) { + entries = entries[order(lengths(entries))] # removing units may have changed the order eliminated = logical(length(entries)) for (i in seq_along(entries)) { - if (eliminated[[i]]) next # can only happen if we do the tautology elimination, which searches forward + if (eliminated[[i]]) next # can only happen if we do the hidden tautology elimination, which searches forward ei = entries[[i]] # If sym(A) is a subset of sym(B) and for each s in sym(A), val(A, s) is a subset of val(B, s), then A implies B, so B can be removed ("subsumption elimination"). for (j in seq_len(i - 1)) { @@ -515,41 +548,111 @@ simplify_cnf = function(entries, universe) { if (all(name_overlap) && all(sapply(names(ej), function(s) all(ej[[s]] %in% ei[[s]])))) { # can't do entries[[i]] = NULL, since we are iterating over entries; the entries[[i]] would break. eliminated[[i]] = TRUE + break } - # simple tautology elimination + # simple self subsumption and hidden tautology elimination + # HTE: # if s is in sym(A) and sym(B), and val(A, s) and val(B, s) are disjoint, then (A - s | B - s) is implied, # and all superset clauses of (A - s | B - s) can be removed. # we could also do this for higher order terms, intersection over X of val(X, s) == 0 etc., but this gets more complex. # tbh, I am not sure if this is actually worth it - if (!eliminated[[i]]) { - which_name_overlap = which(name_overlap) - # - build the union of values of overlapping symbols - # - in the innerloop we will check that most of this is a subset of any other clause - # - "most of" here means: all but the one symbol s where the values are disjoint - # - use delayedAssign to avoid computation if there is no overlap with empty intersect - delayedAssign("cnames", union(names(ei), names(ej))) - delayedAssign("cunion", sapply(cnames, function(s2) union(ei[[s2]], ej[[s2]]), simplify = FALSE)) - for (no in which_name_overlap) { - s = names(ej)[[no]] - # intersection is not 0 --> try next one - if (length(intersect(ej[[s]], ei[[s]]))) next - cnames_s = setdiff(cnames, s) - # loop down from large to small, since then we can break once we find a clause with insufficient entries - for (k in rev(seq_along(entries))) { - if (k == i || k == j) next - ek = entries[[k]] - # all of cnames_s must be in ek, otherwise we can't eliminate - # since we are looping down from large to small ek, we can break once this is not the case - if (length(ek) < length(cnames) - 1) break - if (all(cnames_s %in% names(ek)) && all(sapply(cnames_s, function(s2) all(cunion[[s2]] %in% ek[[s2]])))) { - eliminated[[k]] = TRUE + # SSE: If val(A, s) and val(B, s) are disjoint, and A - s is a subset of B - s, then A & B <=> A & (B - s) + + which_name_overlap = which(name_overlap) + # - build the union of values of overlapping symbols + # - in the innerloop we will check that most of this is a subset of any other clause + # - "most of" here means: all but the one symbol s where the values are disjoint + # - use delayedAssign to avoid computation if there is no overlap with empty intersect + delayedAssign("cnames", union(names(ei), names(ej))) + + # Putting ei[[s2]] first on purpose, since union() preserves the order of the first argument. + # If and only if ej[-s] is a subset of ei[-s], then cunion[-s] will be the same as ei[-s]. + delayedAssign("cunion", sapply(cnames, function(s2) union(ei[[s2]], ej[[s2]]), simplify = FALSE)) + for (no in which_name_overlap) { + s = names(ej)[[no]] + # intersection is not 0 --> try next one + if (length(intersect(ej[[s]], ei[[s]]))) next + cnames_s = setdiff(cnames, s) + + # Let's try self subsumption elimination first + if (length(cnames) == length(ei)) { + # cnames is the union of symbols in ei and ej. + # If it is different from max(length(ei), length(ej)), then ei and ej can not be subsets of one another. + # Since j < i, length(ej) <= length(ei). + + # ej is usually smaller than ei, so often only ej can be a subset of ei. + # They may, however, have the same number of terms, in which case the reverse is also possible. + # Use 'c()' to drop attributes from ei here. + ei_without_s = ei[cnames_s] + do_sse = identical(cnames[cnames_s], c(ei_without_s)) + # if they have the same number of terms, ei could be a subset of ej. + # However, then we can ont rely on the order of values in the union being correct. + do_sse_reverse = (!do_sse && (length(ei) == length(ej)) && + all(sapply(cnames_s, function(s2) all(ei[[s2]] %in% ej[[s2]])))) + if (do_sse_reverse) { + # ei is a subset of ej + # --> eliminate s from ej + ej[[s]] = NULL + new_entry = entries[[j]] = ej + dont_eliminate = j + } else if (do_sse) { + # ej is a subset of ei + # --> eliminate s from ei + new_entry = entries[[i]] = ei_without_s + dont_eliminate = i + } + + if (do_sse || do_sse_reverse) { + + # What can have happened now is that the newly created element can eliminate other elements. + # If it can eliminate the current element i, that means it is a subset of ei, which only happens if ej\s is a subset of ei\s. However, in that case, we always want to keep element i. + # We therefore only need to loop up to i - 1. + # The loop is similar to the subsumption elimination loop; only in this case, we check if we can eliminate the elements that come before i, not like above where we check if we can eliminate i. + + # loop down from large to small, since then we can break once we find a clause with insufficient entries + for (k in rev(seq_len(i - 1))) { + if (k == dont_eliminate || eliminated[[k]]) next + ek = entries[[k]] + if (length(ek) < length(new_entry)) break # once we reached entries that are shorter than the new_entry, we won't find anything longer any more and we can break + if (all(cnames_s %in% names(ek)) && all(sapply(cnames_s, function(s2) all(new_entry[[s2]] %in% ek[[s2]])))) { + eliminated[[k]] = TRUE + } } + + if (length(new_entry) == 1) { + # we have a unit clause now + units[[names(new_entry)]] = new_entry[[1]] + can_simplify = TRUE # do unit elimination all over again + ## TODO: we could probably make this more efficient by only unit-eliminating the terms that are new + } + next + } + } + + # Hidden Tautology Elimination + # + # We only do this if self subsumption elimination did not occur. + # + # We eliminate based on an implied clause (A - s | B - s) + # Since we eill forget about this clause after this iteration, we have to eliminate all clauses with size larger or equal to ||A | B|| - 1 + # loop down from large to small, since then we can break once we find a clause with insufficient entries + for (k in rev(seq_along(entries))) { + if (k == i || k == j || eliminated[[k]]) next + ek = entries[[k]] + # all of cnames_s must be in ek, otherwise we can't eliminate + # since we are looping down from large to small ek, we can break once this is not the case + if (length(ek) < length(cnames) - 1) break + if (all(cnames_s %in% names(ek)) && all(sapply(cnames_s, function(s2) all(cunion[[s2]] %in% ek[[s2]])))) { + eliminated[[k]] = TRUE } } } + } + } entries = entries[!eliminated] + if (length(entries) < 2) break # no need to simplify further, even if can_simplify was set to TRUE by SSE } structure( if (!length(entries)) TRUE else entries, diff --git a/man/CnfClause.Rd b/man/CnfClause.Rd index b586ac881..4db55345b 100644 --- a/man/CnfClause.Rd +++ b/man/CnfClause.Rd @@ -10,8 +10,9 @@ CnfClause(atoms) as.CnfClause(x) } \arguments{ -\item{atoms}{(\code{list} of \code{\link{CnfAtom}}) \cr -A list of \code{\link{CnfAtom}} objects. The clause represents the disjunction of these atoms.} +\item{atoms}{(\code{list} of (\code{\link{CnfAtom}} | \code{CnfClause})) \cr +A list of \code{\link{CnfAtom}} or other \code{CnfClause} objects. +The clause represents the disjunction of these atoms.} \item{x}{(any) \cr The object to be coerced to a \code{CnfClause} by \code{as.CnfClause}. @@ -32,7 +33,10 @@ or implicitly, by using the \code{|} operator on \code{\link{CnfAtom}}s or other Upon construction, the \code{CnfClause} is simplified by (1) removing contradictions, (2) unifying atoms that refer to the same symbol, and (3) evaluating to \code{TRUE} if any atom is \code{TRUE}. -Note that the order of atoms in a clause is not preserved +Note that the order of atoms in a clause is not preserved. + +Using \code{CnfClause()} on lists that contain other \code{CnfClause} objects will create +a clause that is the disjunction of all atoms in all clauses. If a \code{CnfClause} contains no atoms, or only \code{FALSE} atoms, it evaluates to \code{FALSE}. If it contains at least one atom that is always true, the clause evaluates to \code{TRUE}. diff --git a/man/CnfFormula.Rd b/man/CnfFormula.Rd index 1a9b0fda4..6e2f44fbf 100644 --- a/man/CnfFormula.Rd +++ b/man/CnfFormula.Rd @@ -31,10 +31,14 @@ that is true if all of the clauses are true. These are for example of the form or implicitly, by using the \code{&} operator on \code{\link{CnfAtom}}s, \code{\link{CnfClause}}s, or other \code{CnfFormula} objects. Upon construction, the \code{CnfFormula} is simplified by using various heuristics. -This includes unit propagation, subsumption elimination, and hidden tautology elimination +This includes unit propagation, (self) subsumption elimination, and hidden tautology elimination (see examples). Note that the order of clauses in a formula is not preserved. +Using \code{CnfFormula()} on lists that contain other \code{CnfFormula} objects will create +a formula that is the conjunction of all clauses in all formulas. +This may be somewhat more efficient than applying \code{&} many times in a row. + If a \code{CnfFormula} contains no clauses, or only \code{TRUE} clauses, it evaluates to \code{TRUE}. If it contains at least one clause that is, by itself, always false, the formula evaluates to \code{FALSE}. Not all contradictions between clauses are recognized, however. @@ -74,6 +78,12 @@ Z = CnfSymbol(u, "Z", c("g", "h", "i")) (X \%among\% "a" | Y \%among\% c("d", "e")) & (X \%among\% c("a", "b") | Y \%among\% c("d", "e") | Z \%among\% "g") +## self subsumption elimination +# If the first clause is satisfied but X is not "a", then Y must be "e". +# The `Y \%among\% "d"` part of the first clause can therefore be removed. +(X \%among\% c("a", "b") | Y \%among\% "d") & + (X \%among\% "a" | Y \%among\% "e") + ## hidden tautology elimination # The first two statements can only be satisfied if Y is either "d" or "e", # since when X is "a" then Y must be "e", and when X is "b" then Y must be "d". From 59b2b64142d2cfa2afb0e71c5384d45c46e84d50 Mon Sep 17 00:00:00 2001 From: mb706 Date: Mon, 9 Sep 2024 00:21:32 +0200 Subject: [PATCH 14/87] typo --- R/CnfFormula.R | 3 +-- 1 file changed, 1 insertion(+), 2 deletions(-) diff --git a/R/CnfFormula.R b/R/CnfFormula.R index b85d17ed7..d893fbb7d 100644 --- a/R/CnfFormula.R +++ b/R/CnfFormula.R @@ -634,7 +634,7 @@ simplify_cnf = function(entries, universe) { # We only do this if self subsumption elimination did not occur. # # We eliminate based on an implied clause (A - s | B - s) - # Since we eill forget about this clause after this iteration, we have to eliminate all clauses with size larger or equal to ||A | B|| - 1 + # Since we will forget about this clause after this iteration, we have to eliminate all clauses with size larger or equal to ||A | B|| - 1 # loop down from large to small, since then we can break once we find a clause with insufficient entries for (k in rev(seq_along(entries))) { if (k == i || k == j || eliminated[[k]]) next @@ -652,7 +652,6 @@ simplify_cnf = function(entries, universe) { } entries = entries[!eliminated] - if (length(entries) < 2) break # no need to simplify further, even if can_simplify was set to TRUE by SSE } structure( if (!length(entries)) TRUE else entries, From 11b3aaefc08a7dadd171aaa3b85f990bfd8fa77a Mon Sep 17 00:00:00 2001 From: mb706 Date: Mon, 9 Sep 2024 00:27:38 +0200 Subject: [PATCH 15/87] some more edgecases --- R/CnfFormula.R | 23 ++++++++++++++++------- 1 file changed, 16 insertions(+), 7 deletions(-) diff --git a/R/CnfFormula.R b/R/CnfFormula.R index d893fbb7d..0d0b94f78 100644 --- a/R/CnfFormula.R +++ b/R/CnfFormula.R @@ -604,6 +604,22 @@ simplify_cnf = function(entries, universe) { if (do_sse || do_sse_reverse) { + if (length(new_entry) == 1) { + # we have a unit clause now + + # It could happen that we eliminate the entry further, in which + # case units[[]] would get stale, but then we return_false anyway. + units[[names(new_entry)]] = new_entry[[1]] + can_simplify = TRUE # do unit elimination all over again + ## TODO: we could probably make this more efficient by only unit-eliminating the terms that are new + } + + if (!length(new_entry)) { + # we have a contradiction now + # Maybe this could happen if we SS-Eliminate multiple symbols from a clause in a row. + return(return_false) + } + # What can have happened now is that the newly created element can eliminate other elements. # If it can eliminate the current element i, that means it is a subset of ei, which only happens if ej\s is a subset of ei\s. However, in that case, we always want to keep element i. # We therefore only need to loop up to i - 1. @@ -618,13 +634,6 @@ simplify_cnf = function(entries, universe) { eliminated[[k]] = TRUE } } - - if (length(new_entry) == 1) { - # we have a unit clause now - units[[names(new_entry)]] = new_entry[[1]] - can_simplify = TRUE # do unit elimination all over again - ## TODO: we could probably make this more efficient by only unit-eliminating the terms that are new - } next } } From 99b69797ffae22c6a74401c58d2adb9c3f7c2009 Mon Sep 17 00:00:00 2001 From: mb706 Date: Mon, 9 Sep 2024 01:11:51 +0200 Subject: [PATCH 16/87] more precise comment --- R/CnfFormula.R | 3 +-- 1 file changed, 1 insertion(+), 2 deletions(-) diff --git a/R/CnfFormula.R b/R/CnfFormula.R index 0d0b94f78..43b530e91 100644 --- a/R/CnfFormula.R +++ b/R/CnfFormula.R @@ -577,7 +577,7 @@ simplify_cnf = function(entries, universe) { # Let's try self subsumption elimination first if (length(cnames) == length(ei)) { # cnames is the union of symbols in ei and ej. - # If it is different from max(length(ei), length(ej)), then ei and ej can not be subsets of one another. + # If length(cnames) is different from max(length(ei), length(ej)), then ei and ej can not be subsets of one another. # Since j < i, length(ej) <= length(ei). # ej is usually smaller than ei, so often only ej can be a subset of ei. @@ -637,7 +637,6 @@ simplify_cnf = function(entries, universe) { next } } - # Hidden Tautology Elimination # # We only do this if self subsumption elimination did not occur. From 900a8e1b7ff0787ae868364740cb1bec4420e89b Mon Sep 17 00:00:00 2001 From: mb706 Date: Mon, 9 Sep 2024 01:13:00 +0200 Subject: [PATCH 17/87] comment typo --- R/CnfFormula.R | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/R/CnfFormula.R b/R/CnfFormula.R index 43b530e91..ce2442fa1 100644 --- a/R/CnfFormula.R +++ b/R/CnfFormula.R @@ -586,7 +586,7 @@ simplify_cnf = function(entries, universe) { ei_without_s = ei[cnames_s] do_sse = identical(cnames[cnames_s], c(ei_without_s)) # if they have the same number of terms, ei could be a subset of ej. - # However, then we can ont rely on the order of values in the union being correct. + # However, then we can not rely on the order of values in the union being correct. do_sse_reverse = (!do_sse && (length(ei) == length(ej)) && all(sapply(cnames_s, function(s2) all(ei[[s2]] %in% ej[[s2]])))) if (do_sse_reverse) { From 4763ba621972ebe56da98615b398eac0353b4003 Mon Sep 17 00:00:00 2001 From: mb706 Date: Mon, 9 Sep 2024 02:22:26 +0200 Subject: [PATCH 18/87] bugfix --- R/CnfFormula.R | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/R/CnfFormula.R b/R/CnfFormula.R index ce2442fa1..c9e96ce4a 100644 --- a/R/CnfFormula.R +++ b/R/CnfFormula.R @@ -568,8 +568,10 @@ simplify_cnf = function(entries, universe) { # Putting ei[[s2]] first on purpose, since union() preserves the order of the first argument. # If and only if ej[-s] is a subset of ei[-s], then cunion[-s] will be the same as ei[-s]. delayedAssign("cunion", sapply(cnames, function(s2) union(ei[[s2]], ej[[s2]]), simplify = FALSE)) + + nameshift = 0 # in case we eliminate names from ej, we need to shift the indices for later loops iterations for (no in which_name_overlap) { - s = names(ej)[[no]] + s = names(ej)[[no - nameshift]] # intersection is not 0 --> try next one if (length(intersect(ej[[s]], ei[[s]]))) next cnames_s = setdiff(cnames, s) @@ -595,6 +597,7 @@ simplify_cnf = function(entries, universe) { ej[[s]] = NULL new_entry = entries[[j]] = ej dont_eliminate = j + nameshift = nameshift + 1 } else if (do_sse) { # ej is a subset of ei # --> eliminate s from ei From 9bad7b40124487d64b337d90b71dd57ac68bae3b Mon Sep 17 00:00:00 2001 From: mb706 Date: Mon, 9 Sep 2024 03:08:47 +0200 Subject: [PATCH 19/87] correct terms --- R/CnfFormula.R | 14 +++++++------- man/CnfFormula.Rd | 6 +++--- 2 files changed, 10 insertions(+), 10 deletions(-) diff --git a/R/CnfFormula.R b/R/CnfFormula.R index c9e96ce4a..939f67eed 100644 --- a/R/CnfFormula.R +++ b/R/CnfFormula.R @@ -355,7 +355,7 @@ CnfClause = function(atoms) { #' or implicitly, by using the `&` operator on [`CnfAtom`]s, [`CnfClause`]s, or other `CnfFormula` objects. #' #' Upon construction, the `CnfFormula` is simplified by using various heuristics. -#' This includes unit propagation, (self) subsumption elimination, and hidden tautology elimination +#' This includes unit propagation, subsumption elimination, and self/hidden subsumption elimination #' (see examples). #' Note that the order of clauses in a formula is not preserved. #' @@ -396,7 +396,7 @@ CnfClause = function(atoms) { #' Z %among% c("g", "h")) #' #' ## unit propagation -#' # The second clause can not be satisfied when X is "b", so "b" it can be +#' # The second clause can not be satisfied when X is "b", so "b" can be #' # removed from the possibilities in the first clause. #' (X %among% c("a", "b") | Y %among% c("d", "e")) & #' X %among% c("a", "c") @@ -414,7 +414,7 @@ CnfClause = function(atoms) { #' (X %among% c("a", "b") | Y %among% "d") & #' (X %among% "a" | Y %among% "e") #' -#' ## hidden tautology elimination +#' ## hidden subsumption elimination #' # The first two statements can only be satisfied if Y is either "d" or "e", #' # since when X is "a" then Y must be "e", and when X is "b" then Y must be "d". #' # The third statement is therefore implied by the first two, and can be @@ -538,7 +538,7 @@ simplify_cnf = function(entries, universe) { entries = entries[order(lengths(entries))] # removing units may have changed the order eliminated = logical(length(entries)) for (i in seq_along(entries)) { - if (eliminated[[i]]) next # can only happen if we do the hidden tautology elimination, which searches forward + if (eliminated[[i]]) next # can only happen if we do the hidden subsumption elimination, which searches forward ei = entries[[i]] # If sym(A) is a subset of sym(B) and for each s in sym(A), val(A, s) is a subset of val(B, s), then A implies B, so B can be removed ("subsumption elimination"). for (j in seq_len(i - 1)) { @@ -550,8 +550,8 @@ simplify_cnf = function(entries, universe) { eliminated[[i]] = TRUE break } - # simple self subsumption and hidden tautology elimination - # HTE: + # simple self subsumption and hidden subsumption elimination + # HSE: # if s is in sym(A) and sym(B), and val(A, s) and val(B, s) are disjoint, then (A - s | B - s) is implied, # and all superset clauses of (A - s | B - s) can be removed. # we could also do this for higher order terms, intersection over X of val(X, s) == 0 etc., but this gets more complex. @@ -640,7 +640,7 @@ simplify_cnf = function(entries, universe) { next } } - # Hidden Tautology Elimination + # Hidden Subsumption Elimination # # We only do this if self subsumption elimination did not occur. # diff --git a/man/CnfFormula.Rd b/man/CnfFormula.Rd index 6e2f44fbf..abb61c7d1 100644 --- a/man/CnfFormula.Rd +++ b/man/CnfFormula.Rd @@ -31,7 +31,7 @@ that is true if all of the clauses are true. These are for example of the form or implicitly, by using the \code{&} operator on \code{\link{CnfAtom}}s, \code{\link{CnfClause}}s, or other \code{CnfFormula} objects. Upon construction, the \code{CnfFormula} is simplified by using various heuristics. -This includes unit propagation, (self) subsumption elimination, and hidden tautology elimination +This includes unit propagation, subsumption elimination, and self/hidden subsumption elimination (see examples). Note that the order of clauses in a formula is not preserved. @@ -66,7 +66,7 @@ Z = CnfSymbol(u, "Z", c("g", "h", "i")) Z \%among\% c("g", "h")) ## unit propagation -# The second clause can not be satisfied when X is "b", so "b" it can be +# The second clause can not be satisfied when X is "b", so "b" can be # removed from the possibilities in the first clause. (X \%among\% c("a", "b") | Y \%among\% c("d", "e")) & X \%among\% c("a", "c") @@ -84,7 +84,7 @@ Z = CnfSymbol(u, "Z", c("g", "h", "i")) (X \%among\% c("a", "b") | Y \%among\% "d") & (X \%among\% "a" | Y \%among\% "e") -## hidden tautology elimination +## hidden subsumption elimination # The first two statements can only be satisfied if Y is either "d" or "e", # since when X is "a" then Y must be "e", and when X is "b" then Y must be "d". # The third statement is therefore implied by the first two, and can be From 1fc8e66e475f3ed7123beeb571ebb3fd6edeae98 Mon Sep 17 00:00:00 2001 From: mb706 Date: Mon, 9 Sep 2024 22:20:33 +0200 Subject: [PATCH 20/87] notes --- R/CnfFormula.R | 2 +- attic/mvsat.mv | 89 +++++++++++++++++++++++++++++++++++++++++++++++ man/CnfFormula.Rd | 2 +- 3 files changed, 91 insertions(+), 2 deletions(-) create mode 100644 attic/mvsat.mv diff --git a/R/CnfFormula.R b/R/CnfFormula.R index 939f67eed..a58e0202f 100644 --- a/R/CnfFormula.R +++ b/R/CnfFormula.R @@ -430,7 +430,7 @@ CnfClause = function(atoms) { #' #' # But not all contradictions are recognized. #' # Builtin heuristic CnfFormula preprocessing is not a SAT solver. -#' contradiction <- (X %among% "a" | Y %among% "d") & +#' contradiction = (X %among% "a" | Y %among% "d") & #' (X %among% "b" | Y %among% "e") & #' (X %among% "c" | Y %among% "f") #' contradiction diff --git a/attic/mvsat.mv b/attic/mvsat.mv new file mode 100644 index 000000000..c3c66116a --- /dev/null +++ b/attic/mvsat.mv @@ -0,0 +1,89 @@ + + + +# MV SAT simplifier thoughts + +- check how fast symbol-access is by name vs. blowing up vector to access by number, vs. indirect access x[[s[[i]]]] + - vs. hash table environment + - indirect access would enable us to have matrices with cols for 's', we could do colsums? +- is subset-check through all(x %in% y) twice faster than length(union(x, y)), length(x), length(y)? + +- for every clause i, and for every symbol in that clause s, we keep a vector v[i][s] with v[i][s][j] == '0' if j[s] >= i[s]; 1 if j[s] < i[s] + - if s is not in i, then 0 is implied for all other clauses, so don't need to keep this + - likely don't need a matrix here since we will eliminate rows / cols etc. frequently and probably only need col-wise matrix-ops anyways? + - maybe something like colsums? +- we start with i going down from largest to smallest (since largest we can probably eliminate quickly) + - we start with j going up, since we likely can eliminate fastest with small j + - go through all s in i and populate v[i][s][j], as well as v[j][s][i] -- but the latter only for equality! + - it could happen that we can eliminate j? + - no, because we only check subset-ness in one direction + - keep running tally of 1s and save to sum[i][j] + - check right away if we can eliminate [i] + - check right away if we can do HLA + - if so, set all 0s in v[i][s][k < j] we have already set to NA + + +- maybe the other way around? + - i from small to large, keep vector v[i][s][j] with v[i][s][j] = 1 whenever i[s] > v[s] + - i from small to large, j from small to large also (does not matter?) + - fill v[i][s][j] + - it starts with NA? and we fill v[j][s][i] with 0 if we find equality (starts with NA)? + - no we can not do that since in general we are comparing against j+, not j. + - we could potentially eliminate j + - we could potentially HLA to j + - no need to check if v[j][s][i] is 1? so can pre-fill with !v[j][s][i]? + - remember that we track >-relationship for small version vs. large version + + + + + + +- checker for logical equivalence in tests + + + +# Ok, actual asymmetric hidden tautology elimination: +# for a given clause C, look for other clause D that are subsets w/r/t all vars except one var 's'. +# we can then add complement(var(D, s)) to C. +# We might then be able to repeat this, even with clauses for which this didnt work before. +# - why must D be a subset wrt all except one var? Because we can only add not(s). If there are more vars, then not(s, s') are two clauses. +# - does this mean we could replace C with two more clauses? Maybe, but these would have to be eliminated individually. May not be possible, is probablyd ifficult and out of scope. +# - What if D is a subset wrt all vars? Then we can already subsumption eliminate C. +# - D is a subset wrt all vars except 's', and 's' is partial overlap? We can still add the complement of var(D, s)! +# - Why might this be better than what we already have? +# - potentially still quadratic in number of terms, but builds the biggest possible C before checking for elimination. +# - Is this truly more powerful than the current approach? +# - We need to build up C+ and let it refer to C; if we eliminate C+, C is also eliminated. +# - Can we greedily eliminate C / C+? Or are there cases where we need to keep either? +# - Is it worth keeping the larger of C / C+? +# - What is the implication of having a D vs. D+ somewhere for this procedure? +# - To the degree that D has something that is outside of C, we want this to be as small as possible, because we want to grow C as much as possible, so D is preferable to D+ +# - Suppose D has nothing outside of C, in this case we can already subsumption eliminate C, so we are indifferent to D+ +# - Suppose subsumption elimination was not an option. At some point we were able to grow D and add something to it that is neither in C nor in D. Since D is a subset of C wrt to all except s, we can add the same thing to C. With D+ together, we could also add the complement of s and get a tautology. +# - But subsumption *is* an option, see line above. +# - So we never need to look at any C+ for the fattening procedure here. +# - Should we keep D, even if D+ can be eliminated? +# - Suppose we grew D by using some E that does not have the 's' that D and C disagree on. +# - then E can also be used by C, since D-s is a subset of C. +# - Suppose we grew D by using some E that contains values in 's' that are not in C. +# - this may be the wrong question to ask. The question should be: Are we going to miss the complement(D, s) in C? This is the part we can't add to C once we have eliminated D. +# - it would be *really* nice if we could do this greedily! +# - We can always do unit elimination +# - but maybe we should be smarter about it? +# - Can we have a rule about what can be kept, what can be eliminated? +# - Shoutout to 'Clause Elimination Procedures for CNF Formulas' by Marijn Heule, Matti Järvisalo, Armin Biere +# - How do we efficiently calculate subsets wrt all vars except one? +# - How about having a subset relatoinship binary matrix for each variable? +# - e.g. X[v]_i,j == 1 whenever var(i, v) <= var(j, v) +# - doing AND for all X except v on i, j except v=s would give var(i, v) <= var(j, v) for all vsymbols except s, implying that i <= j (subset). +# - we could also sum the matrices up, and wherever sum{v!=s} of X[v] is n-1, we are satisfied. +# - this can be simplified by just calculating the sum over all matrices and subtracting X[s] one by one. +# - can we do transitivity in these matrices? [i] <= [j], [j]<=[k] for any [j] -> [i]<=[k] -- this is a vector dot product... +# - If the domains of vars are small and there are many j, calculating this directly may be faster? +# - Instead, suppose we already have the matrix for columns 1 ... i. We now check i+1. For agiven j +# - no need to check if j < i+1 and [i+1] => [j]. At most we check for equality (length equal). +# - if we find [i+1] <= [j], we can immediately copy over the column of j to i+1. +# - other suggestion: we calculate submatrix 1..(i)x1..(i). Then add new column i+1. We can copy over all 1s immediately whenever we find a col that is a subset of i+1; However, we can at most copy i ones. +# - maybe there is no easy solution; possibly except ordering by size first and only comparing in one direction. +# - does this make self subsumption elimination more efficient? diff --git a/man/CnfFormula.Rd b/man/CnfFormula.Rd index abb61c7d1..b8c9fb3c2 100644 --- a/man/CnfFormula.Rd +++ b/man/CnfFormula.Rd @@ -100,7 +100,7 @@ Z = CnfSymbol(u, "Z", c("g", "h", "i")) # But not all contradictions are recognized. # Builtin heuristic CnfFormula preprocessing is not a SAT solver. -contradiction <- (X \%among\% "a" | Y \%among\% "d") & +contradiction = (X \%among\% "a" | Y \%among\% "d") & (X \%among\% "b" | Y \%among\% "e") & (X \%among\% "c" | Y \%among\% "f") contradiction From 1d08acf9fb91bef405ed5a89875d45a4be032575 Mon Sep 17 00:00:00 2001 From: mb706 Date: Tue, 10 Sep 2024 18:27:12 +0200 Subject: [PATCH 21/87] cleaning up a lil --- R/CnfAtom.R | 235 +++++++++ R/CnfClause.R | 265 ++++++++++ R/CnfFormula.R | 1039 ++++----------------------------------- R/CnfFormula_simplify.R | 217 ++++++++ R/CnfSymbol.R | 64 +++ R/CnfUniverse.R | 64 +++ attic/minibenchmarks.R | 111 +++++ 7 files changed, 1056 insertions(+), 939 deletions(-) create mode 100644 R/CnfAtom.R create mode 100644 R/CnfClause.R create mode 100644 R/CnfFormula_simplify.R create mode 100644 R/CnfSymbol.R create mode 100644 R/CnfUniverse.R create mode 100644 attic/minibenchmarks.R diff --git a/R/CnfAtom.R b/R/CnfAtom.R new file mode 100644 index 000000000..cc6af0ddd --- /dev/null +++ b/R/CnfAtom.R @@ -0,0 +1,235 @@ +# An expression of the form "X %in% {x1, x2, x3}" +#' @title Atoms for CNF Formulas +#' +#' @description +#' `Atom` objects represent a single statement that is used to build up CNF formulae. +#' They are mostly intermediate, created using the [`%among%`] operator or [`CnfAtom()`] +#' directly, and combined into [`CnfClause`] and [`CnfFormula`] objects. +#' [`CnfClause`] and [`CnfFormula`] do not, however, contain [`Atom`] objects directly, +#' +#' `Atom`s contain an indirect reference to a [`CnfSymbol`] by referencing its name +#' and its [`CnfUniverse`]. They furthermore contain a set of values. An `Atom` +#' represents a statement asserting that the given symbol takes up one of the +#' given values. +#' +#' If the set of values is empty, the `Atom` represents a contradiction (FALSE). +#' If it is the full domain of the symbol, the `Atom` represents a tautology (TRUE). +#' These values can be converted to, and from, `logical(1)` values using `as.logical()` +#' and `as.CnfAtom()`. +#' +#' `Atom` objects can be negated using the `!` operator, which will return the `Atom` +#' representing set membership in the complement of the symbol with respect to its domain. +#' `Atom`s can furthermore be combined using the `|` operator to form a [`CnfClause`], +#' and using the `&` operator to form a [`CnfFormula`]. This happens even if the +#' resulting statement could be represented as a single `Atom`. +#' +#' This is part of the CNF representation tooling, which is currently considered +#' experimental; it is for internal use. +#' +#' @details +#' We would have preferred to overload the `%in%` operator, but this is currently +#' not easily possible in R. We therefore created the `%among%` operator. +#' +#' @param symbol ([`CnfSymbol`]) \cr +#' The symbol to which the atom refers. +#' @param values (`character`) \cr +#' The values that the symbol can take. +#' @param e1 (`CnfSymbol`) \cr +#' Left-hand side of the `%among%` operator. +#' Passed as `symbol` to `CnfAtom()`. +#' @param e2 (`character`) \cr +#' Right-hand side of the `%among%` operator. +#' Passed as `values` to `CnfAtom()`. +#' @param x (any) \cr +#' The object to be coerced to a `CnfAtom` by `as.CnfAtom`. +#' Only `logical(1)` and `CnfAtom` itself are currently supported. +#' @return A new `CnfAtom` object. +#' @examples +#' u = CnfUniverse() +#' X = CnfSymbol(u, "X", c("a", "b", "c")) +#' +#' CnfAtom(X, c("a", "b")) +#' X %among% "a" +#' X %among% character(0) +#' X %among% c("a", "b", "c") +#' +#' as.logical(X %among% character(0)) +#' as.CnfAtom(TRUE) +#' +#' !(X %among% "a") +#' +#' X %among% "a" | X %among% "b" # creates a CnfClause +#' +#' X %among% "a" & X %among% c("a", "b") # creates a CnfFormula +#' @family CNF representation objects +#' @keywords internal +#' @export +CnfAtom = function(symbol, values) { + assert_class(symbol, "CnfSymbol") + domain = get(symbol, attr(symbol, "universe")) + assert_subset(values, domain) + if (all(domain %in% values)) { + structure( + TRUE, + universe = attr(symbol, "universe"), + class = "CnfAtom" + ) + } else if (length(values) == 0) { + structure( + FALSE, + universe = attr(symbol, "universe"), + class = "CnfAtom" + ) + } else { + structure( + list(symbol = c(symbol), values = unique(values)), + universe = attr(symbol, "universe"), + class = "CnfAtom" + ) + } +} + +#' @export +print.CnfAtom = function(x, ...) { + if (isTRUE(x)) { + cat("CnfAtom: \n") + } else if (isFALSE(x)) { + cat("CnfAtom: \n") + } else { + cat(sprintf("CnfAtom: %s \U2208 {%s}.\n", x$symbol, paste(x$values, collapse = ", "))) + } + invisible(x) +} + +#' @export +format.CnfAtom = function(x, ...) { + if (isTRUE(x)) { + return("CnfAtom: T") + } else if (isFALSE(x)) { + return("CnfAtom: F") + } else { + return(sprintf("CnfAtom(%s)", x$symbol)) + } +} + +# construct CnfAtom with `X %among% c("a", "b", "c")` +# we cannot overload `%in%`, unfortunately +#' @export +#' @rdname CnfAtom +`%among%` = function(e1, e2) { + UseMethod("%among%") +} + +#' @export +`%among%.CnfSymbol` = function(e1, e2) { + CnfAtom(e1, e2) +} + +#' @export +`%among%.default` = function(e1, e2) { + stop("%among% operation not defined for LHS. %among% should typically be used with a CnfSymbol.") +} + + +#' @rdname CnfAtom +#' @export +as.CnfAtom = function(x) { + UseMethod("as.CnfAtom") +} + +#' @export +as.CnfAtom.default = function(x) { + stop("Cannot convert object to CnfAtom.") +} + +#' @export +as.CnfAtom.logical = function(x) { + assert_flag(x) + return(structure( + x, + universe = attr(x, "universe"), + class = "CnfAtom" + )) +} + +#' @export +as.CnfAtom.CnfAtom = function(x) { + x +} + +#' @export +as.logical.CnfAtom = function(x) { + if (is.logical(x)) { + return(unclass(x)) + } + return(NA) +} + +#' @export +all.equal.CnfAtom = function(target, current, ...) { + if (is.logical(target) && is.logical(current)) { + # compare truth-values directly, even if they disagree on universe + # (since logical atoms sometimes have universe set to NULL) + if (identical(c(target), c(current))) { + return(TRUE) + } + return("target and current are both logicals but not equal") + } + if (is.logical(target) || is.logical(current)) { + return("target and current are not both logicals") + } + if (!inherits(current, "CnfAtom")) { + return("current is not a CnfAtom") + } + target$values = sort(target$values) + current$values = sort(current$values) + all.equal.list(target, current, ...) +} + +#' @rawNamespace if (getRversion() >= "4.3.0") S3method(chooseOpsMethod,CnfAtom) +chooseOpsMethod.CnfAtom <- function(x, y, mx, my, cl, reverse) TRUE + +#' @export +`&.CnfAtom` = function(e1, e2) { + if (isFALSE(e1)) return(e1) + if (isFALSE(e2)) return(e2) + if (isTRUE(e1)) return(e2) + if (isTRUE(e2)) return(e1) + if (inherits(e2, "CnfAtom")) { + e2 = CnfClause(list(e2)) + } + if (inherits(e2, "CnfClause")) { + CnfFormula(list(CnfClause(list(e1)), e2)) + } else { + # e2 is anything else -- go the lazy route + as.CnfFormula(e1) & as.CnfFormula(e2) + } +} + +#' @export +`|.CnfAtom` = function(e1, e2) { + if (isFALSE(e1)) return(e2) + if (isFALSE(e2)) return(e1) + if (isTRUE(e1)) return(e1) + if (isTRUE(e2)) return(e2) + if (inherits(e2, "CnfAtom")) { + CnfClause(list(e1, e2)) + } else { + # e2 is anything else -- go the lazy route + as.CnfFormula(e1) | as.CnfFormula(e2) + } +} + +#' @export +`!.CnfAtom` = function(x) { + if (is.logical(x)) { + not_x = if (x) FALSE else TRUE # can't use '!' here... + attributes(not_x) = attributes(x) # keep class and universe + return(not_x) + } + structure( + list(symbol = x$symbol, values = setdiff(get(x$symbol, attr(x, "universe")), x$values)), + universe = attr(x, "universe"), + class = "CnfAtom" + ) +} diff --git a/R/CnfClause.R b/R/CnfClause.R new file mode 100644 index 000000000..e42b8f002 --- /dev/null +++ b/R/CnfClause.R @@ -0,0 +1,265 @@ +# A clause is a disjunction of atoms. +# X %among% c("a", "b", "c") | Y %among% c("d", "e", "f") + +#' @title Clauses in CNF Formulas +#' +#' @description +#' A `CnfClause` is a disjunction of [`CnfAtom`] objects. It represents a statement +#' that is true if at least one of the atoms is true. These are for example of the form +#' ```r +#' X %among% c("a", "b", "c") | Y %among% c("d", "e", "f") | ... +#' ``` +#' +#' `CnfClause` objects can be constructed explicitly, using the `CnfClause()` constructor, +#' or implicitly, by using the `|` operator on [`CnfAtom`]s or other `CnfClause` objects. +#' +#' Upon construction, the `CnfClause` is simplified by (1) removing contradictions, (2) unifying +#' atoms that refer to the same symbol, and (3) evaluating to `TRUE` if any atom is `TRUE`. +#' Note that the order of atoms in a clause is not preserved. +#' +#' Using `CnfClause()` on lists that contain other `CnfClause` objects will create +#' a clause that is the disjunction of all atoms in all clauses. +#' +#' If a `CnfClause` contains no atoms, or only `FALSE` atoms, it evaluates to `FALSE`. +#' If it contains at least one atom that is always true, the clause evaluates to `TRUE`. +#' These values can be converted to, and from, `logical(1)` values using `as.logical()` +#' and `as.CnfClause()`. +#' +#' `CnfClause` objects can be negated using the `!` operator, and combined using the +#' `&` operator. Both of these operations return a [`CnfFormula`], even if the result +#' could in principle be represented as a single `CnfClause`. +#' +#' This is part of the CNF representation tooling, which is currently considered +#' experimental; it is for internal use. +#' +#' @param atoms (`list` of ([`CnfAtom`] | `CnfClause`)) \cr +#' A list of [`CnfAtom`] or other `CnfClause` objects. +#' The clause represents the disjunction of these atoms. +#' @param x (any) \cr +#' The object to be coerced to a `CnfClause` by `as.CnfClause`. +#' Only `logical(1)`, [`CnfAtom`], and `CnfClause` itself are currently supported. +#' @return A new `CnfClause` object. +#' @examples +#' u = CnfUniverse() +#' X = CnfSymbol(u, "X", c("a", "b", "c")) +#' Y = CnfSymbol(u, "Y", c("d", "e", "f")) +#' +#' CnfClause(list(X %among% c("a", "b"), Y %among% c("d", "e"))) +#' X %among% c("a", "b") | Y %among% c("d", "e") +#' +#' as.CnfClause(X %among% c("a", "b")) +#' +#' # The same symbols are unified +#' X %among% "a" | Y %among% "d" | X %among% "b" +#' +#' # tautology evaluates to TRUE +#' X %among% "a" | X %among% "b" | X %among% "c" +#' +#' # contradictions are removed +#' X %among% "a" | Y %among% character(0) +#' +#' # create CnfFormula: +#' !(X %among% "a" | Y %among% "d") +#' +#' # also a CnfFormula, even if it contains a single clause: +#' !CnfClause(list(X %among% "a")) +#' (X %among% c("a", "c") | Y %among% "d") & +#' (X %among% c("a", "b") | Y %among% "d") +#' @family CNF representation objects +#' @keywords internal +#' @export +CnfClause = function(atoms) { + assert_list(atoms, types = c("CnfAtom", "CnfClause")) + if (!length(atoms)) { + return(structure( + FALSE, + universe = NULL, + class = "CnfClause" + )) + } + entries = list() + universe = attr(atoms[[1]], "universe") + for (a in atoms) { + if (!identical(attr(a, "universe"), universe)) { + stop("All symbols must be in the same universe.") + } + if (isTRUE(a)) { + entries = TRUE + break + } + if (isFALSE(a)) { + next + } + if (inherits(a, "CnfAtom")) { + entries[[a$symbol]] = union(entries[[a$symbol]], a$values) + if (all(get(a$symbol, universe) %in% entries[[a$symbol]])) { + entries = TRUE + break + } + } else { + # union with another CnfClause objects + for (sym in names(a)) { + entries[[sym]] = union(entries[[sym]], a[[sym]]) + if (all(get(sym, universe) %in% entries[[sym]])) { + entries = TRUE + break + } + } + } + } + structure( + if (!length(entries)) FALSE else entries, + universe = universe, + class = "CnfClause" + ) +} + +#' @export +print.CnfClause = function(x, ...) { + if (isTRUE(x)) { + cat("CnfClause: TRUE\n") + } else if (isFALSE(x)) { + cat("CnfClause: FALSE\n") + } else { + cat("CnfClause:\n") + elements = map_chr(names(x), function(sym) { + sprintf("%s \U2208 {%s}", sym, paste(x[[sym]], collapse = ", ")) + }) + cat(strwrap(paste(elements, collapse = " | "), prefix = " "), sep = "\n") + } + invisible(x) +} + +#' @export +format.CnfClause = function(x, ...) { + if (isTRUE(x)) { + return("CnfClause: T") + } else if (isFALSE(x)) { + return("CnfClause: F") + } else { + return(sprintf("CnfClause(%s)", length(x))) + } +} + +#' @rdname CnfClause +#' @export +as.CnfClause = function(x) { + UseMethod("as.CnfClause") +} + +#' @export +as.CnfClause.default = function(x) { + stop("Cannot convert object to CnfClause.") +} + +#' @export +as.CnfClause.logical = function(x) { + assert_flag(x) + return(structure( + x, + universe = attr(x, "universe"), + class = "CnfClause" + )) +} + +#' @export +as.CnfClause.CnfAtom = function(x) { + CnfClause(list(x)) +} + +#' @export +as.CnfClause.CnfClause = function(x) { + x +} + +#' @export +as.logical.CnfClause = function(x) { + if (is.logical(x)) { + return(unclass(x)) + } + return(NA) +} + +#' @export +all.equal.CnfClause = function(target, current, ...) { + if (is.logical(target) && is.logical(current)) { + # compare truth-values directly, even if they disagree on universe + # (since logical atoms sometimes have universe set to NULL) + if (identical(c(target), c(current))) { + return(TRUE) + } + return("target and current are both logicals but not equal") + } + if (is.logical(target) || is.logical(current)) { + return("target and current are not both logicals") + } + if (!inherits(current, "CnfClause")) { + return("current is not a CnfClause") + } + + normalize = function(clause) { + # []-assign to preserve class and attributes + clause[] = lapply(clause[order(names(clause))], sort) + } + + target = normalize(target) + current = normalize(current) + + all.equal.list(target, current, ...) +} + +#' @rawNamespace if (getRversion() >= "4.3.0") S3method(chooseOpsMethod,CnfClause) +chooseOpsMethod.CnfClause <- function(x, y, mx, my, cl, reverse) TRUE + +#' @export +`&.CnfClause` = function(e1, e2) { + if (isFALSE(e1)) return(e1) + if (isFALSE(e2)) return(e2) + if (isTRUE(e1)) return(e2) + if (isTRUE(e2)) return(e1) + if (inherits(e2, "CnfAtom")) { + e2 = CnfClause(list(e2)) + } + if (inherits(e2, "CnfClause")) { + CnfFormula(list(e1, e2)) + } else { + # e2 is anything else -- go the lazy route + as.CnfFormula(e1) & as.CnfFormula(e2) + } +} + +#' @export +`|.CnfClause` = function(e1, e2) { + if (isFALSE(e1)) return(e2) + if (isFALSE(e2)) return(e1) + if (isTRUE(e1)) return(e1) + if (isTRUE(e2)) return(e2) + if (inherits(e2, "CnfAtom")) { + e2 = CnfClause(list(e2)) + } + if (inherits(e2, "CnfClause")) { + for (sym in names(e2)) { + e1[[sym]] = union(e1[[sym]], e2[[sym]]) + if (all(get(sym, attr(e1, "universe")) %in% e1[[sym]])) { + return(structure( + TRUE, + universe = attr(e1, "universe"), + class = "CnfClause" + )) + } + } + return(e1) + } + # e2 is anything else -- go the lazy route + as.CnfFormula(e1) | as.CnfFormula(e2) +} + + +#' @export +`!.CnfClause` = function(x) { + if (is.logical(x)) { + return(as.CnfClause(!unclass(x))) + } + !as.CnfFormula(x) +} + diff --git a/R/CnfFormula.R b/R/CnfFormula.R index a58e0202f..281547023 100644 --- a/R/CnfFormula.R +++ b/R/CnfFormula.R @@ -13,335 +13,9 @@ # Container object for possible branch conditions. - - -#' @title Symbol Table for CNF Formulas -#' -#' @description -#' A symbol table for CNF formulas. The `CnfUniverse` is a by-reference object -#' that stores the domain of each symbol. Symbols are created with [`CnfSymbol()`] -#' and can be retrieved with `[[` or `$`. -#' -#' It is only possible to combine symbols from the same (identical) universe. -#' -#' This is part of the CNF representation tooling, which is currently considered -#' experimental; it is for internal use. -#' -#' @return A new `CnfUniverse` object. -#' @examples -#' u = CnfUniverse() -#' X = CnfSymbol(u, "X", c("a", "b", "c")) -#' Y = CnfSymbol(u, "Y", c("d", "e", "f")) -#' -#' u$X -#' u[["Y"]] -#' -#' X %among% c("a", "d") -#' u$X %among% c("a", "d") -#' Y %among% c("d", "e", "f") -#' Y %among% character(0) -#' -#' u$X %among% "a" | u$Y %among% "d" -#' @family CNF representation objects -#' @keywords internal -#' @export -CnfUniverse = function() structure(new.env(parent = emptyenv()), class = "CnfUniverse") - -# We represent symbols through a name and a pointer to their universe. -# We only allow operations between symbols that are in the same universe. -#' @title Symbols for CNF Formulas -#' -#' @description -#' Representation of Symbols used in CNF formulas. Symbols have a name and a -#' domain (a set of possible values), and are stored in a [`CnfUniverse`]. -#' -#' Once created, it is currently not intended to modify or delete symbols. -#' -#' Symbols can be used in CNF formulas by creating [`CnfAtom`] objects, either -#' by using the `%among%` operator or by using the [`CnfAtom()`] constructor -#' explicitly. -#' -#' This is part of the CNF representation tooling, which is currently considered -#' experimental; it is for internal use. -#' -#' @param universe ([`CnfUniverse`]) \cr -#' The universe in which the symbol is defined. -#' @param name (`character(1)`) \cr -#' The name of the symbol. -#' @param domain (`character`) \cr -#' The domain, i.e. the set of possible values for the symbol. -#' Must not be empty. -#' @return A new `CnfSymbol` object. -#' @examples -#' u = CnfUniverse() -#' X = CnfSymbol(u, "X", c("a", "b", "c")) -#' -#' X %among% c("a", "b") -#' X %among% "a" -#' X %among% character(0) -#' X %among% c("a", "b", "c") -#' @family CNF representation objects -#' @keywords internal -#' @export -CnfSymbol = function(universe, name, domain) { - assert_class(universe, "CnfUniverse") - assert_string(name) - assert_character(domain, any.missing = FALSE, min.len = 1) - if (exists(name, universe)) { - stopf("Variable '%s' already exists in the universe.", name) - } - assign(name, domain, universe) - structure( - name, - universe = universe, - class = "CnfSymbol" - ) -} - -# We allow retrieving symbols from the universe by name. -#' @export -`[[.CnfUniverse` = function(universe, name) { - assert_string(name) - if (!exists(name, universe)) { - stopf("Variable '%s' does not exist in the universe.", name) - } - structure( - name, - universe = universe, - class = "CnfSymbol" - ) -} - -#' @export -`$.CnfUniverse` = `[[.CnfUniverse` - -# An expression of the form "X %in% {x1, x2, x3}" -#' @title Atoms for CNF Formulas -#' -#' @description -#' `Atom` objects represent a single statement that is used to build up CNF formulae. -#' They are mostly intermediate, created using the [`%among%`] operator or [`CnfAtom()`] -#' directly, and combined into [`CnfClause`] and [`CnfFormula`] objects. -#' [`CnfClause`] and [`CnfFormula`] do not, however, contain [`Atom`] objects directly, -#' -#' `Atom`s contain an indirect reference to a [`CnfSymbol`] by referencing its name -#' and its [`CnfUniverse`]. They furthermore contain a set of values. An `Atom` -#' represents a statement asserting that the given symbol takes up one of the -#' given values. -#' -#' If the set of values is empty, the `Atom` represents a contradiction (FALSE). -#' If it is the full domain of the symbol, the `Atom` represents a tautology (TRUE). -#' These values can be converted to, and from, `logical(1)` values using `as.logical()` -#' and `as.CnfAtom()`. -#' -#' `Atom` objects can be negated using the `!` operator, which will return the `Atom` -#' representing set membership in the complement of the symbol with respect to its domain. -#' `Atom`s can furthermore be combined using the `|` operator to form a [`CnfClause`], -#' and using the `&` operator to form a [`CnfFormula`]. This happens even if the -#' resulting statement could be represented as a single `Atom`. -#' -#' This is part of the CNF representation tooling, which is currently considered -#' experimental; it is for internal use. -#' -#' @details -#' We would have preferred to overload the `%in%` operator, but this is currently -#' not easily possible in R. We therefore created the `%among%` operator. -#' -#' @param symbol ([`CnfSymbol`]) \cr -#' The symbol to which the atom refers. -#' @param values (`character`) \cr -#' The values that the symbol can take. -#' @param e1 (`CnfSymbol`) \cr -#' Left-hand side of the `%among%` operator. -#' Passed as `symbol` to `CnfAtom()`. -#' @param e2 (`character`) \cr -#' Right-hand side of the `%among%` operator. -#' Passed as `values` to `CnfAtom()`. -#' @param x (any) \cr -#' The object to be coerced to a `CnfAtom` by `as.CnfAtom`. -#' Only `logical(1)` and `CnfAtom` itself are currently supported. -#' @return A new `CnfAtom` object. -#' @examples -#' u = CnfUniverse() -#' X = CnfSymbol(u, "X", c("a", "b", "c")) -#' -#' CnfAtom(X, c("a", "b")) -#' X %among% "a" -#' X %among% character(0) -#' X %among% c("a", "b", "c") -#' -#' as.logical(X %among% character(0)) -#' as.CnfAtom(TRUE) -#' -#' !(X %among% "a") -#' -#' X %among% "a" | X %among% "b" # creates a CnfClause -#' -#' X %among% "a" & X %among% c("a", "b") # creates a CnfFormula -#' @family CNF representation objects -#' @keywords internal -#' @export -CnfAtom = function(symbol, values) { - assert_class(symbol, "CnfSymbol") - domain = get(symbol, attr(symbol, "universe")) - assert_subset(values, domain) - if (all(domain %in% values)) { - structure( - TRUE, - universe = attr(symbol, "universe"), - class = "CnfAtom" - ) - } else if (length(values) == 0) { - structure( - FALSE, - universe = attr(symbol, "universe"), - class = "CnfAtom" - ) - } else { - structure( - list(symbol = c(symbol), values = unique(values)), - universe = attr(symbol, "universe"), - class = "CnfAtom" - ) - } -} - -# construct CnfAtom with `X %among% c("a", "b", "c")` -# we cannot overload `%in%`, unfortunately -#' @export -#' @rdname CnfAtom -`%among%` = function(e1, e2) { - UseMethod("%among%") -} - -#' @export -`%among%.CnfSymbol` = function(e1, e2) { - CnfAtom(e1, e2) -} - -#' @export -`%among%.default` = function(e1, e2) { - stop("%among% operation not defined for LHS. %among% should typically be used with a CnfSymbol.") -} - -# A clause is a disjunction of atoms. -# X %among% c("a", "b", "c") | Y %among% c("d", "e", "f") - -#' @title Clauses in CNF Formulas -#' -#' @description -#' A `CnfClause` is a disjunction of [`CnfAtom`] objects. It represents a statement -#' that is true if at least one of the atoms is true. These are for example of the form -#' ```r -#' X %among% c("a", "b", "c") | Y %among% c("d", "e", "f") | ... -#' ``` -#' -#' `CnfClause` objects can be constructed explicitly, using the `CnfClause()` constructor, -#' or implicitly, by using the `|` operator on [`CnfAtom`]s or other `CnfClause` objects. -#' -#' Upon construction, the `CnfClause` is simplified by (1) removing contradictions, (2) unifying -#' atoms that refer to the same symbol, and (3) evaluating to `TRUE` if any atom is `TRUE`. -#' Note that the order of atoms in a clause is not preserved. -#' -#' Using `CnfClause()` on lists that contain other `CnfClause` objects will create -#' a clause that is the disjunction of all atoms in all clauses. -#' -#' If a `CnfClause` contains no atoms, or only `FALSE` atoms, it evaluates to `FALSE`. -#' If it contains at least one atom that is always true, the clause evaluates to `TRUE`. -#' These values can be converted to, and from, `logical(1)` values using `as.logical()` -#' and `as.CnfClause()`. -#' -#' `CnfClause` objects can be negated using the `!` operator, and combined using the -#' `&` operator. Both of these operations return a [`CnfFormula`], even if the result -#' could in principle be represented as a single `CnfClause`. -#' -#' This is part of the CNF representation tooling, which is currently considered -#' experimental; it is for internal use. -#' -#' @param atoms (`list` of ([`CnfAtom`] | `CnfClause`)) \cr -#' A list of [`CnfAtom`] or other `CnfClause` objects. -#' The clause represents the disjunction of these atoms. -#' @param x (any) \cr -#' The object to be coerced to a `CnfClause` by `as.CnfClause`. -#' Only `logical(1)`, [`CnfAtom`], and `CnfClause` itself are currently supported. -#' @return A new `CnfClause` object. -#' @examples -#' u = CnfUniverse() -#' X = CnfSymbol(u, "X", c("a", "b", "c")) -#' Y = CnfSymbol(u, "Y", c("d", "e", "f")) -#' -#' CnfClause(list(X %among% c("a", "b"), Y %among% c("d", "e"))) -#' X %among% c("a", "b") | Y %among% c("d", "e") -#' -#' as.CnfClause(X %among% c("a", "b")) -#' -#' # The same symbols are unified -#' X %among% "a" | Y %among% "d" | X %among% "b" -#' -#' # tautology evaluates to TRUE -#' X %among% "a" | X %among% "b" | X %among% "c" -#' -#' # contradictions are removed -#' X %among% "a" | Y %among% character(0) -#' -#' # create CnfFormula: -#' !(X %among% "a" | Y %among% "d") -#' -#' # also a CnfFormula, even if it contains a single clause: -#' !CnfClause(list(X %among% "a")) -#' (X %among% c("a", "c") | Y %among% "d") & -#' (X %among% c("a", "b") | Y %among% "d") -#' @family CNF representation objects -#' @keywords internal -#' @export -CnfClause = function(atoms) { - assert_list(atoms, types = c("CnfAtom", "CnfClause")) - if (!length(atoms)) { - return(structure( - FALSE, - universe = NULL, - class = "CnfClause" - )) - } - entries = list() - universe = attr(atoms[[1]], "universe") - for (a in atoms) { - if (!identical(attr(a, "universe"), universe)) { - stop("All symbols must be in the same universe.") - } - if (isTRUE(a)) { - entries = TRUE - break - } - if (isFALSE(a)) { - next - } - if (inherits(a, "CnfAtom")) { - entries[[a$symbol]] = union(entries[[a$symbol]], a$values) - if (all(get(a$symbol, universe) %in% entries[[a$symbol]])) { - entries = TRUE - break - } - } else { - # union with another CnfClause objects - for (sym in names(a)) { - entries[[sym]] = union(entries[[sym]], a[[sym]]) - if (all(get(sym, universe) %in% entries[[sym]])) { - entries = TRUE - break - } - } - } - } - structure( - if (!length(entries)) FALSE else entries, - universe = universe, - class = "CnfClause" - ) -} - # A formula is a conjunction of clauses. # (X %among% c("a", "b", "c") | Y %among% c("d", "e", "f")) & (Z %among% c("g", "h", "i")) + #' @title CNF Formulas #' #' @description @@ -479,198 +153,118 @@ CnfFormula = function(clauses) { simplify_cnf(entries, universe) } -simplify_cnf = function(entries, universe) { - return_false = structure( - FALSE, - universe = universe, - class = "CnfFormula" - ) - - # can we do unit elimination? - # if we are already TRUE or FALSE no simplification is necessary - # this only works if there actually are units. - can_simplify = !is.logical(entries) - # likewise, if there is only one clause left, no simplification is necessary. - - units = list() - - while (can_simplify && length(entries) > 1) { - # we do the following until we are sure there are no more simplifications to be made. - # this is the case if we have not meaningfully simplified anything in the last iteration. - can_simplify = FALSE - # sort clauses by length, since (1) length-1-clauses are special, and (2) short clauses can only ever subsume longer ones - entries = entries[order(lengths(entries))] - # Let sum(A) be the symbols in clause A, and val(A, s) be the values of symbol s admitted in clause A. - if (any(lengths(entries) == 1)) { - for (i in seq_along(entries)) { - ei = entries[[i]] - # If |sym(A)| == 1, sym(A) == {s} and s is in sym(B), then val(B, s) <- intersect(val(A, s), val(B, s)) ("unit propagation") - # units is a named list of symbols in size-one-clauses, together with their values. - # We iterate over all symbols in ei that are also in units, and intersect their values. - for (unit_symbol in intersect(names(ei), names(units))) { - length_before_ei = length(ei[[unit_symbol]]) - length_before_unit = length(units[[unit_symbol]]) - intersection = intersect(units[[unit_symbol]], ei[[unit_symbol]]) - ei[[unit_symbol]] = intersection - if (length(ei) == 1 && length(intersection) != length_before_unit) { - # we made a unit shorter, this means we need to simplify the entry from which units[[unit_symbol]] came - can_simplify = TRUE - } - if (!length(ei[[unit_symbol]])) { - ei[[unit_symbol]] = NULL - } - if (!length(ei)) { - return(return_false) - } - if (length(intersection) != length_before_ei) { - # need to store changed ei entry only if its length changed; otherwise we know the intersection did not do anything. - entries[[i]] = ei - } - } - if (length(ei) == 1) { - # even if names(ei) is already in units, at this point ei[[1]] is the intersection of the values - units[[names(ei)]] = ei[[1]] - } - } - if (can_simplify) next - } - - entries = entries[order(lengths(entries))] # removing units may have changed the order - eliminated = logical(length(entries)) - for (i in seq_along(entries)) { - if (eliminated[[i]]) next # can only happen if we do the hidden subsumption elimination, which searches forward - ei = entries[[i]] - # If sym(A) is a subset of sym(B) and for each s in sym(A), val(A, s) is a subset of val(B, s), then A implies B, so B can be removed ("subsumption elimination"). - for (j in seq_len(i - 1)) { - if (eliminated[[j]]) next - ej = entries[[j]] - name_overlap = names(ej) %in% names(ei) - if (all(name_overlap) && all(sapply(names(ej), function(s) all(ej[[s]] %in% ei[[s]])))) { - # can't do entries[[i]] = NULL, since we are iterating over entries; the entries[[i]] would break. - eliminated[[i]] = TRUE - break - } - # simple self subsumption and hidden subsumption elimination - # HSE: - # if s is in sym(A) and sym(B), and val(A, s) and val(B, s) are disjoint, then (A - s | B - s) is implied, - # and all superset clauses of (A - s | B - s) can be removed. - # we could also do this for higher order terms, intersection over X of val(X, s) == 0 etc., but this gets more complex. - # tbh, I am not sure if this is actually worth it - # SSE: If val(A, s) and val(B, s) are disjoint, and A - s is a subset of B - s, then A & B <=> A & (B - s) - - which_name_overlap = which(name_overlap) - # - build the union of values of overlapping symbols - # - in the innerloop we will check that most of this is a subset of any other clause - # - "most of" here means: all but the one symbol s where the values are disjoint - # - use delayedAssign to avoid computation if there is no overlap with empty intersect - delayedAssign("cnames", union(names(ei), names(ej))) - - # Putting ei[[s2]] first on purpose, since union() preserves the order of the first argument. - # If and only if ej[-s] is a subset of ei[-s], then cunion[-s] will be the same as ei[-s]. - delayedAssign("cunion", sapply(cnames, function(s2) union(ei[[s2]], ej[[s2]]), simplify = FALSE)) - - nameshift = 0 # in case we eliminate names from ej, we need to shift the indices for later loops iterations - for (no in which_name_overlap) { - s = names(ej)[[no - nameshift]] - # intersection is not 0 --> try next one - if (length(intersect(ej[[s]], ei[[s]]))) next - cnames_s = setdiff(cnames, s) - - # Let's try self subsumption elimination first - if (length(cnames) == length(ei)) { - # cnames is the union of symbols in ei and ej. - # If length(cnames) is different from max(length(ei), length(ej)), then ei and ej can not be subsets of one another. - # Since j < i, length(ej) <= length(ei). +#' @export +print.CnfFormula = function(x, ...) { + if (isTRUE(x)) { + cat("CnfFormula: TRUE\n") + } else if (isFALSE(x)) { + cat("CnfFormula: FALSE\n") + } else { + cat("CnfFormula:\n (") + clauses = map_chr(x, function(clause) { + elements = map_chr(names(clause), function(sym) { + sprintf("%s \U2208 {%s}", sym, paste(clause[[sym]], collapse = ", ")) + }) + paste(elements, collapse = " | ") + }) + clause_paragraphs = map_chr(strwrap(clauses, exdent = 4, simplify = FALSE), paste, collapse = "\n ") + cat(paste0(paste(clause_paragraphs, collapse = ")\n & ("), ")\n")) + } + invisible(x) +} - # ej is usually smaller than ei, so often only ej can be a subset of ei. - # They may, however, have the same number of terms, in which case the reverse is also possible. - # Use 'c()' to drop attributes from ei here. - ei_without_s = ei[cnames_s] - do_sse = identical(cnames[cnames_s], c(ei_without_s)) - # if they have the same number of terms, ei could be a subset of ej. - # However, then we can not rely on the order of values in the union being correct. - do_sse_reverse = (!do_sse && (length(ei) == length(ej)) && - all(sapply(cnames_s, function(s2) all(ei[[s2]] %in% ej[[s2]])))) - if (do_sse_reverse) { - # ei is a subset of ej - # --> eliminate s from ej - ej[[s]] = NULL - new_entry = entries[[j]] = ej - dont_eliminate = j - nameshift = nameshift + 1 - } else if (do_sse) { - # ej is a subset of ei - # --> eliminate s from ei - new_entry = entries[[i]] = ei_without_s - dont_eliminate = i - } +format.CnfFormula = function(x, ...) { + if (isTRUE(x)) { + return("CnfFormula: T") + } else if (isFALSE(x)) { + return("CnfFormula: F") + } else { + return(sprintf("CnfFormula(%s)", length(x))) + } +} - if (do_sse || do_sse_reverse) { +#' @rdname CnfFormula +#' @export +as.CnfFormula = function(x) { + UseMethod("as.CnfFormula") +} - if (length(new_entry) == 1) { - # we have a unit clause now +#' @export +as.CnfFormula.default = function(x) { + stop("Cannot convert object to CnfFormula.") +} - # It could happen that we eliminate the entry further, in which - # case units[[]] would get stale, but then we return_false anyway. - units[[names(new_entry)]] = new_entry[[1]] - can_simplify = TRUE # do unit elimination all over again - ## TODO: we could probably make this more efficient by only unit-eliminating the terms that are new - } +#' @export +as.CnfFormula.logical = function(x) { + assert_flag(x) + return(structure( + x, + universe = attr(x, "universe"), + class = "CnfFormula" + )) +} - if (!length(new_entry)) { - # we have a contradiction now - # Maybe this could happen if we SS-Eliminate multiple symbols from a clause in a row. - return(return_false) - } +#' @export +as.CnfFormula.CnfAtom = function(x) { + as.CnfFormula(as.CnfClause(x)) +} - # What can have happened now is that the newly created element can eliminate other elements. - # If it can eliminate the current element i, that means it is a subset of ei, which only happens if ej\s is a subset of ei\s. However, in that case, we always want to keep element i. - # We therefore only need to loop up to i - 1. - # The loop is similar to the subsumption elimination loop; only in this case, we check if we can eliminate the elements that come before i, not like above where we check if we can eliminate i. +#' @export +as.CnfFormula.CnfClause = function(x) { + CnfFormula(list(x)) +} - # loop down from large to small, since then we can break once we find a clause with insufficient entries - for (k in rev(seq_len(i - 1))) { - if (k == dont_eliminate || eliminated[[k]]) next - ek = entries[[k]] - if (length(ek) < length(new_entry)) break # once we reached entries that are shorter than the new_entry, we won't find anything longer any more and we can break - if (all(cnames_s %in% names(ek)) && all(sapply(cnames_s, function(s2) all(new_entry[[s2]] %in% ek[[s2]])))) { - eliminated[[k]] = TRUE - } - } - next - } - } - # Hidden Subsumption Elimination - # - # We only do this if self subsumption elimination did not occur. - # - # We eliminate based on an implied clause (A - s | B - s) - # Since we will forget about this clause after this iteration, we have to eliminate all clauses with size larger or equal to ||A | B|| - 1 - # loop down from large to small, since then we can break once we find a clause with insufficient entries - for (k in rev(seq_along(entries))) { - if (k == i || k == j || eliminated[[k]]) next - ek = entries[[k]] - # all of cnames_s must be in ek, otherwise we can't eliminate - # since we are looping down from large to small ek, we can break once this is not the case - if (length(ek) < length(cnames) - 1) break - if (all(cnames_s %in% names(ek)) && all(sapply(cnames_s, function(s2) all(cunion[[s2]] %in% ek[[s2]])))) { - eliminated[[k]] = TRUE - } - } - } +#' @export +as.CnfFormula.CnfFormula = function(x) { + x +} - } +#' @export +as.logical.CnfFormula = function(x) { + if (is.logical(x)) { + return(unclass(x)) + } + return(NA) +} +#' @export +all.equal.CnfFormula = function(target, current, ...) { + if (is.logical(target) && is.logical(current)) { + # compare truth-values directly, even if they disagree on universe + # (since logical atoms sometimes have universe set to NULL) + if (identical(c(target), c(current))) { + return(TRUE) } - entries = entries[!eliminated] + return("target and current are both logicals but not equal") } - structure( - if (!length(entries)) TRUE else entries, - universe = universe, - class = "CnfFormula" - ) + if (is.logical(target) || is.logical(current)) { + return("target and current are not both logicals") + } + if (!inherits(current, "CnfFormula")) { + return("current is not a CnfFormula") + } + + normalize = function(formula) { + formula[] = lapply(formula, function(clause) { + clause[] = lapply(clause[order(names(clause))], sort) + clause + }) + # sort by symbol names, then by hash + # note we had to sort elements internally first before we can do this! + formula[] = formula[order(map_chr(target, function(clause) { + paste0(paste(names(clause), collapse = ".__."), digest::digest(c(clause), algo = "xxhash64")) + }))] + formula + } + target = normalize(target) + current = normalize(current) + + all.equal.list(target, current, ...) } +#' @rawNamespace if (getRversion() >= "4.3.0") S3method(chooseOpsMethod,CnfFormula) +chooseOpsMethod.CnfFormula <- function(x, y, mx, my, cl, reverse) TRUE + #' @export `&.CnfFormula` = function(e1, e2) { e1 = as.CnfFormula(e1) @@ -725,101 +319,6 @@ simplify_cnf = function(entries, universe) { simplify_cnf(unlist(distributed, recursive = FALSE), universe) } -#' @export -`&.CnfClause` = function(e1, e2) { - if (isFALSE(e1)) return(e1) - if (isFALSE(e2)) return(e2) - if (isTRUE(e1)) return(e2) - if (isTRUE(e2)) return(e1) - if (inherits(e2, "CnfAtom")) { - e2 = CnfClause(list(e2)) - } - if (inherits(e2, "CnfClause")) { - CnfFormula(list(e1, e2)) - } else { - # e2 is anything else -- go the lazy route - as.CnfFormula(e1) & as.CnfFormula(e2) - } -} - -#' @export -`|.CnfClause` = function(e1, e2) { - if (isFALSE(e1)) return(e2) - if (isFALSE(e2)) return(e1) - if (isTRUE(e1)) return(e1) - if (isTRUE(e2)) return(e2) - if (inherits(e2, "CnfAtom")) { - e2 = CnfClause(list(e2)) - } - if (inherits(e2, "CnfClause")) { - for (sym in names(e2)) { - e1[[sym]] = union(e1[[sym]], e2[[sym]]) - if (all(get(sym, attr(e1, "universe")) %in% e1[[sym]])) { - return(structure( - TRUE, - universe = attr(e1, "universe"), - class = "CnfClause" - )) - } - } - return(e1) - } - # e2 is anything else -- go the lazy route - as.CnfFormula(e1) | as.CnfFormula(e2) -} - -#' @export -`&.CnfAtom` = function(e1, e2) { - if (isFALSE(e1)) return(e1) - if (isFALSE(e2)) return(e2) - if (isTRUE(e1)) return(e2) - if (isTRUE(e2)) return(e1) - if (inherits(e2, "CnfAtom")) { - e2 = CnfClause(list(e2)) - } - if (inherits(e2, "CnfClause")) { - CnfFormula(list(CnfClause(list(e1)), e2)) - } else { - # e2 is anything else -- go the lazy route - as.CnfFormula(e1) & as.CnfFormula(e2) - } -} - -#' @export -`|.CnfAtom` = function(e1, e2) { - if (isFALSE(e1)) return(e2) - if (isFALSE(e2)) return(e1) - if (isTRUE(e1)) return(e1) - if (isTRUE(e2)) return(e2) - if (inherits(e2, "CnfAtom")) { - CnfClause(list(e1, e2)) - } else { - # e2 is anything else -- go the lazy route - as.CnfFormula(e1) | as.CnfFormula(e2) - } -} - -#' @export -`!.CnfAtom` = function(x) { - if (is.logical(x)) { - not_x = if (x) FALSE else TRUE # can't use '!' here... - attributes(not_x) = attributes(x) # keep class and universe - return(not_x) - } - structure( - list(symbol = x$symbol, values = setdiff(get(x$symbol, attr(x, "universe")), x$values)), - universe = attr(x, "universe"), - class = "CnfAtom" - ) -} - -#' @export -`!.CnfClause` = function(x) { - if (is.logical(x)) { - return(as.CnfClause(!unclass(x))) - } - !as.CnfFormula(x) -} #' @export `!.CnfFormula` = function(x) { @@ -838,341 +337,3 @@ simplify_cnf = function(entries, universe) { # can't Reduce(`|`, negated_formulae) here, since for this we'd have to register the `|` S3 method Reduce(function(x, y) x | y, negated_formulae) } - -#' @rdname CnfFormula -#' @export -as.CnfFormula = function(x) { - UseMethod("as.CnfFormula") -} - -#' @rdname CnfClause -#' @export -as.CnfClause = function(x) { - UseMethod("as.CnfClause") -} - -#' @rdname CnfAtom -#' @export -as.CnfAtom = function(x) { - UseMethod("as.CnfAtom") -} - -#' @rawNamespace if (getRversion() >= "4.3.0") S3method(chooseOpsMethod,CnfFormula) -chooseOpsMethod.CnfFormula <- function(x, y, mx, my, cl, reverse) TRUE -#' @rawNamespace if (getRversion() >= "4.3.0") S3method(chooseOpsMethod,CnfClause) -chooseOpsMethod.CnfClause <- function(x, y, mx, my, cl, reverse) TRUE -#' @rawNamespace if (getRversion() >= "4.3.0") S3method(chooseOpsMethod,CnfAtom) -chooseOpsMethod.CnfAtom <- function(x, y, mx, my, cl, reverse) TRUE - -#' @export -as.CnfFormula.logical = function(x) { - assert_flag(x) - return(structure( - x, - universe = NULL, - class = "CnfFormula" - )) -} - -#' @export -as.CnfFormula.CnfAtom = function(x) { - as.CnfFormula(CnfClause(list(x))) -} - -#' @export -as.CnfFormula.CnfClause = function(x) { - CnfFormula(list(x)) -} - -#' @export -as.CnfFormula.CnfFormula = function(x) { - x -} - -#' @export -as.CnfAtom.logical = function(x) { - assert_flag(x) - return(structure( - x, - universe = attr(x, "universe"), - class = "CnfAtom" - )) -} - -#' @export -as.CnfAtom.CnfAtom = function(x) { - x -} - -#' @export -as.CnfClause.logical = function(x) { - assert_flag(x) - return(structure( - x, - universe = attr(x, "universe"), - class = "CnfClause" - )) -} - -#' @export -as.CnfClause.CnfAtom = function(x) { - CnfClause(list(x)) -} - -#' @export -as.CnfClause.CnfClause = function(x) { - x -} - -#' @export -as.CnfFormula.logical = function(x) { - assert_flag(x) - structure( - x, - universe = attr(x, "universe"), - class = "CnfFormula" - ) -} - -#' @export -as.CnfAtom.default = function(x) { - stop("Cannot convert object to CnfAtom.") -} - -#' @export -as.CnfClause.default = function(x) { - stop("Cannot convert object to CnfClause.") -} - -#' @export -as.CnfFormula.default = function(x) { - stop("Cannot convert object to CnfFormula.") -} - -#' @export -as.logical.CnfFormula = function(x) { - if (is.logical(x)) { - return(unclass(x)) - } - return(NA) -} - -#' @export -as.logical.CnfClause = function(x) { - if (is.logical(x)) { - return(unclass(x)) - } - return(NA) -} - -#' @export -as.logical.CnfAtom = function(x) { - if (is.logical(x)) { - return(unclass(x)) - } - return(NA) -} - -#' @export -print.CnfUniverse = function(x, ...) { - if (!length(x)) { - cat("CnfUniverse (empty).\n") - return(invisible(x)) - } - cat("CnfUniverse with variables:\n") - for (var in names(x)) { - cat(sprintf(" %s: {%s}\n", var, paste(get(var, x), collapse = ", "))) - } - invisible(x) -} - -#' @export -print.CnfSymbol = function(x, ...) { - cat(sprintf("CnfSymbol '%s' with domain {%s}.\n", c(x), paste(get(x, attr(x, "universe")), collapse = ", "))) - invisible(x) -} - -#' @export -print.CnfAtom = function(x, ...) { - if (isTRUE(x)) { - cat("CnfAtom: \n") - } else if (isFALSE(x)) { - cat("CnfAtom: \n") - } else { - cat(sprintf("CnfAtom: %s \U2208 {%s}.\n", x$symbol, paste(x$values, collapse = ", "))) - } - invisible(x) -} - -#' @export -format.CnfAtom = function(x, ...) { - if (isTRUE(x)) { - return("CnfAtom(FALSE)") - } else if (isFALSE(x)) { - return("CnfAtom(TRUE)") - } else { - return(sprintf("CnfAtom(%s ...)", x$symbol)) - } -} - -#' @export -print.CnfClause = function(x, ...) { - if (isTRUE(x)) { - cat("CnfClause: TRUE\n") - } else if (isFALSE(x)) { - cat("CnfClause: FALSE\n") - } else { - cat("CnfClause:\n") - elements = map_chr(names(x), function(sym) { - sprintf("%s \U2208 {%s}", sym, paste(x[[sym]], collapse = ", ")) - }) - cat(strwrap(paste(elements, collapse = " | "), prefix = " "), sep = "\n") - } - invisible(x) -} - -#' @export -format.CnfClause = function(x, ...) { - if (isTRUE(x)) { - return("CnfClause(TRUE)") - } else if (isFALSE(x)) { - return("CnfClause(FALSE)") - } else { - return(sprintf("CnfClause(%s)", str_collapse(names(x), sep = "|", n = 2, ellipsis = ".."))) - } -} - -#' @export -format.CnfClause = function(x, ...) { - if (isTRUE(x)) { - return("") - } else if (isFALSE(x)) { - return("") - } else { - return("") - } -} - -#' @export -print.CnfFormula = function(x, ...) { - if (isTRUE(x)) { - cat("CnfFormula: TRUE\n") - } else if (isFALSE(x)) { - cat("CnfFormula: FALSE\n") - } else { - cat("CnfFormula:\n (") - clauses = map_chr(x, function(clause) { - elements = map_chr(names(clause), function(sym) { - sprintf("%s \U2208 {%s}", sym, paste(clause[[sym]], collapse = ", ")) - }) - paste(elements, collapse = " | ") - }) - clause_paragraphs = map_chr(strwrap(clauses, exdent = 4, simplify = FALSE), paste, collapse = "\n ") - cat(paste0(paste(clause_paragraphs, collapse = ")\n & ("), ")\n")) - } - invisible(x) -} - - -#' @export -all.equal.CnfAtom = function(target, current, ...) { - if (is.logical(target) && is.logical(current)) { - # compare truth-values directly, even if they disagree on universe - # (since logical atoms sometimes have universe set to NULL) - if (identical(c(target), c(current))) { - return(TRUE) - } - return("target and current are both logicals but not equal") - } - if (is.logical(target) || is.logical(current)) { - return("target and current are not both logicals") - } - if (!inherits(current, "CnfAtom")) { - return("current is not a CnfAtom") - } - target$values = sort(target$values) - current$values = sort(current$values) - all.equal.list(target, current, ...) -} - -#' @export -all.equal.CnfClause = function(target, current, ...) { - if (is.logical(target) && is.logical(current)) { - # compare truth-values directly, even if they disagree on universe - # (since logical atoms sometimes have universe set to NULL) - if (identical(c(target), c(current))) { - return(TRUE) - } - return("target and current are both logicals but not equal") - } - if (is.logical(target) || is.logical(current)) { - return("target and current are not both logicals") - } - if (!inherits(current, "CnfClause")) { - return("current is not a CnfClause") - } - # []-assign to preserve class and attributes - target[] = lapply(target[order(names(target))], sort) - current[] = lapply(current[order(names(current))], sort) - - all.equal.list(target, current, ...) -} - -#' @export -all.equal.CnfFormula = function(target, current, ...) { - if (is.logical(target) && is.logical(current)) { - # compare truth-values directly, even if they disagree on universe - # (since logical atoms sometimes have universe set to NULL) - if (identical(c(target), c(current))) { - return(TRUE) - } - return("target and current are both logicals but not equal") - } - if (is.logical(target) || is.logical(current)) { - return("target and current are not both logicals") - } - if (!inherits(current, "CnfFormula")) { - return("current is not a CnfFormula") - } - - normalize = function(formula) { - formula[] = lapply(formula, function(clause) { - clause[] = lapply(clause[order(names(clause))], sort) - clause - }) - # sort by symbol names, then by hash - # note we had to sort elements internally first before we can do this! - formula[] = formula[order(map_chr(target, function(clause) { - paste0(paste(names(clause), collapse = ".__."), digest::digest(c(clause), algo = "xxhash64")) - }))] - formula - } - target = normalize(target) - current = normalize(current) - - all.equal.list(target, current, ...) -} - - - -## to test: -# subsumption -# unit elimination -# unit elimination makes large clause smaller, leading to additional u.e. -# unit elimination makes large clause smaller, leading to subsumption - -# branch with totune is swallowed by single unbranch -# branch with totune is swallowed by multiple unbranch -# branches with totune can possibly lead to conflicts, but not always (multiple active inputs to unbranch, or mixed inputs to normal pipeops) -# branches with totune always lead to conflicts (multiple active inputs to unbranch, or mixed inputs to normal pipeops, or choice between both) -# can we recognize that a certain choice would lead to a conflict, making only other choices possible? - -# why does this blow up? -# - -# profvis::profvis(replicate(3000, { !!(((u$A %among% "T" | u$B %among% "F") & (u$A %among% "F" | u$C %among% "T") & (u$B %among% "T" | u$C %among% "F"))) ; NULL }) -> ., simplify = FALSE) - -# This is because we don't eliminate (C | A) & (!C | B) & (B | A) by removing (B | A) -# so, if clause X and clause Y have a symbol in common where the values are disjoint, the disjunction of the rest is implied? - - diff --git a/R/CnfFormula_simplify.R b/R/CnfFormula_simplify.R new file mode 100644 index 000000000..e4ad34330 --- /dev/null +++ b/R/CnfFormula_simplify.R @@ -0,0 +1,217 @@ + + + + + +simplify_cnf = function(entries, universe) { + return_false = structure( + FALSE, + universe = universe, + class = "CnfFormula" + ) + + # can we do unit elimination? + # if we are already TRUE or FALSE no simplification is necessary + # this only works if there actually are units. + can_simplify = !is.logical(entries) + # likewise, if there is only one clause left, no simplification is necessary. + + units = list() + + while (can_simplify && length(entries) > 1) { + # we do the following until we are sure there are no more simplifications to be made. + # this is the case if we have not meaningfully simplified anything in the last iteration. + can_simplify = FALSE + # sort clauses by length, since (1) length-1-clauses are special, and (2) short clauses can only ever subsume longer ones + entries = entries[order(lengths(entries))] + # Let sum(A) be the symbols in clause A, and val(A, s) be the values of symbol s admitted in clause A. + if (any(lengths(entries) == 1)) { + for (i in seq_along(entries)) { + ei = entries[[i]] + # If |sym(A)| == 1, sym(A) == {s} and s is in sym(B), then val(B, s) <- intersect(val(A, s), val(B, s)) ("unit propagation") + # units is a named list of symbols in size-one-clauses, together with their values. + # We iterate over all symbols in ei that are also in units, and intersect their values. + for (unit_symbol in intersect(names(ei), names(units))) { + length_before_ei = length(ei[[unit_symbol]]) + length_before_unit = length(units[[unit_symbol]]) + intersection = intersect(units[[unit_symbol]], ei[[unit_symbol]]) + ei[[unit_symbol]] = intersection + if (length(ei) == 1 && length(intersection) != length_before_unit) { + # we made a unit shorter, this means we need to simplify the entry from which units[[unit_symbol]] came + can_simplify = TRUE + } + if (!length(ei[[unit_symbol]])) { + ei[[unit_symbol]] = NULL + } + if (!length(ei)) { + return(return_false) + } + if (length(intersection) != length_before_ei) { + # need to store changed ei entry only if its length changed; otherwise we know the intersection did not do anything. + entries[[i]] = ei + } + } + if (length(ei) == 1) { + # even if names(ei) is already in units, at this point ei[[1]] is the intersection of the values + units[[names(ei)]] = ei[[1]] + } + } + if (can_simplify) next + } + + entries = entries[order(lengths(entries))] # removing units may have changed the order + eliminated = logical(length(entries)) + for (i in seq_along(entries)) { + if (eliminated[[i]]) next # can only happen if we do the hidden subsumption elimination, which searches forward + ei = entries[[i]] + # If sym(A) is a subset of sym(B) and for each s in sym(A), val(A, s) is a subset of val(B, s), then A implies B, so B can be removed ("subsumption elimination"). + for (j in seq_len(i - 1)) { + if (eliminated[[j]]) next + ej = entries[[j]] + name_overlap = names(ej) %in% names(ei) + if (all(name_overlap) && all(sapply(names(ej), function(s) all(ej[[s]] %in% ei[[s]])))) { + # can't do entries[[i]] = NULL, since we are iterating over entries; the entries[[i]] would break. + eliminated[[i]] = TRUE + break + } + # simple self subsumption and hidden subsumption elimination + # HSE: + # if s is in sym(A) and sym(B), and val(A, s) and val(B, s) are disjoint, then (A - s | B - s) is implied, + # and all superset clauses of (A - s | B - s) can be removed. + # we could also do this for higher order terms, intersection over X of val(X, s) == 0 etc., but this gets more complex. + # tbh, I am not sure if this is actually worth it + # SSE: If val(A, s) and val(B, s) are disjoint, and A - s is a subset of B - s, then A & B <=> A & (B - s) + + which_name_overlap = which(name_overlap) + # - build the union of values of overlapping symbols + # - in the innerloop we will check that most of this is a subset of any other clause + # - "most of" here means: all but the one symbol s where the values are disjoint + # - use delayedAssign to avoid computation if there is no overlap with empty intersect + delayedAssign("cnames", union(names(ei), names(ej))) + + # Putting ei[[s2]] first on purpose, since union() preserves the order of the first argument. + # If and only if ej[-s] is a subset of ei[-s], then cunion[-s] will be the same as ei[-s]. + delayedAssign("cunion", sapply(cnames, function(s2) union(ei[[s2]], ej[[s2]]), simplify = FALSE)) + + nameshift = 0 # in case we eliminate names from ej, we need to shift the indices for later loops iterations + for (no in which_name_overlap) { + s = names(ej)[[no - nameshift]] + # intersection is not 0 --> try next one + if (length(intersect(ej[[s]], ei[[s]]))) next + cnames_s = setdiff(cnames, s) + + # Let's try self subsumption elimination first + if (length(cnames) == length(ei)) { + # cnames is the union of symbols in ei and ej. + # If length(cnames) is different from max(length(ei), length(ej)), then ei and ej can not be subsets of one another. + # Since j < i, length(ej) <= length(ei). + + # ej is usually smaller than ei, so often only ej can be a subset of ei. + # They may, however, have the same number of terms, in which case the reverse is also possible. + # Use 'c()' to drop attributes from ei here. + ei_without_s = ei[cnames_s] + do_sse = identical(cnames[cnames_s], c(ei_without_s)) + # if they have the same number of terms, ei could be a subset of ej. + # However, then we can not rely on the order of values in the union being correct. + do_sse_reverse = (!do_sse && (length(ei) == length(ej)) && + all(sapply(cnames_s, function(s2) all(ei[[s2]] %in% ej[[s2]])))) + if (do_sse_reverse) { + # ei is a subset of ej + # --> eliminate s from ej + ej[[s]] = NULL + new_entry = entries[[j]] = ej + dont_eliminate = j + nameshift = nameshift + 1 + } else if (do_sse) { + # ej is a subset of ei + # --> eliminate s from ei + new_entry = entries[[i]] = ei_without_s + dont_eliminate = i + } + + if (do_sse || do_sse_reverse) { + + if (length(new_entry) == 1) { + # we have a unit clause now + + # It could happen that we eliminate the entry further, in which + # case units[[]] would get stale, but then we return_false anyway. + units[[names(new_entry)]] = new_entry[[1]] + can_simplify = TRUE # do unit elimination all over again + ## TODO: we could probably make this more efficient by only unit-eliminating the terms that are new + } + + if (!length(new_entry)) { + # we have a contradiction now + # Maybe this could happen if we SS-Eliminate multiple symbols from a clause in a row. + return(return_false) + } + + # What can have happened now is that the newly created element can eliminate other elements. + # If it can eliminate the current element i, that means it is a subset of ei, which only happens if ej\s is a subset of ei\s. However, in that case, we always want to keep element i. + # We therefore only need to loop up to i - 1. + # The loop is similar to the subsumption elimination loop; only in this case, we check if we can eliminate the elements that come before i, not like above where we check if we can eliminate i. + + # loop down from large to small, since then we can break once we find a clause with insufficient entries + for (k in rev(seq_len(i - 1))) { + if (k == dont_eliminate || eliminated[[k]]) next + ek = entries[[k]] + if (length(ek) < length(new_entry)) break # once we reached entries that are shorter than the new_entry, we won't find anything longer any more and we can break + if (all(cnames_s %in% names(ek)) && all(sapply(cnames_s, function(s2) all(new_entry[[s2]] %in% ek[[s2]])))) { + eliminated[[k]] = TRUE + } + } + next + } + } + # Hidden Subsumption Elimination + # + # We only do this if self subsumption elimination did not occur. + # + # We eliminate based on an implied clause (A - s | B - s) + # Since we will forget about this clause after this iteration, we have to eliminate all clauses with size larger or equal to ||A | B|| - 1 + # loop down from large to small, since then we can break once we find a clause with insufficient entries + for (k in rev(seq_along(entries))) { + if (k == i || k == j || eliminated[[k]]) next + ek = entries[[k]] + # all of cnames_s must be in ek, otherwise we can't eliminate + # since we are looping down from large to small ek, we can break once this is not the case + if (length(ek) < length(cnames) - 1) break + if (all(cnames_s %in% names(ek)) && all(sapply(cnames_s, function(s2) all(cunion[[s2]] %in% ek[[s2]])))) { + eliminated[[k]] = TRUE + } + } + } + + } + + } + entries = entries[!eliminated] + } + structure( + if (!length(entries)) TRUE else entries, + universe = universe, + class = "CnfFormula" + ) +} + + +## to test: +# subsumption +# unit elimination +# unit elimination makes large clause smaller, leading to additional u.e. +# unit elimination makes large clause smaller, leading to subsumption + +# branch with totune is swallowed by single unbranch +# branch with totune is swallowed by multiple unbranch +# branches with totune can possibly lead to conflicts, but not always (multiple active inputs to unbranch, or mixed inputs to normal pipeops) +# branches with totune always lead to conflicts (multiple active inputs to unbranch, or mixed inputs to normal pipeops, or choice between both) +# can we recognize that a certain choice would lead to a conflict, making only other choices possible? + +# why does this blow up? +# + +# profvis::profvis(replicate(3000, { !!(((u$A %among% "T" | u$B %among% "F") & (u$A %among% "F" | u$C %among% "T") & (u$B %among% "T" | u$C %among% "F"))) ; NULL }) -> ., simplify = FALSE) + +# This is because we don't eliminate (C | A) & (!C | B) & (B | A) by removing (B | A) +# so, if clause X and clause Y have a symbol in common where the values are disjoint, the disjunction of the rest is implied? diff --git a/R/CnfSymbol.R b/R/CnfSymbol.R new file mode 100644 index 000000000..aef77f005 --- /dev/null +++ b/R/CnfSymbol.R @@ -0,0 +1,64 @@ + +# We represent symbols through a name and a pointer to their universe. +# We only allow operations between symbols that are in the same universe. +#' @title Symbols for CNF Formulas +#' +#' @description +#' Representation of Symbols used in CNF formulas. Symbols have a name and a +#' domain (a set of possible values), and are stored in a [`CnfUniverse`]. +#' +#' Once created, it is currently not intended to modify or delete symbols. +#' +#' Symbols can be used in CNF formulas by creating [`CnfAtom`] objects, either +#' by using the `%among%` operator or by using the [`CnfAtom()`] constructor +#' explicitly. +#' +#' This is part of the CNF representation tooling, which is currently considered +#' experimental; it is for internal use. +#' +#' @param universe ([`CnfUniverse`]) \cr +#' The universe in which the symbol is defined. +#' @param name (`character(1)`) \cr +#' The name of the symbol. +#' @param domain (`character`) \cr +#' The domain, i.e. the set of possible values for the symbol. +#' Must not be empty. +#' @return A new `CnfSymbol` object. +#' @examples +#' u = CnfUniverse() +#' X = CnfSymbol(u, "X", c("a", "b", "c")) +#' +#' # Use symbols to create CnfAtom objects +#' X %among% c("a", "b") +#' X %among% "a" +#' X %among% character(0) +#' X %among% c("a", "b", "c") +#' +#' @family CNF representation objects +#' @keywords internal +#' @export +CnfSymbol = function(universe, name, domain) { + assert_class(universe, "CnfUniverse") + assert_string(name) + assert_character(domain, any.missing = FALSE, min.len = 1) + if (exists(name, universe)) { + stopf("Variable '%s' already exists in the universe.", name) + } + assign(name, domain, universe) + structure( + name, + universe = universe, + class = "CnfSymbol" + ) +} + +#' @export +print.CnfSymbol = function(x, ...) { + cat(sprintf("CnfSymbol '%s' with domain {%s}.\n", c(x), paste(attr(x, "universe")[[x]], collapse = ", "))) + invisible(x) +} + +#' @export +format.CnfSymbol = function(x, ...) { + sprintf("CnfSymbol(%s)", c(x)) +} diff --git a/R/CnfUniverse.R b/R/CnfUniverse.R new file mode 100644 index 000000000..1108882b3 --- /dev/null +++ b/R/CnfUniverse.R @@ -0,0 +1,64 @@ +#' @title Symbol Table for CNF Formulas +#' +#' @description +#' A symbol table for CNF formulas. The `CnfUniverse` is a by-reference object +#' that stores the domain of each symbol. Symbols are created with [`CnfSymbol()`] +#' and can be retrieved with `$`. +#' Using `[[` retrieves a given symbol's domain. +#' +#' It is only possible to combine symbols from the same (identical) universe. +#' +#' This is part of the CNF representation tooling, which is currently considered +#' experimental; it is for internal use. +#' +#' @return A new `CnfUniverse` object. +#' @examples +#' u = CnfUniverse() +#' X = CnfSymbol(u, "X", c("a", "b", "c")) +#' Y = CnfSymbol(u, "Y", c("d", "e", "f")) +#' +#' u$X +#' u[["Y"]] +#' +#' X %among% c("a", "d") +#' u$X %among% c("a", "d") +#' Y %among% c("d", "e", "f") +#' Y %among% character(0) +#' +#' u$X %among% "a" | u$Y %among% "d" +#' @family CNF representation objects +#' @keywords internal +#' @export +CnfUniverse = function() structure(new.env(parent = emptyenv()), class = "CnfUniverse") + +# We allow retrieving symbols from the universe by name. +#' @export +`$.CnfUniverse` = function(universe, name) { + assert_string(name) + if (!exists(name, universe)) { + stopf("Variable '%s' does not exist in the universe.", name) + } + structure( + name, + universe = universe, + class = "CnfSymbol" + ) +} + +#' @export +print.CnfUniverse = function(x, ...) { + if (!length(x)) { + cat("CnfUniverse (empty).\n") + return(invisible(x)) + } + cat("CnfUniverse with variables:\n") + for (var in names(x)) { + cat(sprintf(" %s: {%s}\n", var, paste(get(var, x), collapse = ", "))) + } + invisible(x) +} + +#' @export +format.CnfUniverse = function(x, ...) { + return(sprintf("CnfUniverse(%s)", length(x))) +} diff --git a/attic/minibenchmarks.R b/attic/minibenchmarks.R new file mode 100644 index 000000000..ab55dee4f --- /dev/null +++ b/attic/minibenchmarks.R @@ -0,0 +1,111 @@ + + + + + + + +library("ggplot2") +library("microbenchmark") +library("data.table") + +bm_listaccess <- function() { + env <- new.env() + env$a <- 1 + env$b <- "x" + env$c <- 1:10 + env$d <- list(1, 2, 3) + env$e <- data.frame(x = 1:10, y = 11:20) + env$f <- function(x) x + 1 + env$g <- FALSE + + + lst <- as.list(env) + + indirect <- c(1, 3, 7) + indirect_int <- c(1L, 3L, 7L) + + microbenchmark(times = 1000L, + env_dollar = { env$a; env$c; env$g }, + env_dollar_set = { env$a <- 2; env$c <- 2:11; env$g <- TRUE; env$a <- 1; env$c <- 1:10; env$g <- FALSE }, + env_bracket = { env[["a"]]; env[["c"]]; env[["g"]] }, + env_bracket_set = { env[["a"]] <- 2; env[["c"]] <- 2:11; env[["g"]] <- TRUE; env[["a"]] <- 1; env[["c"]] <- 1:10; env[["g"]] <- FALSE }, + env_get = { get("a", env); get("c", env); get("g", env) }, + env_assign = { assign("a", 2, env); assign("c", 2:11, env); assign("g", TRUE, env); assign("a", 1, env); assign("c", 1:10, env); assign("g", FALSE, env) }, + lst_dollar = { lst$a; lst$c; lst$g }, + lst_dollar_set = { lst$a <- 2; lst$c <- 2:11; lst$g <- TRUE; lst$a <- 1; lst$c <- 1:10; lst$g <- FALSE }, + lst_bracket = { lst[["a"]]; lst[["c"]]; lst[["g"]] }, + lst_bracket_set = { lst[["a"]] <- 2; lst[["c"]] <- 2:11; lst[["g"]] <- TRUE; lst[["a"]] <- 1; lst[["c"]] <- 1:10; lst[["g"]] <- FALSE }, + lst_bracket_int = { lst[[1]]; lst[[3]]; lst[[7]] }, + lst_bracket_int_set = { lst[[1]] <- 2; lst[[3]] <- 2:11; lst[[7]] <- TRUE; lst[[1]] <- 1; lst[[3]] <- 1:10; lst[[7]] <- FALSE }, + lst_indirect = { lst[[indirect[1]]]; lst[[indirect[2]]]; lst[[indirect[3]]] }, + lst_indirect_set = { lst[[indirect[1]]] <- 2; lst[[indirect[2]]] <- 2:11; lst[[indirect[3]]] <- TRUE; lst[[indirect[1]]] <- 1; lst[[indirect[2]]] <- 1:10; lst[[indirect[3]]] <- FALSE }, + lst_indirect_int = { lst[[indirect_int[1]]]; lst[[indirect_int[2]]]; lst[[indirect_int[3]]] }, + lst_indirect_int_set = { lst[[indirect_int[1]]] <- 2; lst[[indirect_int[2]]] <- 2:11; lst[[indirect_int[3]]] <- TRUE; lst[[indirect_int[1]]] <- 1; lst[[indirect_int[2]]] <- 1:10; lst[[indirect_int[3]]] <- FALSE } + ) +} + + + +bmr <- bm_listaccess() + + +autoplot(bmr) + +bmrt <- as.data.table(bmr)[, .(mean = mean(time), median = median(time), mean_robust = mean(time, trim = 0.1)), by = expr][order(mean_robust)] + +par(mar = c(8, 4, 4, 2) + 0.1) +matplot(bmrt[, -1], type = "b", pch = 1, xaxt = "n", ylab = "Values", xlab = "expr", main = "List access benchmarks", col = seq_along(bmrt[, -1])) +legend("bottomright", legend = colnames(bmrt)[-1], col = seq_along(bmrt[, -1]), pch = 1, lty = 1) +axis(1, at = seq_along(bmrt$expr), labels = bmrt$expr, las = 2) + +# GET: (lst_bracket_int, env_bracket) is faster than lst_bracket, which is faster than +# env_dollar, which is slightly faster than lst_indirect_(int), which is slightly faster than lst_dollar +# HUGE difference to: env_get +# SET: env_bracket slightly faster than lst_bracket_int, much faster than env_dollar|lst_bracket, which is slightly faster than lst(indirect), which is faster than lst_dollar, which is much faster than env_assign + +# -> envs are faster than named lists for setting; lists with numbers are the same (get) or almost the same (set) as envs +# -> don't use get() / assign() +# -> use brackets +# -> use integers for list access; list with names adds 25% +# -> indirect lst *set* makes barely any difference to named list + + + +bm_subsettest <- function() { + one <- c("elephant", "mouse", "tiger", "cat", "dog") + two <- c("cat", "dog", "mouse", "tiger") + three <- c("dog", "cat", "mouse", "tiger", "fish") + + microbenchmark(times = 1000L, + allin_one_two = { x1 <- all(one %in% two); x2 <- all(two %in% one) }, + allin_one_three = { x1 <- all(one %in% three); x2 <- all(three %in% one) }, + allin_two_three = { x1 <- all(two %in% three); x2 <- all(three %in% two) }, + lengthcmp_one_two = { lu <- length(unique(c(one, two))) ; x1 <- lu == length(two) ; x2 <- lu == length(one) }, + lengthcmp_one_three = { lu <- length(unique(c(one, three))) ; x1 <- lu == length(three) ; x2 <- lu == length(one) }, + lengthcmp_two_three = { lu <- length(unique(c(two, three))) ; x1 <- lu == length(three) ; x2 <- lu == length(two) }, + lengthcmp_union_one_two = { lu <- length(union(one, two)) ; x1 <- lu == length(two) ; x2 <- lu == length(one) }, + lengthcmp_union_one_three = { lu <- length(union(one, three)) ; x1 <- lu == length(three) ; x2 <- lu == length(one) }, + lengthcmp_union_two_three = { lu <- length(union(two, three)) ; x1 <- lu == length(three) ; x2 <- lu == length(two) } + ) +} + + +bmr <- bm_subsettest() + +autoplot(bmr) + +bmrt <- as.data.table(bmr)[, .(mean = mean(time), median = median(time), mean_robust = mean(time, trim = 0.1)), by = expr][order(mean_robust)] + +par(mar = c(8, 4, 4, 2) + 0.1) +matplot(bmrt[, -1], type = "b", pch = 1, xaxt = "n", ylab = "Values", xlab = "expr", main = "List access benchmarks", col = seq_along(bmrt[, -1])) +legend("bottomright", legend = colnames(bmrt)[-1], col = seq_along(bmrt[, -1]), pch = 1, lty = 1) +axis(1, at = seq_along(bmrt$expr), labels = bmrt$expr, las = 2) + +round(sweep(as.matrix(bmrt[, 2:4], rownames = bmrt[[1]]), 2, as.numeric(bmrt[1, 2:4]), "/"), 2) + +round(sweep(as.matrix(bmrt[, 2:4], rownames = bmrt[[1]]), 2, as.numeric(bmrt[5, 2:4]), "/"), 2) + +# length cmp is 28% slower than all (x %in% y) +# union is 2x slower than allin; adds 50% to length cmp +# From 16458409442f38685a16000f0cbf3eb2c98d40cd Mon Sep 17 00:00:00 2001 From: mb706 Date: Tue, 10 Sep 2024 20:09:47 +0200 Subject: [PATCH 22/87] cleaning up considerably --- DESCRIPTION | 5 +++ NAMESPACE | 6 ++- R/CnfAtom.R | 70 +++++++++++++-------------------- R/CnfClause.R | 88 ++++++++++++++++++++---------------------- R/CnfFormula.R | 68 ++++++++++++++++++-------------- attic/minibenchmarks.R | 83 +++++++++++++++++++++++++++++++++++++++ man/CnfAtom.Rd | 4 +- man/CnfClause.Rd | 18 ++++++++- man/CnfFormula.Rd | 9 ++++- man/CnfSymbol.Rd | 4 +- man/CnfUniverse.Rd | 5 ++- 11 files changed, 233 insertions(+), 127 deletions(-) diff --git a/DESCRIPTION b/DESCRIPTION index cf7be202d..a856345cc 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -98,7 +98,12 @@ Roxygen: list(markdown = TRUE, r6 = FALSE) RoxygenNote: 7.3.2 VignetteBuilder: knitr Collate: + 'CnfAtom.R' + 'CnfClause.R' 'CnfFormula.R' + 'CnfFormula_simplify.R' + 'CnfSymbol.R' + 'CnfUniverse.R' 'Graph.R' 'GraphLearner.R' 'mlr_pipeops.R' diff --git a/NAMESPACE b/NAMESPACE index 736cd7a51..0450995c3 100644 --- a/NAMESPACE +++ b/NAMESPACE @@ -9,7 +9,6 @@ S3method("%among%",default) S3method("&",CnfAtom) S3method("&",CnfClause) S3method("&",CnfFormula) -S3method("[[",CnfUniverse) S3method("|",CnfAtom) S3method("|",CnfClause) S3method("|",CnfFormula) @@ -30,6 +29,8 @@ S3method(as.CnfFormula,default) S3method(as.CnfFormula,logical) S3method(as.data.table,DictionaryGraph) S3method(as.data.table,DictionaryPipeOp) +S3method(as.list,CnfClause) +S3method(as.list,CnfFormula) S3method(as.logical,CnfAtom) S3method(as.logical,CnfClause) S3method(as.logical,CnfFormula) @@ -44,6 +45,9 @@ S3method(as_pipeop,PipeOp) S3method(as_pipeop,default) S3method(format,CnfAtom) S3method(format,CnfClause) +S3method(format,CnfFormula) +S3method(format,CnfSymbol) +S3method(format,CnfUniverse) S3method(marshal_model,Multiplicity) S3method(marshal_model,graph_learner_model) S3method(marshal_model,pipeop_impute_learner_state) diff --git a/R/CnfAtom.R b/R/CnfAtom.R index cc6af0ddd..428d00a14 100644 --- a/R/CnfAtom.R +++ b/R/CnfAtom.R @@ -30,6 +30,8 @@ #' We would have preferred to overload the `%in%` operator, but this is currently #' not easily possible in R. We therefore created the `%among%` operator. #' +#' The internal representation of a `CnfAtom` may change in the future. +#' #' @param symbol ([`CnfSymbol`]) \cr #' The symbol to which the atom refers. #' @param values (`character`) \cr @@ -66,27 +68,20 @@ #' @export CnfAtom = function(symbol, values) { assert_class(symbol, "CnfSymbol") - domain = get(symbol, attr(symbol, "universe")) + domain = attr(symbol, "universe")[[symbol]] assert_subset(values, domain) if (all(domain %in% values)) { - structure( - TRUE, - universe = attr(symbol, "universe"), - class = "CnfAtom" - ) + entry = TRUE } else if (length(values) == 0) { - structure( - FALSE, - universe = attr(symbol, "universe"), - class = "CnfAtom" - ) + entry = FALSE } else { - structure( - list(symbol = c(symbol), values = unique(values)), - universe = attr(symbol, "universe"), - class = "CnfAtom" - ) + entry = list(symbol = c(symbol), values = unique(values)) } + structure( + entry, + universe = attr(symbol, "universe"), + class = "CnfAtom" + ) } #' @export @@ -145,11 +140,11 @@ as.CnfAtom.default = function(x) { #' @export as.CnfAtom.logical = function(x) { assert_flag(x) - return(structure( + structure( x, universe = attr(x, "universe"), class = "CnfAtom" - )) + ) } #' @export @@ -191,44 +186,31 @@ chooseOpsMethod.CnfAtom <- function(x, y, mx, my, cl, reverse) TRUE #' @export `&.CnfAtom` = function(e1, e2) { - if (isFALSE(e1)) return(e1) - if (isFALSE(e2)) return(e2) - if (isTRUE(e1)) return(e2) - if (isTRUE(e2)) return(e1) - if (inherits(e2, "CnfAtom")) { - e2 = CnfClause(list(e2)) - } - if (inherits(e2, "CnfClause")) { - CnfFormula(list(CnfClause(list(e1)), e2)) - } else { - # e2 is anything else -- go the lazy route - as.CnfFormula(e1) & as.CnfFormula(e2) - } + # Will return a CnfFormula, so we can just delegate to there. + # `&.CnfFormula` handles conversion. + `&.CnfFormula`(e1, e2) } #' @export `|.CnfAtom` = function(e1, e2) { - if (isFALSE(e1)) return(e2) - if (isFALSE(e2)) return(e1) - if (isTRUE(e1)) return(e1) - if (isTRUE(e2)) return(e2) - if (inherits(e2, "CnfAtom")) { - CnfClause(list(e1, e2)) - } else { - # e2 is anything else -- go the lazy route - as.CnfFormula(e1) | as.CnfFormula(e2) + if (inherits(e2, "CnfFormula")) { + # `|.CnfFormula` handles conversion + return(`|.CnfFormula`(e1, e2)) + } else if (is.logical(e2) || inherits(e2, "CnfAtom")) { + if (isFALSE(e1) || isTRUE(e2)) return(as.CnfAtom(e2)) + if (isFALSE(e2) || isTRUE(e1)) return(e1) } + # either two proper CnfAtoms, or e2 is a CnfClause. + CnfClause(list(e1, e2)) } #' @export `!.CnfAtom` = function(x) { if (is.logical(x)) { - not_x = if (x) FALSE else TRUE # can't use '!' here... - attributes(not_x) = attributes(x) # keep class and universe - return(not_x) + return(as.CnfAtom(!unclass(x))) } structure( - list(symbol = x$symbol, values = setdiff(get(x$symbol, attr(x, "universe")), x$values)), + list(symbol = x$symbol, values = setdiff(attr(x, "universe")[[x$symbol]], x$values)), universe = attr(x, "universe"), class = "CnfAtom" ) diff --git a/R/CnfClause.R b/R/CnfClause.R index e42b8f002..e6cd496ac 100644 --- a/R/CnfClause.R +++ b/R/CnfClause.R @@ -13,6 +13,11 @@ #' `CnfClause` objects can be constructed explicitly, using the `CnfClause()` constructor, #' or implicitly, by using the `|` operator on [`CnfAtom`]s or other `CnfClause` objects. #' +#' `CnfClause` objects which are not tautologies or contradictions are named lists; +#' the value ranges of each symbol can be accessed using `[[`. +#' However, to get a list of [`CnfAtom`] objects, use `as.list()`. +#' Note that the simplified form of a clause containing a contradiction is the empty list. +#' #' Upon construction, the `CnfClause` is simplified by (1) removing contradictions, (2) unifying #' atoms that refer to the same symbol, and (3) evaluating to `TRUE` if any atom is `TRUE`. #' Note that the order of atoms in a clause is not preserved. @@ -32,6 +37,12 @@ #' This is part of the CNF representation tooling, which is currently considered #' experimental; it is for internal use. #' +#' @details +#' We are undecided whether it is a better idea to have `as.list()` return a named list +#' or an unnamed one. Calling `as.list()` on a `CnfClause` with a tautology returns +#' a tautology-atom, which does not have a name. We therefore decided to return an +#' unnamed list in general. However, this behaviour may change in the future. +#' #' @param atoms (`list` of ([`CnfAtom`] | `CnfClause`)) \cr #' A list of [`CnfAtom`] or other `CnfClause` objects. #' The clause represents the disjunction of these atoms. @@ -45,7 +56,10 @@ #' Y = CnfSymbol(u, "Y", c("d", "e", "f")) #' #' CnfClause(list(X %among% c("a", "b"), Y %among% c("d", "e"))) -#' X %among% c("a", "b") | Y %among% c("d", "e") +#' cls = X %among% c("a", "b") | Y %among% c("d", "e") +#' cls +#' +#' as.list(cls) #' #' as.CnfClause(X %among% c("a", "b")) #' @@ -70,13 +84,8 @@ #' @export CnfClause = function(atoms) { assert_list(atoms, types = c("CnfAtom", "CnfClause")) - if (!length(atoms)) { - return(structure( - FALSE, - universe = NULL, - class = "CnfClause" - )) - } + if (!length(atoms)) return(as.CnfClause(FALSE)) + entries = list() universe = attr(atoms[[1]], "universe") for (a in atoms) { @@ -91,20 +100,21 @@ CnfClause = function(atoms) { next } if (inherits(a, "CnfAtom")) { - entries[[a$symbol]] = union(entries[[a$symbol]], a$values) - if (all(get(a$symbol, universe) %in% entries[[a$symbol]])) { + entries[[a$symbol]] = unique(c(entries[[a$symbol]], a$values)) + if (all(universe[[a$symbol]] %in% entries[[a$symbol]])) { entries = TRUE break } } else { # union with another CnfClause objects for (sym in names(a)) { - entries[[sym]] = union(entries[[sym]], a[[sym]]) - if (all(get(sym, universe) %in% entries[[sym]])) { + entries[[sym]] = unique(c(entries[[sym]], a[[sym]])) + if (all(universe[[sym]] %in% entries[[sym]])) { entries = TRUE break } } + if (identical(entries, TRUE)) break } } structure( @@ -172,6 +182,16 @@ as.CnfClause.CnfClause = function(x) { x } +#' @export +as.list.CnfClause = function(x) { + if (isFALSE(x)) return(list()) + x = unclass(x) + if (isTRUE(x)) return(as.CnfAtom(x)) + lapply(names(x), function(sym) { + structure(list(symbol = sym, values = x[[sym]]), universe = attr(x, "universe"), class = "CnfAtom") + }) +} + #' @export as.logical.CnfClause = function(x) { if (is.logical(x)) { @@ -213,48 +233,22 @@ chooseOpsMethod.CnfClause <- function(x, y, mx, my, cl, reverse) TRUE #' @export `&.CnfClause` = function(e1, e2) { - if (isFALSE(e1)) return(e1) - if (isFALSE(e2)) return(e2) - if (isTRUE(e1)) return(e2) - if (isTRUE(e2)) return(e1) - if (inherits(e2, "CnfAtom")) { - e2 = CnfClause(list(e2)) - } - if (inherits(e2, "CnfClause")) { - CnfFormula(list(e1, e2)) - } else { - # e2 is anything else -- go the lazy route - as.CnfFormula(e1) & as.CnfFormula(e2) - } + # Will return a CnfFormula, so we can just delegate to there. + # `&.CnfFormula` handles conversion. + `&.CnfFormula`(e1, e2) } #' @export `|.CnfClause` = function(e1, e2) { - if (isFALSE(e1)) return(e2) - if (isFALSE(e2)) return(e1) - if (isTRUE(e1)) return(e1) - if (isTRUE(e2)) return(e2) - if (inherits(e2, "CnfAtom")) { - e2 = CnfClause(list(e2)) + if (inherits(e2, "CnfFormula")) { + # `|.CnfFormula` handles conversion + return(`|.CnfFormula`(e1, e2)) } - if (inherits(e2, "CnfClause")) { - for (sym in names(e2)) { - e1[[sym]] = union(e1[[sym]], e2[[sym]]) - if (all(get(sym, attr(e1, "universe")) %in% e1[[sym]])) { - return(structure( - TRUE, - universe = attr(e1, "universe"), - class = "CnfClause" - )) - } - } - return(e1) - } - # e2 is anything else -- go the lazy route - as.CnfFormula(e1) | as.CnfFormula(e2) + if (isFALSE(e1) || isTRUE(e2)) return(as.CnfClause(e2)) + if (isFALSE(e2) || isTRUE(e1)) return(e1) + CnfClause(list(e1, e2)) } - #' @export `!.CnfClause` = function(x) { if (is.logical(x)) { diff --git a/R/CnfFormula.R b/R/CnfFormula.R index 281547023..837e70760 100644 --- a/R/CnfFormula.R +++ b/R/CnfFormula.R @@ -28,6 +28,9 @@ #' `CnfFormula` objects can be constructed explicitly, using the `CnfFormula()` constructor, #' or implicitly, by using the `&` operator on [`CnfAtom`]s, [`CnfClause`]s, or other `CnfFormula` objects. #' +#' To get individual clauses from a formula, `[[` should not be used; instead, use `as.list()`. +#' Note that the simplified form of a formula containing a tautology is the empty list. +#' #' Upon construction, the `CnfFormula` is simplified by using various heuristics. #' This includes unit propagation, subsumption elimination, and self/hidden subsumption elimination #' (see examples). @@ -61,8 +64,12 @@ #' Y = CnfSymbol(u, "Y", c("d", "e", "f")) #' Z = CnfSymbol(u, "Z", c("g", "h", "i")) #' -#' (X %among% c("a", "b") | Y %among% c("d", "e")) & +#' frm = (X %among% c("a", "b") | Y %among% c("d", "e")) & #' Z %among% c("g", "h") +#' frm +#' +#' # retrieve individual clauses +#' as.list(frm) #' #' # Negation of a formula #' # Note the parentheses, otherwise `!` would be applied to the first clause only. @@ -119,15 +126,11 @@ #' @export CnfFormula = function(clauses) { assert_list(clauses, types = c("CnfClause", "CnfFormula")) - if (!length(clauses)) { - return(structure( - TRUE, - universe = NULL, - class = "CnfFormula" - )) - } - universe = attr(clauses[[1]], "universe") + if (!length(clauses)) return(as.CnfFormula(TRUE)) + entries = list() + other_entries = list() + universe = attr(clauses[[1]], "universe") for (cl in clauses) { if (isFALSE(cl)) { entries = FALSE @@ -141,15 +144,18 @@ CnfFormula = function(clauses) { # universe; however, in that case we will break before coming here. stop("All clauses must be in the same universe.") } - attr(cl, "universe") = NULL + ## don't unclass() here, since we check the class in the next line! if (inherits(cl, "CnfClause")) { - entries[[length(entries) + 1]] = unclass(cl) + entries[[length(entries) + 1]] = c(cl) } else { # union with another CnfFormula object - entries = c(entries, unclass(cl)) + other_entries[[length(other_entries) + 1]] = cl } } + if (length(other_entries)) { + entries = c(entries, unlist(other_entries, recursive = FALSE)) + } simplify_cnf(entries, universe) } @@ -161,7 +167,7 @@ print.CnfFormula = function(x, ...) { cat("CnfFormula: FALSE\n") } else { cat("CnfFormula:\n (") - clauses = map_chr(x, function(clause) { + clauses = map_chr(unclass(x), function(clause) { elements = map_chr(names(clause), function(sym) { sprintf("%s \U2208 {%s}", sym, paste(clause[[sym]], collapse = ", ")) }) @@ -173,6 +179,7 @@ print.CnfFormula = function(x, ...) { invisible(x) } +#' @export format.CnfFormula = function(x, ...) { if (isTRUE(x)) { return("CnfFormula: T") @@ -219,6 +226,12 @@ as.CnfFormula.CnfFormula = function(x) { x } +#' @export +as.list.CnfFormula = function(x, ...) { + if (isTRUE(x)) return(list()) + lapply(unclass(x), structure, class = "CnfClause", universe = attr(x, "universe")) +} + #' @export as.logical.CnfFormula = function(x) { if (is.logical(x)) { @@ -245,13 +258,13 @@ all.equal.CnfFormula = function(target, current, ...) { } normalize = function(formula) { - formula[] = lapply(formula, function(clause) { + formula[] = lapply(unclass(formula), function(clause) { clause[] = lapply(clause[order(names(clause))], sort) clause }) # sort by symbol names, then by hash # note we had to sort elements internally first before we can do this! - formula[] = formula[order(map_chr(target, function(clause) { + formula[] = formula[order(map_chr(unclass(target), function(clause) { paste0(paste(names(clause), collapse = ".__."), digest::digest(c(clause), algo = "xxhash64")) }))] formula @@ -269,10 +282,8 @@ chooseOpsMethod.CnfFormula <- function(x, y, mx, my, cl, reverse) TRUE `&.CnfFormula` = function(e1, e2) { e1 = as.CnfFormula(e1) e2 = as.CnfFormula(e2) - if (isTRUE(e1)) return(e2) - if (isTRUE(e2)) return(e1) - if (isFALSE(e1)) return(e1) - if (isFALSE(e2)) return(e2) + if (isTRUE(e1) || isFALSE(e2)) return(e2) + if (isTRUE(e2) || isFALSE(e1)) return(e1) if (!identical(attr(e1, "universe"), attr(e2, "universe"))) { stop("Both formulas must be in the same universe.") } @@ -283,10 +294,8 @@ chooseOpsMethod.CnfFormula <- function(x, y, mx, my, cl, reverse) TRUE `|.CnfFormula` = function(e1, e2) { e1 = as.CnfFormula(e1) e2 = as.CnfFormula(e2) - if (isFALSE(e1)) return(e2) - if (isFALSE(e2)) return(e1) - if (isTRUE(e1)) return(e1) - if (isTRUE(e2)) return(e2) + if (isFALSE(e1) || isTRUE(e2)) return(e2) + if (isFALSE(e2) || isFALSE(e1)) return(e1) if (!identical(attr(e1, "universe"), attr(e2, "universe"))) { stop("Both formulas must be in the same universe.") } @@ -298,16 +307,16 @@ chooseOpsMethod.CnfFormula <- function(x, y, mx, my, cl, reverse) TRUE e2 = tmp } # distribute || into clauses - distributed = lapply(e1, function(e1_clause) { + distributed = lapply(unclass(e1), function(e1_clause) { eliminated = logical(length(e2)) for (i2 in seq_along(e2)) { e2_clause = e2[[i2]] for (sym in names(e1_clause)) { # add the symbols from e1_clause to e2_clause # (if e2_clause does not contain a symbol, it is added) - e2_clause[[sym]] = union(e1_clause[[sym]], e2_clause[[sym]]) + e2_clause[[sym]] = unique(c(e1_clause[[sym]], e2_clause[[sym]])) # faster than test_set_equal - if (all(get(sym, universe) %in% e2_clause[[sym]])) { + if (all(universe[[sym]] %in% e2_clause[[sym]])) { eliminated[[i2]] = TRUE break } @@ -322,12 +331,15 @@ chooseOpsMethod.CnfFormula <- function(x, y, mx, my, cl, reverse) TRUE #' @export `!.CnfFormula` = function(x) { + if (is.logical(x)) { + return(as.CnfFormula(!unclass(x))) + } universe = attr(x, "universe") - negated_formulae = lapply(x, function(clause) { + negated_formulae = lapply(unclass(x), function(clause) { CnfFormula(lapply(names(clause), function(sym) { # !CnfAtom(universe[[sym]], clause[[sym]]) structure( - list(setdiff(get(sym, universe), clause[[sym]])), + list(setdiff(universe[[sym]], clause[[sym]])), names = sym, universe = universe, class = "CnfClause" diff --git a/attic/minibenchmarks.R b/attic/minibenchmarks.R index ab55dee4f..be1345536 100644 --- a/attic/minibenchmarks.R +++ b/attic/minibenchmarks.R @@ -91,6 +91,8 @@ bm_subsettest <- function() { } + + bmr <- bm_subsettest() autoplot(bmr) @@ -109,3 +111,84 @@ round(sweep(as.matrix(bmrt[, 2:4], rownames = bmrt[[1]]), 2, as.numeric(bmrt[5, # length cmp is 28% slower than all (x %in% y) # union is 2x slower than allin; adds 50% to length cmp # + + +bm_extend_list <- function(times = 1) { + concatenating = list( + c("elephant", "mouse", "tiger", "cat", "dog"), + list(c("green", "blue", "purple"), c(1, 1, 1), 10:0), + c(1, 2, 3, 4, 5), + list(c(1, 2, 3), c("a", "b", "c"), c(1, 2, 3, 4, 5)) + ) + + concatenating <- rep(concatenating, times) + + microbenchmark( + expand = { + entries = list() + for (element in concatenating) { + if (is.list(element)) { + entries <- c(entries, element) + } else { + entries[[length(entries) + 1]] <- element + } + } + }, + unlist = { + entries = list() + for (element in concatenating) { + if (!is.list(element)) { + element <- list(element) + } + entries[[length(entries) + 1]] <- element + } + entries <- unlist(entries, recursive = FALSE) + } + ) +} + +bm_extend_list() +# unlist() is clearly slower + +bm_extend_list(10) + +bm_extend_list(100) +# unlist() is clearly faster + + + +bm_create_list <- function() { + names <- c("elephant", "mouse", "tiger", "cat", "dog", "mouse") + microbenchmark(times = 1000, + list_plain = { + result = list() + for (n in names) { + result[[n]] <- n + } + }, + list_from_env = { + env <- new.env() + for (n in names) { + env[[n]] <- n + } + result <- as.list(env, all.names = TRUE) + }, + list_from_precise_env = { + env <- new.env(size = length(names)) + for (n in names) { + env[[n]] <- n + } + result <- as.list(env, all.names = TRUE) + }, + list_from_precise_x2_env = { + env <- new.env(size = length(names), parent = emptyenv()) + for (n in names) { + env[[n]] <- n + } + result <- as.list(env, all.names = TRUE) + } + ) +} + +bm_create_list() |> autoplot() +# plain list is faster than creating an env first; setting the size of the env and making parent = emptyenv() makes a small difference! diff --git a/man/CnfAtom.Rd b/man/CnfAtom.Rd index 11fd8dd07..6398eea1d 100644 --- a/man/CnfAtom.Rd +++ b/man/CnfAtom.Rd @@ -1,5 +1,5 @@ % Generated by roxygen2: do not edit by hand -% Please edit documentation in R/CnfFormula.R +% Please edit documentation in R/CnfAtom.R \name{CnfAtom} \alias{CnfAtom} \alias{\%among\%} @@ -62,6 +62,8 @@ experimental; it is for internal use. \details{ We would have preferred to overload the \code{\%in\%} operator, but this is currently not easily possible in R. We therefore created the \verb{\%among\%} operator. + +The internal representation of a \code{CnfAtom} may change in the future. } \examples{ u = CnfUniverse() diff --git a/man/CnfClause.Rd b/man/CnfClause.Rd index 4db55345b..c3499e9ce 100644 --- a/man/CnfClause.Rd +++ b/man/CnfClause.Rd @@ -1,5 +1,5 @@ % Generated by roxygen2: do not edit by hand -% Please edit documentation in R/CnfFormula.R +% Please edit documentation in R/CnfClause.R \name{CnfClause} \alias{CnfClause} \alias{as.CnfClause} @@ -31,6 +31,11 @@ that is true if at least one of the atoms is true. These are for example of the \code{CnfClause} objects can be constructed explicitly, using the \code{CnfClause()} constructor, or implicitly, by using the \code{|} operator on \code{\link{CnfAtom}}s or other \code{CnfClause} objects. +\code{CnfClause} objects which are not tautologies or contradictions are named lists; +the value ranges of each symbol can be accessed using \code{[[}. +However, to get a list of \code{\link{CnfAtom}} objects, use \code{as.list()}. +Note that the simplified form of a clause containing a contradiction is the empty list. + Upon construction, the \code{CnfClause} is simplified by (1) removing contradictions, (2) unifying atoms that refer to the same symbol, and (3) evaluating to \code{TRUE} if any atom is \code{TRUE}. Note that the order of atoms in a clause is not preserved. @@ -50,13 +55,22 @@ could in principle be represented as a single \code{CnfClause}. This is part of the CNF representation tooling, which is currently considered experimental; it is for internal use. } +\details{ +We are undecided whether it is a better idea to have \code{as.list()} return a named list +or an unnamed one. Calling \code{as.list()} on a \code{CnfClause} with a tautology returns +a tautology-atom, which does not have a name. We therefore decided to return an +unnamed list in general. However, this behaviour may change in the future. +} \examples{ u = CnfUniverse() X = CnfSymbol(u, "X", c("a", "b", "c")) Y = CnfSymbol(u, "Y", c("d", "e", "f")) CnfClause(list(X \%among\% c("a", "b"), Y \%among\% c("d", "e"))) -X \%among\% c("a", "b") | Y \%among\% c("d", "e") +cls = X \%among\% c("a", "b") | Y \%among\% c("d", "e") +cls + +as.list(cls) as.CnfClause(X \%among\% c("a", "b")) diff --git a/man/CnfFormula.Rd b/man/CnfFormula.Rd index b8c9fb3c2..8d7e006f9 100644 --- a/man/CnfFormula.Rd +++ b/man/CnfFormula.Rd @@ -30,6 +30,9 @@ that is true if all of the clauses are true. These are for example of the form \code{CnfFormula} objects can be constructed explicitly, using the \code{CnfFormula()} constructor, or implicitly, by using the \code{&} operator on \code{\link{CnfAtom}}s, \code{\link{CnfClause}}s, or other \code{CnfFormula} objects. +To get individual clauses from a formula, \code{[[} should not be used; instead, use \code{as.list()}. +Note that the simplified form of a formula containing a tautology is the empty list. + Upon construction, the \code{CnfFormula} is simplified by using various heuristics. This includes unit propagation, subsumption elimination, and self/hidden subsumption elimination (see examples). @@ -57,8 +60,12 @@ X = CnfSymbol(u, "X", c("a", "b", "c")) Y = CnfSymbol(u, "Y", c("d", "e", "f")) Z = CnfSymbol(u, "Z", c("g", "h", "i")) -(X \%among\% c("a", "b") | Y \%among\% c("d", "e")) & +frm = (X \%among\% c("a", "b") | Y \%among\% c("d", "e")) & Z \%among\% c("g", "h") +frm + +# retrieve individual clauses +as.list(frm) # Negation of a formula # Note the parentheses, otherwise `!` would be applied to the first clause only. diff --git a/man/CnfSymbol.Rd b/man/CnfSymbol.Rd index 2dccb0d70..8f3a3826e 100644 --- a/man/CnfSymbol.Rd +++ b/man/CnfSymbol.Rd @@ -1,5 +1,5 @@ % Generated by roxygen2: do not edit by hand -% Please edit documentation in R/CnfFormula.R +% Please edit documentation in R/CnfSymbol.R \name{CnfSymbol} \alias{CnfSymbol} \title{Symbols for CNF Formulas} @@ -37,10 +37,12 @@ experimental; it is for internal use. u = CnfUniverse() X = CnfSymbol(u, "X", c("a", "b", "c")) +# Use symbols to create CnfAtom objects X \%among\% c("a", "b") X \%among\% "a" X \%among\% character(0) X \%among\% c("a", "b", "c") + } \seealso{ Other CNF representation objects: diff --git a/man/CnfUniverse.Rd b/man/CnfUniverse.Rd index bb031e699..484dc2c63 100644 --- a/man/CnfUniverse.Rd +++ b/man/CnfUniverse.Rd @@ -1,5 +1,5 @@ % Generated by roxygen2: do not edit by hand -% Please edit documentation in R/CnfFormula.R +% Please edit documentation in R/CnfUniverse.R \name{CnfUniverse} \alias{CnfUniverse} \title{Symbol Table for CNF Formulas} @@ -12,7 +12,8 @@ A new \code{CnfUniverse} object. \description{ A symbol table for CNF formulas. The \code{CnfUniverse} is a by-reference object that stores the domain of each symbol. Symbols are created with \code{\link[=CnfSymbol]{CnfSymbol()}} -and can be retrieved with \code{[[} or \code{$}. +and can be retrieved with \code{$}. +Using \code{[[} retrieves a given symbol's domain. It is only possible to combine symbols from the same (identical) universe. From 1855d39edb531705092d5ccf03146c7e63368cee Mon Sep 17 00:00:00 2001 From: mb706 Date: Tue, 10 Sep 2024 20:49:47 +0200 Subject: [PATCH 23/87] more convenience functions --- NAMESPACE | 1 + R/CnfAtom.R | 20 +++++++++--------- R/CnfClause.R | 51 +++++++++++++++++++++++++++++++++++++++++----- R/CnfFormula.R | 4 ++-- R/CnfUniverse.R | 4 ++-- man/CnfAtom.Rd | 18 ++++++++-------- man/CnfClause.Rd | 8 +++++--- man/CnfUniverse.Rd | 4 ++-- 8 files changed, 77 insertions(+), 33 deletions(-) diff --git a/NAMESPACE b/NAMESPACE index 0450995c3..6e38e5873 100644 --- a/NAMESPACE +++ b/NAMESPACE @@ -9,6 +9,7 @@ S3method("%among%",default) S3method("&",CnfAtom) S3method("&",CnfClause) S3method("&",CnfFormula) +S3method("[",CnfClause) S3method("|",CnfAtom) S3method("|",CnfClause) S3method("|",CnfFormula) diff --git a/R/CnfAtom.R b/R/CnfAtom.R index 428d00a14..2d7a5ab93 100644 --- a/R/CnfAtom.R +++ b/R/CnfAtom.R @@ -2,26 +2,26 @@ #' @title Atoms for CNF Formulas #' #' @description -#' `Atom` objects represent a single statement that is used to build up CNF formulae. +#' `CnfAtom` objects represent a single statement that is used to build up CNF formulae. #' They are mostly intermediate, created using the [`%among%`] operator or [`CnfAtom()`] #' directly, and combined into [`CnfClause`] and [`CnfFormula`] objects. -#' [`CnfClause`] and [`CnfFormula`] do not, however, contain [`Atom`] objects directly, +#' [`CnfClause`] and [`CnfFormula`] do not, however, contain [`CnfAtom`] objects directly, #' -#' `Atom`s contain an indirect reference to a [`CnfSymbol`] by referencing its name -#' and its [`CnfUniverse`]. They furthermore contain a set of values. An `Atom` +#' `CnfAtom`s contain an indirect reference to a [`CnfSymbol`] by referencing its name +#' and its [`CnfUniverse`]. They furthermore contain a set of values. An `CnfAtom` #' represents a statement asserting that the given symbol takes up one of the #' given values. #' -#' If the set of values is empty, the `Atom` represents a contradiction (FALSE). -#' If it is the full domain of the symbol, the `Atom` represents a tautology (TRUE). +#' If the set of values is empty, the `CnfAtom` represents a contradiction (FALSE). +#' If it is the full domain of the symbol, the `CnfAtom` represents a tautology (TRUE). #' These values can be converted to, and from, `logical(1)` values using `as.logical()` #' and `as.CnfAtom()`. #' -#' `Atom` objects can be negated using the `!` operator, which will return the `Atom` +#' `CnfAtom` objects can be negated using the `!` operator, which will return the `CnfAtom` #' representing set membership in the complement of the symbol with respect to its domain. -#' `Atom`s can furthermore be combined using the `|` operator to form a [`CnfClause`], +#' `CnfAtom`s can furthermore be combined using the `|` operator to form a [`CnfClause`], #' and using the `&` operator to form a [`CnfFormula`]. This happens even if the -#' resulting statement could be represented as a single `Atom`. +#' resulting statement could be represented as a single `CnfAtom`. #' #' This is part of the CNF representation tooling, which is currently considered #' experimental; it is for internal use. @@ -153,7 +153,7 @@ as.CnfAtom.CnfAtom = function(x) { } #' @export -as.logical.CnfAtom = function(x) { +as.logical.CnfAtom = function(x, ...) { if (is.logical(x)) { return(unclass(x)) } diff --git a/R/CnfClause.R b/R/CnfClause.R index e6cd496ac..6d766d270 100644 --- a/R/CnfClause.R +++ b/R/CnfClause.R @@ -14,7 +14,8 @@ #' or implicitly, by using the `|` operator on [`CnfAtom`]s or other `CnfClause` objects. #' #' `CnfClause` objects which are not tautologies or contradictions are named lists; -#' the value ranges of each symbol can be accessed using `[[`. +#' the value ranges of each symbol can be accessed using `[[`, and these clauses +#' can be subset using `[` to get clauses containing only the indicated symbols. #' However, to get a list of [`CnfAtom`] objects, use `as.list()`. #' Note that the simplified form of a clause containing a contradiction is the empty list. #' @@ -40,8 +41,9 @@ #' @details #' We are undecided whether it is a better idea to have `as.list()` return a named list #' or an unnamed one. Calling `as.list()` on a `CnfClause` with a tautology returns -#' a tautology-atom, which does not have a name. We therefore decided to return an -#' unnamed list in general. However, this behaviour may change in the future. +#' a tautology-atom, which does not have a name. We currently return a named list +#' for other clauses, as this makes subsetting by name commute with `as.list()`. +#' However, this behaviour may change in the future. #' #' @param atoms (`list` of ([`CnfAtom`] | `CnfClause`)) \cr #' A list of [`CnfAtom`] or other `CnfClause` objects. @@ -193,13 +195,52 @@ as.list.CnfClause = function(x) { } #' @export -as.logical.CnfClause = function(x) { +as.logical.CnfClause = function(x, ...) { if (is.logical(x)) { return(unclass(x)) } return(NA) } +#' @export +`[.CnfClause` = function(x, i) { + if (missing(i)) return(x) + assert_atomic(i) + i = c(i) + x_bare = unclass(x) + true_length = if (isFALSE(x)) 0 else length(x_bare) + + if (is.numeric(i)) { + i = unique(floor(i)) + } else if (is.character(i)) { + i = unique(i) + } else if (!is.logical(i) && length(i) != 0) { + # we explicitly allow length(i) == 0 (empty subset) + stop("Invalid index type.") + } + if (length(i) == 0 || identical(i, 0) || (identical(i, FALSE) && !isFALSE((x)))) { + return(as.CnfClause(structure(FALSE, universe = attr(x, "universe")))) + } + if (isFALSE(x)) { + stop("Cannot subset a FALSE clause with anything other than 0, [], or 0-length-vector.") + } + if (isTRUE(x)) { + if (identical(i, 1) || identical(i, TRUE)) return(x) + stop("Cannot subset a TRUE clause with anything other than 0, 1, [], or 0-length-vector.") + } + assert( + check_numeric(i, lower = 0, upper = true_length, any.missing = FALSE), + check_subset(i, names(x_bare)), + check_logical(i, len = true_length), + .var.name = "i" + ) + structure( + unclass(x)[i], + universe = attr(x, "universe"), + class = "CnfClause" + ) +} + #' @export all.equal.CnfClause = function(target, current, ...) { if (is.logical(target) && is.logical(current)) { @@ -219,7 +260,7 @@ all.equal.CnfClause = function(target, current, ...) { normalize = function(clause) { # []-assign to preserve class and attributes - clause[] = lapply(clause[order(names(clause))], sort) + clause[] = lapply(unclass(clause)[order(names(clause))], sort) } target = normalize(target) diff --git a/R/CnfFormula.R b/R/CnfFormula.R index 837e70760..99b6d016e 100644 --- a/R/CnfFormula.R +++ b/R/CnfFormula.R @@ -233,7 +233,7 @@ as.list.CnfFormula = function(x, ...) { } #' @export -as.logical.CnfFormula = function(x) { +as.logical.CnfFormula = function(x, ...) { if (is.logical(x)) { return(unclass(x)) } @@ -259,7 +259,7 @@ all.equal.CnfFormula = function(target, current, ...) { normalize = function(formula) { formula[] = lapply(unclass(formula), function(clause) { - clause[] = lapply(clause[order(names(clause))], sort) + clause[] = lapply(unclass(clause)[order(names(clause))], sort) clause }) # sort by symbol names, then by hash diff --git a/R/CnfUniverse.R b/R/CnfUniverse.R index 1108882b3..f95e77aeb 100644 --- a/R/CnfUniverse.R +++ b/R/CnfUniverse.R @@ -20,8 +20,8 @@ #' u$X #' u[["Y"]] #' -#' X %among% c("a", "d") -#' u$X %among% c("a", "d") +#' X %among% c("a", "c") +#' u$X %among% c("a", "c") #' Y %among% c("d", "e", "f") #' Y %among% character(0) #' diff --git a/man/CnfAtom.Rd b/man/CnfAtom.Rd index 6398eea1d..71e4a9138 100644 --- a/man/CnfAtom.Rd +++ b/man/CnfAtom.Rd @@ -35,26 +35,26 @@ Only \code{logical(1)} and \code{CnfAtom} itself are currently supported.} A new \code{CnfAtom} object. } \description{ -\code{Atom} objects represent a single statement that is used to build up CNF formulae. +\code{CnfAtom} objects represent a single statement that is used to build up CNF formulae. They are mostly intermediate, created using the \code{\link{\%among\%}} operator or \code{\link[=CnfAtom]{CnfAtom()}} directly, and combined into \code{\link{CnfClause}} and \code{\link{CnfFormula}} objects. -\code{\link{CnfClause}} and \code{\link{CnfFormula}} do not, however, contain \code{\link{Atom}} objects directly, +\code{\link{CnfClause}} and \code{\link{CnfFormula}} do not, however, contain \code{\link{CnfAtom}} objects directly, -\code{Atom}s contain an indirect reference to a \code{\link{CnfSymbol}} by referencing its name -and its \code{\link{CnfUniverse}}. They furthermore contain a set of values. An \code{Atom} +\code{CnfAtom}s contain an indirect reference to a \code{\link{CnfSymbol}} by referencing its name +and its \code{\link{CnfUniverse}}. They furthermore contain a set of values. An \code{CnfAtom} represents a statement asserting that the given symbol takes up one of the given values. -If the set of values is empty, the \code{Atom} represents a contradiction (FALSE). -If it is the full domain of the symbol, the \code{Atom} represents a tautology (TRUE). +If the set of values is empty, the \code{CnfAtom} represents a contradiction (FALSE). +If it is the full domain of the symbol, the \code{CnfAtom} represents a tautology (TRUE). These values can be converted to, and from, \code{logical(1)} values using \code{as.logical()} and \code{as.CnfAtom()}. -\code{Atom} objects can be negated using the \code{!} operator, which will return the \code{Atom} +\code{CnfAtom} objects can be negated using the \code{!} operator, which will return the \code{CnfAtom} representing set membership in the complement of the symbol with respect to its domain. -\code{Atom}s can furthermore be combined using the \code{|} operator to form a \code{\link{CnfClause}}, +\code{CnfAtom}s can furthermore be combined using the \code{|} operator to form a \code{\link{CnfClause}}, and using the \code{&} operator to form a \code{\link{CnfFormula}}. This happens even if the -resulting statement could be represented as a single \code{Atom}. +resulting statement could be represented as a single \code{CnfAtom}. This is part of the CNF representation tooling, which is currently considered experimental; it is for internal use. diff --git a/man/CnfClause.Rd b/man/CnfClause.Rd index c3499e9ce..32ec964ff 100644 --- a/man/CnfClause.Rd +++ b/man/CnfClause.Rd @@ -32,7 +32,8 @@ that is true if at least one of the atoms is true. These are for example of the or implicitly, by using the \code{|} operator on \code{\link{CnfAtom}}s or other \code{CnfClause} objects. \code{CnfClause} objects which are not tautologies or contradictions are named lists; -the value ranges of each symbol can be accessed using \code{[[}. +the value ranges of each symbol can be accessed using \code{[[}, and these clauses +can be subset using \code{[} to get clauses containing only the indicated symbols. However, to get a list of \code{\link{CnfAtom}} objects, use \code{as.list()}. Note that the simplified form of a clause containing a contradiction is the empty list. @@ -58,8 +59,9 @@ experimental; it is for internal use. \details{ We are undecided whether it is a better idea to have \code{as.list()} return a named list or an unnamed one. Calling \code{as.list()} on a \code{CnfClause} with a tautology returns -a tautology-atom, which does not have a name. We therefore decided to return an -unnamed list in general. However, this behaviour may change in the future. +a tautology-atom, which does not have a name. We currently return a named list +for other clauses, as this makes subsetting by name commute with \code{as.list()}. +However, this behaviour may change in the future. } \examples{ u = CnfUniverse() diff --git a/man/CnfUniverse.Rd b/man/CnfUniverse.Rd index 484dc2c63..50e35d37b 100644 --- a/man/CnfUniverse.Rd +++ b/man/CnfUniverse.Rd @@ -28,8 +28,8 @@ Y = CnfSymbol(u, "Y", c("d", "e", "f")) u$X u[["Y"]] -X \%among\% c("a", "d") -u$X \%among\% c("a", "d") +X \%among\% c("a", "c") +u$X \%among\% c("a", "c") Y \%among\% c("d", "e", "f") Y \%among\% character(0) From 6449b461152ef9d6001d23ab22b849411808fd67 Mon Sep 17 00:00:00 2001 From: mb706 Date: Wed, 11 Sep 2024 15:58:28 +0200 Subject: [PATCH 24/87] some tests --- R/CnfAtom.R | 6 +- R/CnfClause.R | 32 ++-- R/CnfFormula.R | 32 ++-- R/CnfFormula_simplify.R | 20 --- attic/mvsat.mv | 22 +++ tests/testthat/test_CnfAtom.R | 163 ++++++++++++++++++++ tests/testthat/test_CnfClause.R | 240 ++++++++++++++++++++++++++++++ tests/testthat/test_CnfSymbol.R | 61 ++++++++ tests/testthat/test_CnfUniverse.R | 63 ++++++++ 9 files changed, 589 insertions(+), 50 deletions(-) create mode 100644 tests/testthat/test_CnfAtom.R create mode 100644 tests/testthat/test_CnfClause.R create mode 100644 tests/testthat/test_CnfSymbol.R create mode 100644 tests/testthat/test_CnfUniverse.R diff --git a/R/CnfAtom.R b/R/CnfAtom.R index 2d7a5ab93..16b881f8a 100644 --- a/R/CnfAtom.R +++ b/R/CnfAtom.R @@ -196,10 +196,10 @@ chooseOpsMethod.CnfAtom <- function(x, y, mx, my, cl, reverse) TRUE if (inherits(e2, "CnfFormula")) { # `|.CnfFormula` handles conversion return(`|.CnfFormula`(e1, e2)) - } else if (is.logical(e2) || inherits(e2, "CnfAtom")) { - if (isFALSE(e1) || isTRUE(e2)) return(as.CnfAtom(e2)) - if (isFALSE(e2) || isTRUE(e1)) return(e1) } + if (isFALSE(e1) || isTRUE(e2)) return(as.CnfClause(e2)) + if (isFALSE(e2) || isTRUE(e1)) return(as.CnfClause(e1)) + # either two proper CnfAtoms, or e2 is a CnfClause. CnfClause(list(e1, e2)) } diff --git a/R/CnfClause.R b/R/CnfClause.R index 6d766d270..47025b3d2 100644 --- a/R/CnfClause.R +++ b/R/CnfClause.R @@ -91,14 +91,15 @@ CnfClause = function(atoms) { entries = list() universe = attr(atoms[[1]], "universe") for (a in atoms) { + a_bare = c(a) if (!identical(attr(a, "universe"), universe)) { stop("All symbols must be in the same universe.") } - if (isTRUE(a)) { + if (isTRUE(a_bare)) { entries = TRUE break } - if (isFALSE(a)) { + if (isFALSE(a_bare)) { next } if (inherits(a, "CnfAtom")) { @@ -128,9 +129,10 @@ CnfClause = function(atoms) { #' @export print.CnfClause = function(x, ...) { - if (isTRUE(x)) { + x_bare = c(x) + if (isTRUE(x_bare)) { cat("CnfClause: TRUE\n") - } else if (isFALSE(x)) { + } else if (isFALSE(x_bare)) { cat("CnfClause: FALSE\n") } else { cat("CnfClause:\n") @@ -144,9 +146,10 @@ print.CnfClause = function(x, ...) { #' @export format.CnfClause = function(x, ...) { - if (isTRUE(x)) { + x_bare = c(x) + if (isTRUE(x_bare)) { return("CnfClause: T") - } else if (isFALSE(x)) { + } else if (isFALSE(x_bare)) { return("CnfClause: F") } else { return(sprintf("CnfClause(%s)", length(x))) @@ -208,7 +211,7 @@ as.logical.CnfClause = function(x, ...) { assert_atomic(i) i = c(i) x_bare = unclass(x) - true_length = if (isFALSE(x)) 0 else length(x_bare) + true_length = if (isFALSE(x_bare)) 0 else length(x_bare) if (is.numeric(i)) { i = unique(floor(i)) @@ -218,13 +221,13 @@ as.logical.CnfClause = function(x, ...) { # we explicitly allow length(i) == 0 (empty subset) stop("Invalid index type.") } - if (length(i) == 0 || identical(i, 0) || (identical(i, FALSE) && !isFALSE((x)))) { + if (length(i) == 0 || identical(i, 0) || (identical(i, FALSE) && !isFALSE((x_bare)))) { return(as.CnfClause(structure(FALSE, universe = attr(x, "universe")))) } - if (isFALSE(x)) { + if (isFALSE(x_bare)) { stop("Cannot subset a FALSE clause with anything other than 0, [], or 0-length-vector.") } - if (isTRUE(x)) { + if (isTRUE(x_bare)) { if (identical(i, 1) || identical(i, TRUE)) return(x) stop("Cannot subset a TRUE clause with anything other than 0, 1, [], or 0-length-vector.") } @@ -285,16 +288,15 @@ chooseOpsMethod.CnfClause <- function(x, y, mx, my, cl, reverse) TRUE # `|.CnfFormula` handles conversion return(`|.CnfFormula`(e1, e2)) } - if (isFALSE(e1) || isTRUE(e2)) return(as.CnfClause(e2)) - if (isFALSE(e2) || isTRUE(e1)) return(e1) + e1_bare = c(e1) + e2_bare = c(e2) + if (isFALSE(e1_bare) || isTRUE(e2_bare)) return(as.CnfClause(e2)) + if (isFALSE(e2_bare) || isTRUE(e1_bare)) return(e1) CnfClause(list(e1, e2)) } #' @export `!.CnfClause` = function(x) { - if (is.logical(x)) { - return(as.CnfClause(!unclass(x))) - } !as.CnfFormula(x) } diff --git a/R/CnfFormula.R b/R/CnfFormula.R index 99b6d016e..4aff7f4f3 100644 --- a/R/CnfFormula.R +++ b/R/CnfFormula.R @@ -132,11 +132,12 @@ CnfFormula = function(clauses) { other_entries = list() universe = attr(clauses[[1]], "universe") for (cl in clauses) { - if (isFALSE(cl)) { + cl_bare = c(cl) + if (isFALSE(cl_bare)) { entries = FALSE break } - if (isTRUE(cl)) { + if (isTRUE(cl_bare)) { next } if (!identical(attr(cl, "universe"), universe)) { @@ -161,9 +162,10 @@ CnfFormula = function(clauses) { #' @export print.CnfFormula = function(x, ...) { - if (isTRUE(x)) { + x_bare = c(x) + if (isTRUE(x_bare)) { cat("CnfFormula: TRUE\n") - } else if (isFALSE(x)) { + } else if (isFALSE(x_bare)) { cat("CnfFormula: FALSE\n") } else { cat("CnfFormula:\n (") @@ -181,9 +183,10 @@ print.CnfFormula = function(x, ...) { #' @export format.CnfFormula = function(x, ...) { - if (isTRUE(x)) { + x_bare = c(x) + if (isTRUE(x_bare)) { return("CnfFormula: T") - } else if (isFALSE(x)) { + } else if (isFALSE(x_bare)) { return("CnfFormula: F") } else { return(sprintf("CnfFormula(%s)", length(x))) @@ -228,8 +231,9 @@ as.CnfFormula.CnfFormula = function(x) { #' @export as.list.CnfFormula = function(x, ...) { - if (isTRUE(x)) return(list()) - lapply(unclass(x), structure, class = "CnfClause", universe = attr(x, "universe")) + x_bare = c(x) + if (isTRUE(x_bare)) return(list()) + lapply(x_bare, structure, class = "CnfClause", universe = attr(x, "universe")) } #' @export @@ -280,10 +284,12 @@ chooseOpsMethod.CnfFormula <- function(x, y, mx, my, cl, reverse) TRUE #' @export `&.CnfFormula` = function(e1, e2) { + e1_bare = c(e1) + e2_bare = c(e2) e1 = as.CnfFormula(e1) e2 = as.CnfFormula(e2) - if (isTRUE(e1) || isFALSE(e2)) return(e2) - if (isTRUE(e2) || isFALSE(e1)) return(e1) + if (isTRUE(e1_bare) || isFALSE(e2_bare)) return(e2) + if (isTRUE(e2_bare) || isFALSE(e1_bare)) return(e1) if (!identical(attr(e1, "universe"), attr(e2, "universe"))) { stop("Both formulas must be in the same universe.") } @@ -292,10 +298,12 @@ chooseOpsMethod.CnfFormula <- function(x, y, mx, my, cl, reverse) TRUE #' @export `|.CnfFormula` = function(e1, e2) { + e1_bare = c(e1) + e2_bare = c(e2) e1 = as.CnfFormula(e1) e2 = as.CnfFormula(e2) - if (isFALSE(e1) || isTRUE(e2)) return(e2) - if (isFALSE(e2) || isFALSE(e1)) return(e1) + if (isFALSE(e1_bare) || isTRUE(e2_bare)) return(e2) + if (isFALSE(e2_bare) || isFALSE(e1_bare)) return(e1) if (!identical(attr(e1, "universe"), attr(e2, "universe"))) { stop("Both formulas must be in the same universe.") } diff --git a/R/CnfFormula_simplify.R b/R/CnfFormula_simplify.R index e4ad34330..bd3854d35 100644 --- a/R/CnfFormula_simplify.R +++ b/R/CnfFormula_simplify.R @@ -195,23 +195,3 @@ simplify_cnf = function(entries, universe) { ) } - -## to test: -# subsumption -# unit elimination -# unit elimination makes large clause smaller, leading to additional u.e. -# unit elimination makes large clause smaller, leading to subsumption - -# branch with totune is swallowed by single unbranch -# branch with totune is swallowed by multiple unbranch -# branches with totune can possibly lead to conflicts, but not always (multiple active inputs to unbranch, or mixed inputs to normal pipeops) -# branches with totune always lead to conflicts (multiple active inputs to unbranch, or mixed inputs to normal pipeops, or choice between both) -# can we recognize that a certain choice would lead to a conflict, making only other choices possible? - -# why does this blow up? -# - -# profvis::profvis(replicate(3000, { !!(((u$A %among% "T" | u$B %among% "F") & (u$A %among% "F" | u$C %among% "T") & (u$B %among% "T" | u$C %among% "F"))) ; NULL }) -> ., simplify = FALSE) - -# This is because we don't eliminate (C | A) & (!C | B) & (B | A) by removing (B | A) -# so, if clause X and clause Y have a symbol in common where the values are disjoint, the disjunction of the rest is implied? diff --git a/attic/mvsat.mv b/attic/mvsat.mv index c3c66116a..46e7105c0 100644 --- a/attic/mvsat.mv +++ b/attic/mvsat.mv @@ -87,3 +87,25 @@ # - other suggestion: we calculate submatrix 1..(i)x1..(i). Then add new column i+1. We can copy over all 1s immediately whenever we find a col that is a subset of i+1; However, we can at most copy i ones. # - maybe there is no easy solution; possibly except ordering by size first and only comparing in one direction. # - does this make self subsumption elimination more efficient? + + + +## to test: +# subsumption +# unit elimination +# unit elimination makes large clause smaller, leading to additional u.e. +# unit elimination makes large clause smaller, leading to subsumption + +# branch with totune is swallowed by single unbranch +# branch with totune is swallowed by multiple unbranch +# branches with totune can possibly lead to conflicts, but not always (multiple active inputs to unbranch, or mixed inputs to normal pipeops) +# branches with totune always lead to conflicts (multiple active inputs to unbranch, or mixed inputs to normal pipeops, or choice between both) +# can we recognize that a certain choice would lead to a conflict, making only other choices possible? + +# why does this blow up? +# + +# profvis::profvis(replicate(3000, { !!(((u$A %among% "T" | u$B %among% "F") & (u$A %among% "F" | u$C %among% "T") & (u$B %among% "T" | u$C %among% "F"))) ; NULL }) -> ., simplify = FALSE) + +# This is because we don't eliminate (C | A) & (!C | B) & (B | A) by removing (B | A) +# so, if clause X and clause Y have a symbol in common where the values are disjoint, the disjunction of the rest is implied? diff --git a/tests/testthat/test_CnfAtom.R b/tests/testthat/test_CnfAtom.R new file mode 100644 index 000000000..fad1d685e --- /dev/null +++ b/tests/testthat/test_CnfAtom.R @@ -0,0 +1,163 @@ + + +# Test the creation of a CnfAtom +test_that("CnfAtom is created correctly from CnfSymbol", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + + atom = CnfAtom(X, c("a", "b")) + + expect_s3_class(atom, "CnfAtom") + expect_equal(atom$symbol, "X") + expect_equal(atom$values, c("a", "b")) +}) + +# Test the creation of a tautology and contradiction with CnfAtom +test_that("CnfAtom handles tautologies and contradictions correctly", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + + tautology = CnfAtom(X, c("a", "b", "c")) + contradiction = CnfAtom(X, character(0)) + + # Tautology should evaluate to TRUE + expect_true(as.logical(tautology)) + + # Contradiction should evaluate to FALSE + expect_false(as.logical(contradiction)) +}) + +# Test negation of CnfAtom +test_that("Negation of CnfAtom works correctly", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + + atom = CnfAtom(X, c("a", "b")) + negated_atom = !atom + + # Check that negation works correctly + expect_s3_class(negated_atom, "CnfAtom") + expect_equal(negated_atom$symbol, "X") + expect_equal(negated_atom$values, "c") # Negation should result in the complement of the original values + + # Check that negation of a tautology is a contradiction + expect_false(as.logical(!CnfAtom(X, c("a", "b", "c")))) + + # Check that negation of a contradiction is a tautology + expect_true(as.logical(!CnfAtom(X, character(0)))) +}) + +# Test conjunction (&) of CnfAtoms +test_that("Conjunction of CnfAtoms works correctly", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + Y = CnfSymbol(u, "Y", c("d", "e", "f")) + + atom1 = CnfAtom(X, c("a", "b")) + atom2 = CnfAtom(Y, c("d", "e")) + + formula = atom1 & atom2 + + expect_s3_class(formula, "CnfFormula") + expect_length(as.list(formula), 2) + + atoms = unlist(lapply(as.list(formula), as.list), recursive = FALSE) + # we don't know if atoms[[1]] is atom1 or atom2 + if (identical(atoms[[1]]$symbol, "X")) { + expect_identical(atoms[[1]], atom1) + expect_identical(atoms[[2]], atom2) + } else { + expect_identical(atoms[[1]], atom2) + expect_identical(atoms[[2]], atom1) + } + + # Check that conjunction of a tautology with another atom is the other atom + ttl = CnfAtom(X, c("a", "b", "c")) & atom2 + expect_s3_class(ttl, "CnfFormula") + expect_identical(lapply(as.list(ttl), as.list), list(list(atom2))) + + # Check that conjunction of a contradiction with another atom is a contradiction + ctn = CnfAtom(X, character(0)) & atom2 + expect_s3_class(ctn, "CnfFormula") + expect_false(as.logical(ctn)) +}) + +# Test disjunction (|) of CnfAtoms +test_that("Disjunction of CnfAtoms works correctly", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + Y = CnfSymbol(u, "Y", c("d", "e", "f")) + + atom1 = CnfAtom(X, c("a", "b")) + atom2 = CnfAtom(Y, c("d", "e")) + + clause = atom1 | atom2 + + expect_s3_class(clause, "CnfClause") + expect_length(as.list(clause), 2) + atoms = as.list(clause) + if (identical(atoms[[1]]$symbol, "X")) { + expect_identical(atoms[[1]], atom1) + expect_identical(atoms[[2]], atom2) + } else { + expect_identical(atoms[[1]], atom2) + expect_identical(atoms[[2]], atom1) + } + + # Check that disjunction of a tautology with another atom is a tautology + ttl = CnfAtom(X, c("a", "b", "c")) | atom2 + expect_true(as.logical(ttl)) + expect_s3_class(ttl, "CnfClause") + + # Check that disjunction of a contradiction with another atom is the other atom + ctn = CnfAtom(X, character(0)) | atom2 + expect_identical(as.list(ctn), list(atom2)) +}) + +# Test print and format methods for CnfAtom +test_that("print and format methods for CnfAtom work correctly", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + + atom = CnfAtom(X, c("a", "b")) + + # Test print method + expect_output(print(atom), "CnfAtom: X ∈ \\{a, b\\}.") + + # Test format method + expect_equal(format(atom), "CnfAtom(X)") +}) + +# Test conversion between logical and CnfAtom +test_that("as.logical and as.CnfAtom conversions work correctly", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + + atom_true = CnfAtom(X, c("a", "b", "c")) + atom_false = CnfAtom(X, character(0)) + atom_neither = CnfAtom(X, c("a", "b")) + + # Convert CnfAtom to logical + expect_true(as.logical(atom_true)) + expect_false(as.logical(atom_false)) + expect_identical(as.logical(atom_neither), NA) + + # Convert logical to CnfAtom + expect_s3_class(as.CnfAtom(TRUE), "CnfAtom") + expect_true(as.logical(as.CnfAtom(TRUE))) + + expect_s3_class(as.CnfAtom(FALSE), "CnfAtom") + expect_false(as.logical(as.CnfAtom(FALSE))) + + expect_error(as.CnfAtom(NA), "May not be NA") + expect_error(as.CnfAtom(c(TRUE, TRUE)), "Must have length 1.") +}) + +# Test invalid creation of CnfAtom with values not in the domain +test_that("CnfAtom throws error when values are not in the symbol's domain", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + + expect_error(CnfAtom(X, c("d", "e")), "Must be a subset of \\{'a','b','c'\\}") +}) + diff --git a/tests/testthat/test_CnfClause.R b/tests/testthat/test_CnfClause.R new file mode 100644 index 000000000..4e187c4a5 --- /dev/null +++ b/tests/testthat/test_CnfClause.R @@ -0,0 +1,240 @@ +# Test the creation of a CnfClause from CnfAtoms +test_that("CnfClause is created correctly from CnfAtoms", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + Y = CnfSymbol(u, "Y", c("d", "e", "f")) + + atom1 = CnfAtom(X, c("a", "b")) + atom2 = CnfAtom(Y, c("d", "e")) + clause = CnfClause(list(atom1, atom2)) + + expect_s3_class(clause, "CnfClause") + expect_length(as.list(clause), 2) + + atoms = as.list(clause) + if (identical(atoms[[1]]$symbol, "X")) { + expect_identical(atoms[[1]], atom1) + expect_identical(atoms[[2]], atom2) + } else { + expect_identical(atoms[[1]], atom2) + expect_identical(atoms[[2]], atom1) + } + +}) + +test_that("CnfClause with overlapping symbols works correctly", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + Y = CnfSymbol(u, "Y", c("d", "e", "f")) + + atom1 = CnfAtom(X, c("a", "b")) + atom2 = CnfAtom(Y, c("d", "e")) + atom1_sub = CnfAtom(X, c("a")) + atom2_sub = CnfAtom(Y, c("d")) + + expect_identical( + CnfClause(list(atom1, atom1_sub)), + CnfClause(list(atom1)) + ) + + expect_identical(CnfClause(list(atom1, atom1)), CnfClause(list(atom1))) + + combined1 = CnfClause(list(atom1, atom2, atom1_sub, atom2_sub)) + combined2 = CnfClause(list(atom1, atom2)) + combinedswitched = CnfClause(list(atom2, atom1)) + + expect_true(identical(combined1, combined2) || identical(combined1, combinedswitched)) + + # only one of them is identical! + # this must be taken out if at any point we decide to sort the atoms + expect_true(!identical(combined1, combined2) || !identical(combined1, combinedswitched)) + + combined1 = CnfClause(list(atom1, atom2, atom1_sub)) + combined2 = CnfClause(list(atom1, atom2)) + combinedswitched = CnfClause(list(atom2, atom1)) + + expect_true(identical(combined1, combined2) || identical(combined1, combinedswitched)) + + # only one of them is identical! + # this must be taken out if at any point we decide to sort the atoms + expect_true(!identical(combined1, combined2) || !identical(combined1, combinedswitched)) + +}) + +# Test the handling of tautologies and contradictions in CnfClause +test_that("CnfClause handles tautologies and contradictions correctly", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + + tautology = CnfClause(list(CnfAtom(X, c("a", "b", "c")))) + contradiction = CnfClause(list(CnfAtom(X, character(0)))) + + # Tautology should evaluate to TRUE + expect_true(as.logical(tautology)) + + # Contradiction should evaluate to FALSE + expect_false(as.logical(contradiction)) +}) + +# Test disjunction (|) of CnfClauses +test_that("Disjunction of CnfClauses works correctly", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + Y = CnfSymbol(u, "Y", c("d", "e", "f")) + + atom1 = CnfAtom(X, c("a")) + atom2 = CnfAtom(Y, c("d")) + atom3 = CnfAtom(X, c("b")) + atom4 = CnfAtom(Y, c("e")) + + clause1 = CnfClause(list(atom1, atom2)) + clause2 = CnfClause(list(atom3, atom4)) + + disjunct = clause1 | clause2 + + expect_s3_class(disjunct, "CnfClause") + expect_length(as.list(disjunct), 2) + + # Check that the disjunction has unified the atoms correctly + atoms = as.list(disjunct) + if (identical(atoms[[1]]$symbol, "X")) { + expect_equal(atoms[[1]]$values, c("a", "b")) + expect_equal(atoms[[2]]$values, c("d", "e")) + } else { + expect_equal(atoms[[1]]$values, c("d", "e")) + expect_equal(atoms[[2]]$values, c("a", "b")) + } + + tautology = CnfClause(list(CnfAtom(X, c("a", "b", "c")))) + contradiction = CnfClause(list(CnfAtom(X, character(0)))) + + # Check that disjunction of a tautology with another clause is a tautology + ttl = tautology | clause1 + expect_true(as.logical(ttl)) + + # Check that disjunction of a contradiction with another clause is the other clause + ctn = contradiction | clause1 + expect_identical(as.list(ctn), as.list(clause1)) + + + # tautologies that come up in the middle of a disjunction also work + + atom1_complement = CnfAtom(X, c("b", "c")) + expect_identical( + CnfClause(list(atom1, atom1_complement)), + tautology + ) + +}) + +# Test conjunction (&) of CnfClauses +test_that("Conjunction of CnfClauses works correctly", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + Y = CnfSymbol(u, "Y", c("d", "e", "f")) + tautology = CnfClause(list(CnfAtom(X, c("a", "b", "c")))) + contradiction = CnfClause(list(CnfAtom(X, character(0)))) + + + atom1 = CnfAtom(X, c("a", "b")) + atom2 = CnfAtom(Y, c("d", "e")) + + clause1 = CnfClause(list(atom1)) + clause2 = CnfClause(list(atom2)) + + formula = clause1 & clause2 + + expect_s3_class(formula, "CnfFormula") + expect_length(as.list(formula), 2) + if (identical(as.list(as.list(formula)[[1]])[[1]]$symbol, "X")) { + expect_identical(lapply(as.list(formula), as.list), list(list(atom1), list(atom2))) + } else { + expect_identical(lapply(as.list(formula), as.list), list(list(atom2), list(atom1))) + } + + # Check that conjunction of a tautology with another clause is the other clause + ttl = tautology & clause2 + expect_s3_class(ttl, "CnfFormula") + expect_identical(lapply(as.list(ttl), as.list), list(list(atom2))) + + # Check that conjunction of a contradiction with another clause is a contradiction + ctn = contradiction & clause2 + expect_s3_class(ctn, "CnfFormula") + expect_false(as.logical(ctn)) +}) + +# Test negation of CnfClause +test_that("Negation of CnfClause works correctly", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + Y = CnfSymbol(u, "Y", c("d", "e", "f")) + tautology = CnfClause(list(CnfAtom(X, c("a", "b", "c")))) + contradiction = CnfClause(list(CnfAtom(X, character(0)))) + + clause = CnfClause(list(CnfAtom(X, c("a", "b")), CnfAtom(Y, c("d")))) + negated_clause = !clause + + expect_s3_class(negated_clause, "CnfFormula") + expect_length(as.list(negated_clause), 2) + + + # Check that negation of a tautology is a contradiction + expect_false(as.logical(!tautology)) + expect_s3_class(!tautology, "CnfFormula") + + # Check that negation of a contradiction is a tautology + expect_true(as.logical(!contradiction)) +}) + +# Test subset operations on CnfClause +test_that("Subsetting of CnfClause works correctly", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + Y = CnfSymbol(u, "Y", c("d", "e", "f")) + + clause = CnfClause(list(CnfAtom(X, c("a", "b")), CnfAtom(Y, c("d", "e")))) + + subset_clause = clause["X"] + + expect_s3_class(subset_clause, "CnfClause") + expect_length(as.list(subset_clause), 1) + expect_identical(as.list(subset_clause)[[1]]$symbol, "X") + + expect_error(clause[0], "Cannot subset a FALSE clause") + expect_error(clause["Z"], "Invalid index type.") +}) + +# Test print and format methods for CnfClause +test_that("print and format methods for CnfClause work correctly", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + Y = CnfSymbol(u, "Y", c("d", "e", "f")) + + clause = CnfClause(list(CnfAtom(X, c("a", "b")), CnfAtom(Y, c("d")))) + + # Test print method + expect_output(print(clause), "CnfClause") + + # Test format method + expect_equal(format(clause), "CnfClause(2)") +}) + +# Test conversion between logical and CnfClause +test_that("as.logical and as.CnfClause conversions work correctly", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + + atom_true = CnfClause(list(CnfAtom(X, c("a", "b", "c")))) + atom_false = CnfClause(list(CnfAtom(X, character(0)))) + + # Convert CnfClause to logical + expect_true(as.logical(atom_true)) + expect_false(as.logical(atom_false)) + + # Convert logical to CnfClause + expect_s3_class(as.CnfClause(TRUE), "CnfClause") + expect_true(as.logical(as.CnfClause(TRUE))) + + expect_s3_class(as.CnfClause(FALSE), "CnfClause") + expect_false(as.logical(as.CnfClause(FALSE))) +}) diff --git a/tests/testthat/test_CnfSymbol.R b/tests/testthat/test_CnfSymbol.R new file mode 100644 index 000000000..44adf2e28 --- /dev/null +++ b/tests/testthat/test_CnfSymbol.R @@ -0,0 +1,61 @@ + +# Test the creation of a CnfSymbol in a CnfUniverse +test_that("CnfSymbol is created correctly in CnfUniverse", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + + expect_s3_class(X, "CnfSymbol") + expect_equal(c(X), "X") + + expect_equal(u[["X"]], c("a", "b", "c")) +}) + +# Test that CnfSymbol cannot be created with an empty domain +test_that("CnfSymbol cannot be created with an empty domain", { + u = CnfUniverse() + + expect_error(CnfSymbol(u, "X", character(0)), + "Must have length >= 1") +}) + +# Test print and format methods for CnfSymbol +test_that("print and format methods for CnfSymbol work correctly", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + + # Test print method + expect_output(print(X), "CnfSymbol 'X' with domain \\{a, b, c\\}.") + + # Test format method + expect_equal(format(X), "CnfSymbol(X)") +}) + +# Test the %among% operator with CnfSymbol +test_that("%among% operator works correctly for CnfSymbol", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + + # Test valid uses of %among% + atom1 = X %among% c("a", "b") + expect_s3_class(atom1, "CnfAtom") + + atom2 = X %among% "a" + expect_s3_class(atom2, "CnfAtom") + + atom3 = X %among% character(0) # Contradiction case + expect_s3_class(atom3, "CnfAtom") + expect_true(isFALSE(as.logical(atom3))) + + atom4 = X %among% c("a", "b", "c") # Tautology case + expect_s3_class(atom4, "CnfAtom") + expect_true(isTRUE(as.logical(atom4))) +}) + +# Test invalid use of %among% operator with values not in the domain +test_that("Invalid values in %among% operator throw an error", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + + expect_error(X %among% c("d", "e"), + "values.*Must be a subset of") +}) diff --git a/tests/testthat/test_CnfUniverse.R b/tests/testthat/test_CnfUniverse.R new file mode 100644 index 000000000..47bb9bcef --- /dev/null +++ b/tests/testthat/test_CnfUniverse.R @@ -0,0 +1,63 @@ +# Test the creation of a CnfUniverse +test_that("CnfUniverse is created correctly", { + u = CnfUniverse() + + expect_s3_class(u, "CnfUniverse") + expect_environment(u) +}) + +# Test symbol creation in CnfUniverse and retrieval by name +test_that("CnfSymbol can be added and retrieved", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + + # Test retrieval using $ + expect_s3_class(u$X, "CnfSymbol") + expect_equal(u$X, X) + + # Test retrieval using [[ + expect_equal(u[["X"]], c("a", "b", "c")) +}) + +# Test that retrieving non-existent symbols throws an error +test_that("Accessing non-existent symbol throws an error", { + u = CnfUniverse() + + expect_error(u$Z, "Variable 'Z' does not exist in the universe.") +}) + +# Test that duplicate symbols cannot be created +test_that("Cannot add duplicate symbols to CnfUniverse", { + u = CnfUniverse() + CnfSymbol(u, "X", c("a", "b", "c")) + + expect_error(CnfSymbol(u, "X", c("d", "e")), "Variable 'X' already exists in the universe.") +}) + +# Test print and format methods for CnfUniverse +test_that("print and format methods for CnfUniverse work correctly", { + u = CnfUniverse() + CnfSymbol(u, "X", c("a", "b", "c")) + + # Test print method + expect_output(print(u), "CnfUniverse with variables:\n X: \\{a, b, c\\}") + + # Test format method + expect_equal(format(u), "CnfUniverse(1)") + + CnfSymbol(u, "Y", c("d", "e", "f")) + + expect_output(print(u), "CnfUniverse with variables:\n Y: \\{d, e, f\\}\n X: \\{a, b, c\\}|CnfUniverse with variables:\n X: \\{a, b, c\\}\n Y: \\{d, e, f\\}") + expect_equal(format(u), "CnfUniverse(2)") +}) + +# Test print and format methods for an empty CnfUniverse +test_that("print and format methods for empty CnfUniverse work correctly", { + u = CnfUniverse() + + # Test print method + expect_output(print(u), "CnfUniverse \\(empty\\)\\.") + + # Test format method + expect_equal(format(u), "CnfUniverse(0)") +}) From bf63f57007456faba4b0ef4dc83ac7c0bcc5a90c Mon Sep 17 00:00:00 2001 From: mb706 Date: Wed, 11 Sep 2024 19:04:09 +0200 Subject: [PATCH 25/87] preliminary progress --- R/CnfClause.R | 3 ++- tests/testthat/test_CnfClause.R | 31 ++++++++++++++++++++++++++++--- 2 files changed, 30 insertions(+), 4 deletions(-) diff --git a/R/CnfClause.R b/R/CnfClause.R index 47025b3d2..08274772c 100644 --- a/R/CnfClause.R +++ b/R/CnfClause.R @@ -237,8 +237,9 @@ as.logical.CnfClause = function(x, ...) { check_logical(i, len = true_length), .var.name = "i" ) + entries = unclass(x)[i] structure( - unclass(x)[i], + if (length(entries)) entries else FALSE, universe = attr(x, "universe"), class = "CnfClause" ) diff --git a/tests/testthat/test_CnfClause.R b/tests/testthat/test_CnfClause.R index 4e187c4a5..4884a5ed9 100644 --- a/tests/testthat/test_CnfClause.R +++ b/tests/testthat/test_CnfClause.R @@ -184,6 +184,7 @@ test_that("Negation of CnfClause works correctly", { # Check that negation of a contradiction is a tautology expect_true(as.logical(!contradiction)) + expect_s3_class(!contradiction, "CnfFormula") }) # Test subset operations on CnfClause @@ -199,9 +200,20 @@ test_that("Subsetting of CnfClause works correctly", { expect_s3_class(subset_clause, "CnfClause") expect_length(as.list(subset_clause), 1) expect_identical(as.list(subset_clause)[[1]]$symbol, "X") + expect_identical(subset_clause, CnfClause(list(CnfAtom(X, c("a", "b"))))) + + expect_identical(clause[0], CnfClause(list(CnfAtom(X, character(0))))) + expect_identical(clause[integer(0)], CnfClause(list(CnfAtom(X, character(0))))) + expect_identical(clause[c(FALSE, FALSE)], CnfClause(list(CnfAtom(X, character(0))))) + + expect_error(clause["Z"], "Must be a subset of \\{'X','Y'\\}") + + expect_identical(clause[c(1, 2)], clause) + expect_identical(clause[c(TRUE, TRUE)], clause) + + expect_identical(clause[c(1, 2, 1, 2)], clause) + expect_identical(clause[c(1, 0, 2, 0)], clause) - expect_error(clause[0], "Cannot subset a FALSE clause") - expect_error(clause["Z"], "Invalid index type.") }) # Test print and format methods for CnfClause @@ -213,7 +225,7 @@ test_that("print and format methods for CnfClause work correctly", { clause = CnfClause(list(CnfAtom(X, c("a", "b")), CnfAtom(Y, c("d")))) # Test print method - expect_output(print(clause), "CnfClause") + expect_output(print(clause), "CnfClause:\n X . \\{a, b\\} \\| Y . \\{d\\}|CnfClause:\n Y . \\{d\\} \\| X . \\{a, b\\}") # Test format method expect_equal(format(clause), "CnfClause(2)") @@ -237,4 +249,17 @@ test_that("as.logical and as.CnfClause conversions work correctly", { expect_s3_class(as.CnfClause(FALSE), "CnfClause") expect_false(as.logical(as.CnfClause(FALSE))) + + atom_neither = CnfClause(list(CnfAtom(X, c("a", "b")))) + expect_identical(as.logical(atom_neither), NA) +}) + +# Test invalid creation of CnfClause with clauses from different universes +test_that("CnfClause throws error when clauses are from different universes", { + u1 = CnfUniverse() + u2 = CnfUniverse() + X1 = CnfSymbol(u1, "X", c("a", "b", "c")) + X2 = CnfSymbol(u2, "X", c("a", "b", "c")) + + expect_error(CnfClause(list(CnfAtom(X1, c("a", "b")), CnfAtom(X2, c("a", "b")))), "All symbols must be in the same universe") }) From 1b2d474549636446cae6ac0c4bdd09a0ba746d85 Mon Sep 17 00:00:00 2001 From: mb706 Date: Wed, 11 Sep 2024 19:04:13 +0200 Subject: [PATCH 26/87] preliminary progress II --- tests/testthat/test_CnfFormula.R | 222 +++++++++++++++++++++++++++++++ 1 file changed, 222 insertions(+) create mode 100644 tests/testthat/test_CnfFormula.R diff --git a/tests/testthat/test_CnfFormula.R b/tests/testthat/test_CnfFormula.R new file mode 100644 index 000000000..61582b9e6 --- /dev/null +++ b/tests/testthat/test_CnfFormula.R @@ -0,0 +1,222 @@ +# Test the creation of a CnfFormula from CnfClauses +test_that("CnfFormula is created correctly from CnfClauses", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + Y = CnfSymbol(u, "Y", c("d", "e", "f")) + + clause1 = CnfClause(list(CnfAtom(X, c("a", "b")))) + clause2 = CnfClause(list(CnfAtom(Y, c("d", "e")))) + + formula = CnfFormula(list(clause1, clause2)) + + expect_s3_class(formula, "CnfFormula") + expect_length(as.list(formula), 2) + + clauses = as.list(formula) + expect_true(identical(clauses[[1]], clause1) || identical(clauses[[1]], clause2)) + expect_true(identical(clauses[[2]], clause1) || identical(clauses[[2]], clause2)) +}) + +# Test the handling of tautologies and contradictions in CnfFormula +test_that("CnfFormula handles tautologies and contradictions correctly", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + Y = CnfSymbol(u, "Y", c("d", "e", "f")) + + tautology = CnfFormula(list(CnfClause(list(CnfAtom(X, c("a", "b", "c")))))) + contradiction = CnfFormula(list(CnfClause(list(CnfAtom(X, character(0)))))) + + # Tautology should evaluate to TRUE + expect_true(as.logical(tautology)) + + # Contradiction should evaluate to FALSE + expect_false(as.logical(contradiction)) + + # Conjunction of a tautology and a clause should result in the clause + atom = CnfAtom(X, c("a")) + clause = CnfClause(list(atom)) + formula = tautology & clause + expect_identical(as.list(formula), list(clause)) + + # Conjunction of a contradiction with a clause should result in contradiction + formula_ctn = contradiction & clause + expect_s3_class(formula_ctn, "CnfFormula") + expect_false(as.logical(formula_ctn)) +}) + +# Test conjunction (&) of CnfFormulas +test_that("Conjunction of CnfFormulas works correctly", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + Y = CnfSymbol(u, "Y", c("d", "e", "f")) + + clause1 = CnfClause(list(CnfAtom(X, c("a", "b")))) + clause2 = CnfClause(list(CnfAtom(Y, c("d", "e")))) + + formula1 = CnfFormula(list(clause1)) + formula2 = CnfFormula(list(clause2)) + + conjunction = formula1 & formula2 + + expect_s3_class(conjunction, "CnfFormula") + expect_length(as.list(conjunction), 2) + + clauses = as.list(conjunction) + expect_true(identical(clauses[[1]], clause1) || identical(clauses[[1]], clause2)) + expect_true(identical(clauses[[2]], clause1) || identical(clauses[[2]], clause2)) + + # Check that conjunction of a tautology with a formula is the formula + tautology = CnfFormula(list(CnfClause(list(CnfAtom(X, c("a", "b", "c")))))) + conjunction_with_tautology = tautology & formula1 + expect_identical(as.list(conjunction_with_tautology), list(clause1)) +}) + +# Test disjunction (|) of CnfFormulas +test_that("Disjunction of CnfFormulas works correctly", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + Y = CnfSymbol(u, "Y", c("d", "e", "f")) + + clause1 = CnfClause(list(CnfAtom(X, c("a")))) + clause2 = CnfClause(list(CnfAtom(Y, c("d")))) + clause3 = CnfClause(list(CnfAtom(X, c("b")))) + clause4 = CnfClause(list(CnfAtom(Y, c("e")))) + + formula1 = CnfFormula(list(clause1, clause2)) + formula2 = CnfFormula(list(clause3, clause4)) + + disjunction = formula1 | formula2 + + expect_s3_class(disjunction, "CnfFormula") + expect_length(as.list(disjunction), 2) + + formula1 + formula2 + + # (X = a & Y = d) | (X = b & Y = e) <=> + # (X = a | X = b) & (Y = d | Y = e) & (X = a | Y = e) & (X = b | Y = d) + ## can drop the first two clauses as they are always true whenever the latter two are true + expected_clause_1 = CnfClause(list(CnfAtom(X, "a"), CnfAtom(Y, "e"))) + expected_clause_2 = CnfClause(list(CnfAtom(X, "b"), CnfAtom(Y, "d"))) + + clauses = as.list(disjunction) + expect_true(isTRUE(all.equal(clauses[[1]], expected_clause_1)) || isTRUE(all.equal(clauses[[1]], expected_clause_2))) + expect_true(isTRUE(all.equal(clauses[[1]], expected_clause_2)) || isTRUE(all.equal(clauses[[1]], expected_clause_1))) + + # Check that disjunction of a tautology with a formula is the same formula + tautology = CnfFormula(list(CnfClause(list(CnfAtom(X, c("a", "b", "c")))))) + disjunction_with_tautology = tautology | formula1 + expect_s3_class(disjunction_with_tautology, "CnfFormula") + expect_true( + identical(as.list(disjunction_with_tautology), list(clause1, clause2)) || + identical(as.list(disjunction_with_tautology), list(clause2, clause1)) + ) +}) + +# Test negation of CnfFormula +test_that("Negation of CnfFormula works correctly", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + Y = CnfSymbol(u, "Y", c("d", "e", "f")) + + clause = CnfClause(list(CnfAtom(X, c("a", "b")), CnfAtom(Y, c("d")))) + formula = CnfFormula(list(clause)) + + negated_formula = !formula + + expect_s3_class(negated_formula, "CnfFormula") + expect_length(as.list(negated_formula), 2) + + expect_true( + identical(as.list(negated_formula), list(CnfClause(list(CnfAtom(X, "c"))), CnfClause(list(CnfAtom(Y, c("e", "f")))))) || + identical(as.list(negated_formula), list(CnfClause(list(CnfAtom(Y, c("e", "f")))), CnfClause(list(CnfAtom(X, "c"))))) + ) + + # Check that negation of a tautology is a contradiction + tautology = CnfFormula(list(CnfClause(list(CnfAtom(X, c("a", "b", "c")))))) + expect_false(as.logical(!tautology)) + + # Check that negation of a contradiction is a tautology + contradiction = CnfFormula(list(CnfClause(list(CnfAtom(X, character(0)))))) + expect_true(as.logical(!contradiction)) +}) + +# Test complex conjunction and disjunction operations on CnfFormula +test_that("Complex operations on CnfFormula work correctly", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + Y = CnfSymbol(u, "Y", c("d", "e", "f")) + Z = CnfSymbol(u, "Z", c("g", "h", "i")) + + formula1 = (CnfAtom(X, c("a", "b")) | CnfAtom(Y, c("d", "e"))) & CnfAtom(Z, c("g", "h")) + formula2 = !(CnfAtom(X, c("a", "b")) | CnfAtom(Y, c("d", "e"))) + + expect_s3_class(formula1, "CnfFormula") + expect_s3_class(formula2, "CnfFormula") + + # Check that complex formula works correctly with negation and conjunction + negated_formula1 = !formula1 + expect_s3_class(negated_formula1, "CnfFormula") + + conjunction_formula = formula1 & formula2 + expect_s3_class(conjunction_formula, "CnfFormula") + + # conjunction_formula is a contradiction, since formula2 is the negation of the + # first part of formula1. + # We don't yet test whether this is obvious enough for the simplification algorithm + # to catch, but negating it should give a tautology that can directly be recognized; + expect_true(!conjunction_formula) +}) + +# Test print and format methods for CnfFormula +test_that("print and format methods for CnfFormula work correctly", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + Y = CnfSymbol(u, "Y", c("d", "e", "f")) + + formula = CnfFormula(list(CnfClause(list(CnfAtom(X, c("a", "b")), CnfAtom(Y, c("d")))))) + + # Test print method + expect_output(print(formula), "CnfFormula:\n \\(X . \\{a, b\\} \\| Y . \\{d\\}\\)|CnfFormula:\n \\(Y . \\{d\\} \\| X . \\{a, b\\}\\)") + + # Test format method + expect_equal(format(formula), "CnfFormula(1)") +}) + +# Test conversion between logical and CnfFormula +test_that("as.logical and as.CnfFormula conversions work correctly", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + Y = CnfSymbol(u, "Y", c("d", "e", "f")) + + formula_true = CnfFormula(list(CnfClause(list(CnfAtom(X, c("a", "b", "c")))))) + formula_false = CnfFormula(list(CnfClause(list(CnfAtom(X, character(0)))))) + + # Convert CnfFormula to logical + expect_true(as.logical(formula_true)) + expect_false(as.logical(formula_false)) + + # Convert logical to CnfFormula + expect_s3_class(as.CnfFormula(TRUE), "CnfFormula") + expect_true(as.logical(as.CnfFormula(TRUE))) + + expect_s3_class(as.CnfFormula(FALSE), "CnfFormula") + expect_false(as.logical(as.CnfFormula(FALSE))) + + expect_identical(as.logical(CnfFormula(list(CnfClause(list(CnfAtom(X, c("a", "b")))))) & CnfFormula(list(CnfClause(list(CnfAtom(Y, c("d"))))))), + NA + ) +}) + +# Test invalid creation of CnfFormula with clauses from different universes +test_that("CnfFormula throws error when clauses are from different universes", { + u1 = CnfUniverse() + u2 = CnfUniverse() + X1 = CnfSymbol(u1, "X", c("a", "b", "c")) + X2 = CnfSymbol(u2, "X", c("a", "b", "c")) + + clause1 = CnfClause(list(CnfAtom(X1, c("a", "b")))) + clause2 = CnfClause(list(CnfAtom(X2, c("a", "b")))) + + expect_error(CnfFormula(list(clause1, clause2)), "All clauses must be in the same universe") +}) From 43951821755589db537d3ace7c6ee8f61cf84400 Mon Sep 17 00:00:00 2001 From: mb706 Date: Thu, 12 Sep 2024 00:03:51 +0200 Subject: [PATCH 27/87] more tests and some fixes --- R/CnfClause.R | 5 +- R/CnfFormula.R | 12 ++- tests/testthat/test_CnfAtom.R | 85 ++++++++++++++++ tests/testthat/test_CnfClause.R | 122 +++++++++++++++++++++++ tests/testthat/test_CnfFormula.R | 158 ++++++++++++++++++++++++++++++ tests/testthat/test_CnfSymbol.R | 23 +++++ tests/testthat/test_CnfUniverse.R | 27 +++++ 7 files changed, 427 insertions(+), 5 deletions(-) diff --git a/R/CnfClause.R b/R/CnfClause.R index 08274772c..f61991644 100644 --- a/R/CnfClause.R +++ b/R/CnfClause.R @@ -263,8 +263,11 @@ all.equal.CnfClause = function(target, current, ...) { } normalize = function(clause) { + reorder = order(names(clause)) # []-assign to preserve class and attributes - clause[] = lapply(unclass(clause)[order(names(clause))], sort) + clause[] = lapply(unclass(clause)[reorder], sort) + names(clause) = names(clause)[reorder] # also reorder names + clause } target = normalize(target) diff --git a/R/CnfFormula.R b/R/CnfFormula.R index 4aff7f4f3..113101d49 100644 --- a/R/CnfFormula.R +++ b/R/CnfFormula.R @@ -263,14 +263,18 @@ all.equal.CnfFormula = function(target, current, ...) { normalize = function(formula) { formula[] = lapply(unclass(formula), function(clause) { - clause[] = lapply(unclass(clause)[order(names(clause))], sort) - clause + lapply(unclass(clause)[order(names(clause))], sort) }) # sort by symbol names, then by hash # note we had to sort elements internally first before we can do this! - formula[] = formula[order(map_chr(unclass(target), function(clause) { + reorder = order(map_chr(unclass(formula), function(clause) { paste0(paste(names(clause), collapse = ".__."), digest::digest(c(clause), algo = "xxhash64")) - }))] + })) + formula[] = formula[reorder] + # formula should not have names, but in case this ever changes: + # change the names in the same order as the clauses + names(formula) = names(formula)[reorder] + formula } target = normalize(target) diff --git a/tests/testthat/test_CnfAtom.R b/tests/testthat/test_CnfAtom.R index fad1d685e..43d682b9c 100644 --- a/tests/testthat/test_CnfAtom.R +++ b/tests/testthat/test_CnfAtom.R @@ -161,3 +161,88 @@ test_that("CnfAtom throws error when values are not in the symbol's domain", { expect_error(CnfAtom(X, c("d", "e")), "Must be a subset of \\{'a','b','c'\\}") }) + +test_that("all.equal recognizes (in)equality", { +# Test equality between identical CnfAtoms + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + + atom1 = CnfAtom(X, c("a", "b")) + atom2 = CnfAtom(X, c("a", "b")) + + expect_true(all.equal(atom1, atom2)) + + # Test equality for different CnfAtoms with the same symbol but different values + + atom1 = CnfAtom(X, c("a", "b")) + atom2 = CnfAtom(X, c("b", "c")) + + expect_string(all.equal(atom1, atom2), pattern = "string mismatch") + + # Test equality for different CnfAtoms with the same values but different order + atom1 = CnfAtom(X, c("a", "b")) + atom2 = CnfAtom(X, c("b", "a")) + + expect_true(all.equal(atom1, atom2)) + + # Test equality for CnfAtoms with different symbols + Y = CnfSymbol(u, "Y", c("d", "e", "f")) + + atom1 = CnfAtom(X, c("a", "b")) + atom2 = CnfAtom(Y, c("d")) + + expect_string(paste(all.equal(atom1, atom2), collapse = "\n"), pattern = "string mismatch") + + # Test equality between a logical CnfAtom and a CnfAtom object + + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + + atom1 = CnfAtom(X, c("a", "b")) + atom2 = CnfAtom(X, c("a", "b", "c")) + + + expect_string(all.equal(atom1, atom2), pattern = "not both logicals") + expect_string(all.equal(atom2, atom1), pattern = "not both logicals") + + # Test equality for a logical TRUE CnfAtom and another logical TRUE CnfAtom + atom3 = CnfAtom(Y, c("d", "e", "f")) + + expect_true(all.equal(atom2, atom3)) + expect_true(all.equal(atom2, as.CnfAtom(TRUE))) + + # Test equality for a logical FALSE CnfAtom and another logical FALSE CnfAtom + + logical_atom1 = CnfAtom(X, character(0)) + logical_atom2 = CnfAtom(Y, character(0)) + + expect_true(all.equal(logical_atom1, logical_atom2)) + expect_string(all.equal(atom1, logical_atom1), pattern = "not both logicals") + expect_string(all.equal(atom2, logical_atom1), pattern = "both logicals but not equal") + expect_true(all.equal(logical_atom1, as.CnfAtom(FALSE))) + + # Test for a case where a CnfAtom is compared with a non-CnfAtom object + + + expect_string(all.equal(atom1, "not a CnfAtom"), pattern = "current is not a CnfAtom") + + # Test that all.equal accepts differences in the universe of the CnfAtoms + + u1 = CnfUniverse() + u2 = CnfUniverse() + X1 = CnfSymbol(u1, "X", c("a", "b", "c")) + X2 = CnfSymbol(u2, "X", c("a", "b", "c")) + + atom1 = CnfAtom(X1, c("a", "b")) + atom2 = CnfAtom(X2, c("a", "b")) + + expect_true(all.equal(atom1, atom2)) + + # .. unless the universes differ + u3 = CnfUniverse() + X3 = CnfSymbol(u3, "X", c("a", "b", "c", "d")) + atom3 = CnfAtom(X3, c("a", "b")) + + expect_string(all.equal(atom1, atom3), pattern = "Lengths \\(3, 4\\) differ") + +}) diff --git a/tests/testthat/test_CnfClause.R b/tests/testthat/test_CnfClause.R index 4884a5ed9..cf6033ee2 100644 --- a/tests/testthat/test_CnfClause.R +++ b/tests/testthat/test_CnfClause.R @@ -263,3 +263,125 @@ test_that("CnfClause throws error when clauses are from different universes", { expect_error(CnfClause(list(CnfAtom(X1, c("a", "b")), CnfAtom(X2, c("a", "b")))), "All symbols must be in the same universe") }) + + +test_that("all.equal recognizes (in)equality for CnfClause", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + Y = CnfSymbol(u, "Y", c("d", "e", "f")) + + # Test equality between identical CnfClauses + atom1 = CnfAtom(X, c("a", "b")) + atom2 = CnfAtom(Y, c("d", "e")) + clause1 = CnfClause(list(atom1, atom2)) + clause2 = CnfClause(list(atom1, atom2)) + + expect_true(all.equal(clause1, clause2)) + + # Test equality with the same atoms but in different order + clause2 = CnfClause(list(atom2, atom1)) + + expect_true(all.equal(clause1, clause2)) + + # Test inequality for different CnfClauses with the same symbols but different values + atom3 = CnfAtom(X, c("b", "c")) + clause2 = CnfClause(list(atom3, atom2)) + + expect_string(all.equal(clause1, clause2), pattern = "string mismatches") + + # Test equality for CnfClauses where the values of one symbol are in a different order + atom4 = CnfAtom(X, c("b", "a")) # same values, different order + clause2 = CnfClause(list(atom4, atom2)) + + expect_true(all.equal(clause1, clause2)) + + # Test inequality when symbols in CnfClauses differ + Z = CnfSymbol(u, "Z", c("g", "h", "i")) + atom5 = CnfAtom(Z, c("g")) + clause2 = CnfClause(list(atom1, atom5)) + + expect_string(paste(all.equal(clause1, clause2), collapse = "\n"), pattern = "string mismatch") + + # Test equality for logical CnfClause (TRUE and FALSE) vs a clause + clause_tautology = CnfClause(list(CnfAtom(X, c("a", "b", "c")))) # tautology (TRUE) + clause_contradiction = CnfClause(list(CnfAtom(X, character(0)))) # contradiction (FALSE) + + expect_string(all.equal(clause1, clause_tautology), pattern = "not both logicals") + expect_string(all.equal(clause1, clause_contradiction), pattern = "not both logicals") + expect_string(all.equal(clause_tautology, clause_contradiction), pattern = "logicals but not equal") + + # Test equality for a logical TRUE clause and another logical TRUE clause + atom_ttl1 = CnfAtom(X, c("a", "b", "c")) + atom_ttl2 = CnfAtom(Y, c("d", "e", "f")) + clause_ttl1 = CnfClause(list(atom_ttl1)) + clause_ttl2 = CnfClause(list(atom_ttl2)) + + expect_true(all.equal(clause_ttl1, clause_ttl2)) + expect_true(all.equal(clause_ttl1, as.CnfClause(TRUE))) + + # Test equality for a logical FALSE clause and another logical FALSE clause + clause_false1 = CnfClause(list(CnfAtom(X, character(0)))) + clause_false2 = CnfClause(list(CnfAtom(Y, character(0)))) + + expect_true(all.equal(clause_false1, clause_false2)) + expect_true(all.equal(clause_false1, as.CnfClause(FALSE))) + + # Test inequality between a CnfClause and a non-CnfClause object + expect_string(all.equal(clause1, "not a CnfClause"), pattern = "current is not a CnfClause") + + # Test equality between CnfClauses in different universes + u1 = CnfUniverse() + u2 = CnfUniverse() + X1 = CnfSymbol(u1, "X", c("a", "b", "c")) + X2 = CnfSymbol(u2, "X", c("a", "b", "c")) + + atom_u1 = CnfAtom(X1, c("a", "b")) + atom_u2 = CnfAtom(X2, c("a", "b")) + clause_u1 = CnfClause(list(atom_u1)) + clause_u2 = CnfClause(list(atom_u2)) + + expect_true(all.equal(clause_u1, clause_u2)) + + # Test inequality when universes differ in length + u3 = CnfUniverse() + X3 = CnfSymbol(u3, "X", c("a", "b", "c", "d")) + atom_u3 = CnfAtom(X3, c("a", "b")) + clause_u3 = CnfClause(list(atom_u3)) + + expect_string(all.equal(clause_u1, clause_u3), pattern = "Lengths \\(3, 4\\) differ") + + # Explicitly constructed object all.equals test + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + Y = CnfSymbol(u, "Y", c("d", "e", "f")) + Z = CnfSymbol(u, "Z", c("g", "h", "i")) + + c1 = structure(list( + X = c("a", "b"), Y = c("d") + ), universe = u, class = "CnfClause") + c2 = structure(list( + X = c("b", "a"), Y = c("d") + ), universe = u, class = "CnfClause") + c3 = structure(list( + Y = c("d"), X = c("a", "b") + ), universe = u, class = "CnfClause") + c4 = structure(list( + Y = c("d"), X = c("b", "a") + ), universe = u, class = "CnfClause") + c_unequal = structure(list( + X = c("a", "b"), Z = c("g") + ), universe = u, class = "CnfClause") + + + for (cx in list(c1, c2, c3, c4)) { + for (cy in list(c1, c2, c3, c4)) { + expect_true(all.equal(cx, cy)) + } + } + + for (cx in list(c1, c2, c3, c4)) { + expect_string(paste(all.equal(cx, c_unequal), collapse = "\n"), pattern = "string mismatch|[Ll]ength mismatch") + } + + +}) diff --git a/tests/testthat/test_CnfFormula.R b/tests/testthat/test_CnfFormula.R index 61582b9e6..fe0fc2a19 100644 --- a/tests/testthat/test_CnfFormula.R +++ b/tests/testthat/test_CnfFormula.R @@ -220,3 +220,161 @@ test_that("CnfFormula throws error when clauses are from different universes", { expect_error(CnfFormula(list(clause1, clause2)), "All clauses must be in the same universe") }) + + +test_that("all.equal recognizes (in)equality for CnfFormula", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + Y = CnfSymbol(u, "Y", c("d", "e", "f")) + Z = CnfSymbol(u, "Z", c("g", "h", "i")) + + # Test equality between identical CnfFormulas + atom1 = CnfAtom(X, c("a", "b")) + atom2 = CnfAtom(Y, c("d", "e")) + clause1 = CnfClause(list(atom1, atom2)) + + atom3 = CnfAtom(Z, c("g")) + clause2 = CnfClause(list(atom3)) + + formula1 = CnfFormula(list(clause1, clause2)) + formula2 = CnfFormula(list(clause1, clause2)) + + expect_true(all.equal(formula1, formula2)) + + # Test equality with the same clauses but in different order + formula2 = CnfFormula(list(clause2, clause1)) + + expect_true(all.equal(formula1, formula2)) + + # Test inequality for different CnfFormulas with different atoms + atom4 = CnfAtom(X, c("b", "c")) + clause3 = CnfClause(list(atom4, atom2)) + formula2 = CnfFormula(list(clause3, clause2)) + + expect_string(all.equal(formula1, formula2), pattern = "string mismatch") + + # Test equality for CnfFormulas where the values of one symbol in clauses are in a different order + atom5 = CnfAtom(X, c("b", "a")) # same values, different order + clause4 = CnfClause(list(atom5, atom2)) + formula2 = CnfFormula(list(clause4, clause2)) + + expect_true(all.equal(formula1, formula2)) + + # Test inequality when formulas have different symbols + atom6 = CnfAtom(Z, c("h")) + clause5 = CnfClause(list(atom6)) + formula2 = CnfFormula(list(clause1, clause5)) + + expect_string(all.equal(formula1, formula2), pattern = "string mismatch") + + # Test equality for logical CnfFormula (TRUE and FALSE) vs a formula + formula_tautology = CnfFormula(list(CnfClause(list(CnfAtom(X, c("a", "b", "c")))))) # tautology (TRUE) + formula_contradiction = CnfFormula(list(CnfClause(list(CnfAtom(X, character(0)))))) # contradiction (FALSE) + + expect_string(all.equal(formula1, formula_tautology), pattern = "not both logicals") + expect_string(all.equal(formula1, formula_contradiction), pattern = "not both logicals") + + # Test equality for a logical TRUE formula and another logical TRUE formula + clause_ttl1 = CnfClause(list(CnfAtom(X, c("a", "b", "c")))) + clause_ttl2 = CnfClause(list(CnfAtom(Y, c("d", "e", "f")))) + formula_ttl1 = CnfFormula(list(clause_ttl1)) + formula_ttl2 = CnfFormula(list(clause_ttl2)) + + expect_true(all.equal(formula_ttl1, formula_ttl2)) + expect_true(all.equal(formula_ttl1, as.CnfFormula(TRUE))) + + # Test equality for a logical FALSE formula and another logical FALSE formula + formula_false1 = CnfFormula(list(CnfClause(list(CnfAtom(X, character(0)))))) + formula_false2 = CnfFormula(list(CnfClause(list(CnfAtom(Y, character(0)))))) + + expect_true(all.equal(formula_false1, formula_false2)) + expect_string(all.equal(formula1, formula_false1), pattern = "not both logicals") + expect_true(all.equal(formula_false1, as.CnfFormula(FALSE))) + + # Test inequality between a CnfFormula and a non-CnfFormula object + expect_string(all.equal(formula1, "not a CnfFormula"), pattern = "current is not a CnfFormula") + + # Test equality between CnfFormulas in different universes + u1 = CnfUniverse() + u2 = CnfUniverse() + X1 = CnfSymbol(u1, "X", c("a", "b", "c")) + X2 = CnfSymbol(u2, "X", c("a", "b", "c")) + + atom_u1 = CnfAtom(X1, c("a", "b")) + atom_u2 = CnfAtom(X2, c("a", "b")) + clause_u1 = CnfClause(list(atom_u1)) + clause_u2 = CnfClause(list(atom_u2)) + formula_u1 = CnfFormula(list(clause_u1)) + formula_u2 = CnfFormula(list(clause_u2)) + + expect_true(all.equal(formula_u1, formula_u2)) + + # Test inequality when universes differ in length + u3 = CnfUniverse() + X3 = CnfSymbol(u3, "X", c("a", "b", "c", "d")) + atom_u3 = CnfAtom(X3, c("a", "b")) + clause_u3 = CnfClause(list(atom_u3)) + formula_u3 = CnfFormula(list(clause_u3)) + + expect_string(all.equal(formula_u1, formula_u3), pattern = "Lengths \\(3, 4\\) differ") + + # Test disjunction and conjunction in CnfFormula + atom7 = CnfAtom(X, c("a")) + atom8 = CnfAtom(Y, c("d")) + clause6 = CnfClause(list(atom7, atom8)) + clause7 = CnfClause(list(atom1, atom2)) + + formula1 = CnfFormula(list(clause6)) + formula2 = CnfFormula(list(clause7)) + + formula_disjunction = formula1 | formula2 + formula_conjunction = formula1 & formula2 + + # Test all.equal on conjunction and disjunction cases + expect_string(paste(all.equal(formula_disjunction, formula1), collapse = "\n"), pattern = "Lengths \\(2, 1\\) differ") + expect_true(all.equal(formula_conjunction, formula1)) + + + # Explicitly constructed object all.equals test + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + Y = CnfSymbol(u, "Y", c("d", "e", "f")) + Z = CnfSymbol(u, "Z", c("g", "h", "i")) + + f1 = structure(list( + list(X = c("a", "b"), Y = c("d")), + list(Z = c("g")) + ), universe = u, class = "CnfFormula") + f2 = structure(list( + list(Y = c("d"), X = c("a", "b")), + list(Z = c("g")) + ), universe = u, class = "CnfFormula") + f3 = structure(list( + list(X = c("b", "a"), Y = c("d")), + list(Z = c("g")) + ), universe = u, class = "CnfFormula") + f4 = structure(list( + list(Y = c("d"), X = c("b", "a")), + list(Z = c("g")) + ), universe = u, class = "CnfFormula") + f5 = structure(list( + list(Z = c("g")), + list(X = c("a", "b"), Y = c("d")) + ), universe = u, class = "CnfFormula") + + f1_unequal = structure(list( + list(X = c("a", "b")), + list(Z = c("g")) + ), universe = u, class = "CnfFormula") + + for (fx in list(f1, f2, f3, f4, f5)) { + for (fy in list(f1, f2, f3, f4, f5)) { + expect_true(all.equal(fx, fy)) + } + } + + for (fx in list(f1, f2, f3, f4, f5)) { + expect_string(all.equal(fx, f1_unequal), pattern = "string mismatch|[Ll]ength mismatch") + } + +}) diff --git a/tests/testthat/test_CnfSymbol.R b/tests/testthat/test_CnfSymbol.R index 44adf2e28..0e52db6ca 100644 --- a/tests/testthat/test_CnfSymbol.R +++ b/tests/testthat/test_CnfSymbol.R @@ -59,3 +59,26 @@ test_that("Invalid values in %among% operator throw an error", { expect_error(X %among% c("d", "e"), "values.*Must be a subset of") }) + +test_that("all.equal recognizes (in)equality", { + + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + + expect_true(all.equal(X, X)) + + u2 = CnfUniverse() + X2 = CnfSymbol(u2, "X", c("a", "b", "c")) + + expect_true(all.equal(X, X2)) + + u3 = CnfUniverse() + X3 = CnfSymbol(u3, "X", c("a", "b", "c")) + Y3 = CnfSymbol(u3, "Y", c("d", "e", "f")) + + expect_string(all.equal(X2, X3), pattern = "Attributes") + + expect_string(all.equal(X3, Y3), "string mismatch") + + +}) diff --git a/tests/testthat/test_CnfUniverse.R b/tests/testthat/test_CnfUniverse.R index 47bb9bcef..16b3fe913 100644 --- a/tests/testthat/test_CnfUniverse.R +++ b/tests/testthat/test_CnfUniverse.R @@ -61,3 +61,30 @@ test_that("print and format methods for empty CnfUniverse work correctly", { # Test format method expect_equal(format(u), "CnfUniverse(0)") }) + + +test_that("all.equal recognizes (in)equality", { + + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + + expect_true(all.equal(u, u)) + + u2 = CnfUniverse() + X2 = CnfSymbol(u2, "X", c("a", "b", "c")) + + expect_true(all.equal(u, u2)) + + u_empty = CnfUniverse() + u_empty_2 = CnfUniverse() + + expect_true(all.equal(u_empty, u_empty_2)) + + u3 = CnfUniverse() + X3 = CnfSymbol(u3, "X", c("c", "b", "a")) + + expect_string(all.equal(u, u3), pattern = "string mismatch") + + expect_string(paste(all.equal(u, u_empty), collapse = "\n"), pattern = "Length mismatch") + +}) From b0267d8f8ce29e46fa5f16d6425bb70bc8ce4c09 Mon Sep 17 00:00:00 2001 From: mb706 Date: Thu, 12 Sep 2024 03:45:17 +0200 Subject: [PATCH 28/87] omg I can't believe I did this --- R/CnfClause.R | 5 +- R/CnfFormula.R | 2 +- R/CnfFormula_simplify.R | 10 +- tests/testthat/test_CnfClause.R | 24 +++ tests/testthat/test_CnfFormula.R | 307 ++++++++++++++++++++++++++++++- 5 files changed, 336 insertions(+), 12 deletions(-) diff --git a/R/CnfClause.R b/R/CnfClause.R index f61991644..99d087f3a 100644 --- a/R/CnfClause.R +++ b/R/CnfClause.R @@ -189,9 +189,10 @@ as.CnfClause.CnfClause = function(x) { #' @export as.list.CnfClause = function(x) { - if (isFALSE(x)) return(list()) + x_bare = c(x) + if (isFALSE(x_bare)) return(list()) x = unclass(x) - if (isTRUE(x)) return(as.CnfAtom(x)) + if (isTRUE(x_bare)) return(as.CnfAtom(x)) lapply(names(x), function(sym) { structure(list(symbol = sym, values = x[[sym]]), universe = attr(x, "universe"), class = "CnfAtom") }) diff --git a/R/CnfFormula.R b/R/CnfFormula.R index 113101d49..ebd657085 100644 --- a/R/CnfFormula.R +++ b/R/CnfFormula.R @@ -307,7 +307,7 @@ chooseOpsMethod.CnfFormula <- function(x, y, mx, my, cl, reverse) TRUE e1 = as.CnfFormula(e1) e2 = as.CnfFormula(e2) if (isFALSE(e1_bare) || isTRUE(e2_bare)) return(e2) - if (isFALSE(e2_bare) || isFALSE(e1_bare)) return(e1) + if (isFALSE(e2_bare) || isTRUE(e1_bare)) return(e1) if (!identical(attr(e1, "universe"), attr(e2, "universe"))) { stop("Both formulas must be in the same universe.") } diff --git a/R/CnfFormula_simplify.R b/R/CnfFormula_simplify.R index bd3854d35..52ebb3097 100644 --- a/R/CnfFormula_simplify.R +++ b/R/CnfFormula_simplify.R @@ -65,15 +65,18 @@ simplify_cnf = function(entries, universe) { if (eliminated[[i]]) next # can only happen if we do the hidden subsumption elimination, which searches forward ei = entries[[i]] # If sym(A) is a subset of sym(B) and for each s in sym(A), val(A, s) is a subset of val(B, s), then A implies B, so B can be removed ("subsumption elimination"). - for (j in seq_len(i - 1)) { + for (j in seq_along(entries)) { + if (j == i) next if (eliminated[[j]]) next ej = entries[[j]] + if (length(ej) > length(ei)) break # we can't just do j in 1:(i-1), since some clauses have the same length, in which case we need to check subsumption. name_overlap = names(ej) %in% names(ei) if (all(name_overlap) && all(sapply(names(ej), function(s) all(ej[[s]] %in% ei[[s]])))) { # can't do entries[[i]] = NULL, since we are iterating over entries; the entries[[i]] would break. eliminated[[i]] = TRUE break } + if (j >= i) next # everything that follows already checks in both directions in case of equal lengths. # simple self subsumption and hidden subsumption elimination # HSE: # if s is in sym(A) and sym(B), and val(A, s) and val(B, s) are disjoint, then (A - s | B - s) is implied, @@ -110,7 +113,7 @@ simplify_cnf = function(entries, universe) { # They may, however, have the same number of terms, in which case the reverse is also possible. # Use 'c()' to drop attributes from ei here. ei_without_s = ei[cnames_s] - do_sse = identical(cnames[cnames_s], c(ei_without_s)) + do_sse = identical(cunion[cnames_s], c(ei_without_s)) # if they have the same number of terms, ei could be a subset of ej. # However, then we can not rely on the order of values in the union being correct. do_sse_reverse = (!do_sse && (length(ei) == length(ej)) && @@ -125,7 +128,7 @@ simplify_cnf = function(entries, universe) { } else if (do_sse) { # ej is a subset of ei # --> eliminate s from ei - new_entry = entries[[i]] = ei_without_s + new_entry = entries[[i]] = ei = ei_without_s dont_eliminate = i } @@ -161,6 +164,7 @@ simplify_cnf = function(entries, universe) { eliminated[[k]] = TRUE } } + if (eliminated[[j]]) break # we eliminated one of the entries we are currently looking at, no more need to look at other symbols next } } diff --git a/tests/testthat/test_CnfClause.R b/tests/testthat/test_CnfClause.R index cf6033ee2..452490068 100644 --- a/tests/testthat/test_CnfClause.R +++ b/tests/testthat/test_CnfClause.R @@ -61,6 +61,30 @@ test_that("CnfClause with overlapping symbols works correctly", { }) +test_that("CnfClause can be called with CnfClauses", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + Y = CnfSymbol(u, "Y", c("d", "e", "f")) + + atom1 = CnfAtom(X, "a") + atom2 = CnfAtom(Y, "d") + atom3 = CnfAtom(X, "b") + atom4 = CnfAtom(Y, "e") + clause1 = CnfClause(list(atom1)) + clause2 = CnfClause(list(atom2)) + clause3 = CnfClause(list(atom3)) + clause4 = CnfClause(list(atom4)) + + clause_1_3 = CnfClause(list(atom1, atom3)) + clause_2_4 = CnfClause(list(atom2, atom4)) + + expect_true(all.equal(clause_1_3, CnfClause(list(clause1, clause3)))) + expect_true(all.equal(clause_1_3 | clause2, CnfClause(list(clause1, clause3, atom2)))) + expect_true(all.equal(CnfClause(list(clause_1_3, clause_2_4)), CnfClause(list(clause1, clause2, clause3, clause4)))) + expect_true(all.equal(CnfClause(list(clause_1_3, clause_2_4)), CnfClause(list(atom1, atom2, atom3, atom4)))) + +}) + # Test the handling of tautologies and contradictions in CnfClause test_that("CnfClause handles tautologies and contradictions correctly", { u = CnfUniverse() diff --git a/tests/testthat/test_CnfFormula.R b/tests/testthat/test_CnfFormula.R index fe0fc2a19..082c886d8 100644 --- a/tests/testthat/test_CnfFormula.R +++ b/tests/testthat/test_CnfFormula.R @@ -44,6 +44,55 @@ test_that("CnfFormula handles tautologies and contradictions correctly", { expect_false(as.logical(formula_ctn)) }) + + +test_that("CnfClause can be called with CnfClauses", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + Y = CnfSymbol(u, "Y", c("d", "e", "f")) + + atom1 = CnfAtom(X, "a") + atom2 = CnfAtom(Y, "d") + atom3 = CnfAtom(X, "b") + atom4 = CnfAtom(Y, "e") + clause1 = CnfClause(list(atom1)) + clause2 = CnfClause(list(atom2)) + clause3 = CnfClause(list(atom3)) + clause4 = CnfClause(list(atom4)) + + clause_1_3 = CnfClause(list(atom1, atom3)) + clause_2_4 = CnfClause(list(atom2, atom4)) + + expect_true(all.equal(clause_1_3, CnfClause(list(clause1, clause3)))) + expect_true(all.equal(clause_1_3 | clause2, CnfClause(list(clause1, clause3, atom2)))) + expect_true(all.equal(CnfClause(list(clause_1_3, clause_2_4)), CnfClause(list(clause1, clause2, clause3, clause4)))) + expect_true(all.equal(CnfClause(list(clause_1_3, clause_2_4)), CnfClause(list(atom1, atom2, atom3, atom4)))) + +}) + + +test_that("CnfFormula can be called with CnfFormulas", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + Y = CnfSymbol(u, "Y", c("d", "e", "f")) + + clause1 = CnfClause(list(CnfAtom(X, c("a", "b")))) + clause2 = CnfClause(list(CnfAtom(Y, c("d", "e")))) + clause3 = CnfClause(list(CnfAtom(X, c("b")))) + + formula1 = CnfFormula(list(clause1)) + formula2 = CnfFormula(list(clause2)) + formula3 = CnfFormula(list(clause3)) + + formula1_2 = CnfFormula(list(clause1, clause2)) + formula1_3 = CnfFormula(list(clause1, clause3)) + + expect_true(all.equal(formula1_2, CnfFormula(list(formula1_2)))) + expect_true(all.equal(formula1_2, CnfFormula(list(formula1, formula2)))) + expect_true(all.equal(formula1_2 & formula1_3, CnfFormula(list(clause1, clause2, clause3)))) + +}) + # Test conjunction (&) of CnfFormulas test_that("Conjunction of CnfFormulas works correctly", { u = CnfUniverse() @@ -103,13 +152,13 @@ test_that("Disjunction of CnfFormulas works correctly", { expect_true(isTRUE(all.equal(clauses[[1]], expected_clause_1)) || isTRUE(all.equal(clauses[[1]], expected_clause_2))) expect_true(isTRUE(all.equal(clauses[[1]], expected_clause_2)) || isTRUE(all.equal(clauses[[1]], expected_clause_1))) - # Check that disjunction of a tautology with a formula is the same formula - tautology = CnfFormula(list(CnfClause(list(CnfAtom(X, c("a", "b", "c")))))) - disjunction_with_tautology = tautology | formula1 - expect_s3_class(disjunction_with_tautology, "CnfFormula") + # Check that disjunction of a contradiction with a formula is the same formula + contradiction = CnfFormula(list(CnfClause(list(CnfAtom(X, character(0)))))) + disjunction_with_contradiction = contradiction | formula1 + expect_s3_class(disjunction_with_contradiction, "CnfFormula") expect_true( - identical(as.list(disjunction_with_tautology), list(clause1, clause2)) || - identical(as.list(disjunction_with_tautology), list(clause2, clause1)) + identical(as.list(disjunction_with_contradiction), list(clause1, clause2)) || + identical(as.list(disjunction_with_contradiction), list(clause2, clause1)) ) }) @@ -378,3 +427,249 @@ test_that("all.equal recognizes (in)equality for CnfFormula", { } }) + + +# Test unit propagation in CnfFormula +test_that("CnfFormula performs unit propagation correctly", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + Y = CnfSymbol(u, "Y", c("d", "e", "f")) + + clause1 = CnfClause(list(CnfAtom(X, c("a", "c")))) # Unit clause: X ∈ {a, c} + clause2 = CnfClause(list(CnfAtom(X, c("a", "b")), CnfAtom(Y, c("d", "e")))) + + formula = CnfFormula(list(clause1, clause2)) + + # Expected: clause2 should be simplified to just X ∈ {a}, Y ∈ {d, e}, since clause1 implies X ∈ {a, c} and c is not in clause2. + expected_formula = CnfFormula(list(clause1, CnfClause(list(CnfAtom(X, c("a")), CnfAtom(Y, c("d", "e")))))) + + expect_true(all.equal(formula, expected_formula)) +}) + +# Test subsumption elimination in CnfFormula +test_that("CnfFormula performs subsumption elimination correctly", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + Y = CnfSymbol(u, "Y", c("d", "e", "f")) + Z = CnfSymbol(u, "Z", c("g", "h", "i")) + + clause1 = CnfClause(list(CnfAtom(X, c("a")), CnfAtom(Y, c("d")))) + clause2 = CnfClause(list(CnfAtom(X, c("a", "b")), CnfAtom(Y, c("d", "e")))) + + formula = CnfFormula(list(clause1, clause2)) + + # Expected: clause2 is subsumed by clause1, so the result should only contain clause1 + expected_formula = CnfFormula(list(clause1)) + + expect_true(all.equal(formula, expected_formula)) + + + expect_true(all.equal( + CnfFormula(list(CnfClause(list(CnfAtom(X, c("a", "b")), CnfAtom(Y, c("d", "e")))), CnfClause(list(CnfAtom(X, c("a")), CnfAtom(Y, c("d", "e")))))), + CnfFormula(list(CnfClause(list(CnfAtom(X, c("a")), CnfAtom(Y, c("d", "e")))))) + )) + + expect_true(all.equal( + CnfFormula(list(CnfClause(list(CnfAtom(X, c("a")), CnfAtom(Y, c("e", "d")))), CnfClause(list(CnfAtom(X, c("a", "b")), CnfAtom(Y, c("d", "e")))))), + CnfFormula(list(CnfClause(list(CnfAtom(X, c("a")), CnfAtom(Y, c("d", "e")))))) + )) + + expect_true(all.equal( + CnfFormula(list(CnfClause(list(CnfAtom(X, c("a")), CnfAtom(Y, c("d", "e")))), CnfClause(list(CnfAtom(X, c("a", "b")), CnfAtom(Y, c("d", "e")), CnfAtom(Z, c("g", "h")))))), + CnfFormula(list(CnfClause(list(CnfAtom(X, c("a")), CnfAtom(Y, c("d", "e")))))) + )) + +}) + +# Test self-subsumption elimination in CnfFormula +test_that("CnfFormula performs self-subsumption elimination correctly", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + Y = CnfSymbol(u, "Y", c("d", "e", "f")) + + clause1 = CnfClause(list(CnfAtom(X, c("a", "b")), CnfAtom(Y, c("d")))) # X ∈ {a, b} | Y ∈ {d} + clause2 = CnfClause(list(CnfAtom(X, c("a")), CnfAtom(Y, c("e")))) # X ∈ {a} | Y ∈ {e} + + # Expected: self-subsumption should simplify the formula + expected_formula = CnfFormula(list(CnfClause(list(CnfAtom(X, c("a", "b")))), CnfClause(list(CnfAtom(X, c("a")), CnfAtom(Y, c("e")))))) + + expect_true(all.equal(CnfFormula(list(clause1, clause2)), expected_formula)) + expect_true(all.equal(CnfFormula(list(clause2, clause1)), expected_formula)) + + clause1 = CnfClause(list(CnfAtom(X, c("a", "b")), CnfAtom(Y, c("d")))) # X ∈ {a, b} | Y ∈ {d} + clause2 = CnfClause(list(CnfAtom(X, c("a", "c")), CnfAtom(Y, c("d")))) # X ∈ {a, b} | Y ∈ {d} + clause3 = CnfClause(list(CnfAtom(X, c("a")), CnfAtom(Y, c("e")))) # X ∈ {a} | Y ∈ {e} + + # Expected: self-subsumption should simplify the formula + expected_formula = CnfFormula(list(CnfClause(list(CnfAtom(X, c("a", "b")))), + CnfClause(list(CnfAtom(X, c("a", "c")))), CnfClause(list(CnfAtom(X, c("a")), CnfAtom(Y, c("e")))))) + + expect_true(all.equal(CnfFormula(list(clause1, clause2, clause3)), expected_formula)) + expect_true(all.equal(CnfFormula(list(clause3, clause2, clause1)), expected_formula)) + expect_true(all.equal(CnfFormula(list(clause1, clause3, clause2)), expected_formula)) + +}) + +# Test hidden subsumption elimination in CnfFormula +test_that("CnfFormula performs hidden subsumption elimination correctly", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + Y = CnfSymbol(u, "Y", c("d", "e", "f")) + + clause1 = CnfClause(list(CnfAtom(X, c("a")), CnfAtom(Y, c("d")))) # X ∈ {a} | Y ∈ {d} + clause2 = CnfClause(list(CnfAtom(X, c("b")), CnfAtom(Y, c("e")))) # X ∈ {b} | Y ∈ {e} + clause3 = CnfClause(list(CnfAtom(Y, c("d", "e")))) # Y ∈ {d, e} + + formula = CnfFormula(list(clause1, clause2, clause3)) + + # Expected: clause3 is implied by clause1 and clause2, so it should be removed + expected_formula = CnfFormula(list(clause1, clause2)) + + expect_true(all.equal(formula, expected_formula)) +}) + +# Test contradiction recognition in CnfFormula +test_that("CnfFormula recognizes simple contradictions", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + + clause1 = CnfClause(list(CnfAtom(X, c("a")))) # X ∈ {a} + clause2 = CnfClause(list(CnfAtom(X, c("b")))) # X ∈ {b} + + formula = CnfFormula(list(clause1, clause2)) + + # Expected: this should be a contradiction + expected_formula = as.CnfFormula(FALSE) + + expect_true(all.equal(formula, expected_formula)) +}) + +# Test simplifications in a larger formula +test_that("CnfFormula performs all simplifications in a complex formula", { + u = CnfUniverse() + X = CnfSymbol(u, "X", c("a", "b", "c")) + Y = CnfSymbol(u, "Y", c("d", "e", "f")) + Z = CnfSymbol(u, "Z", c("g", "h", "i")) + + clause1 = CnfClause(list(CnfAtom(X, c("b", "c")))) # X ∈ {a} + clause2 = CnfClause(list(CnfAtom(X, c("a", "b")), CnfAtom(Y, c("d", "e")))) # X ∈ {b} | Y ∈ {d, e} + clause3 = CnfClause(list(CnfAtom(Y, c("d", "e")), CnfAtom(Z, c("g", "h")))) # Y ∈ {d, e} | Z ∈ {g, h} + clause4 = CnfClause(list(CnfAtom(Z, c("g", "h")))) # Z ∈ {g, h} + + formula = CnfFormula(list(clause1, clause2, clause3, clause4)) + + # Expected: clause3 should be removed, and unit propagation should simplify clause2 + expected_formula = CnfFormula(list( + clause1, clause4, + CnfClause(list(CnfAtom(X, c("b")), CnfAtom(Y, c("d", "e")))) + )) + + expect_true(all.equal(formula, expected_formula)) +}) + + +test_that("Brute-force test", { + skip_on_cran() + + u = CnfUniverse() + W = CnfSymbol(u, "W", c("p", "q", "r")) + X = CnfSymbol(u, "X", c("s", "t", "u")) + Y = CnfSymbol(u, "Y", c("v", "w", "x")) + Z = CnfSymbol(u, "Z", c("y", "z", "a")) + + random_atom_expression = function() { + symbol = sample(alist(W, X, Y, Z), 1)[[1]] + values = sample(u[[deparse(symbol)]], sample(2, 1)) + substitute(symbol %among% values, list(symbol = symbol, values = values)) + } + + random_cnf_expression = function(depth, do_cnf = FALSE, ddepth = 0) { + if (depth <= 1) { + # base case: return a random symbol expression call + return(random_atom_expression()) + } + # recursively build a random tree of expressions + if (do_cnf) { + op = if (depth <= ddepth) quote(`|`) else quote(`&`) + } else { + op = sample(alist(`&`, `|`), 1)[[1]] # randomly choose between AND and OR + } + left_expr = random_cnf_expression(depth - 1, do_cnf, ddepth) + right_expr = random_cnf_expression(depth - 1, do_cnf, ddepth) + + # create a call object for the expression: (left_expr op right_expr) + substitute(op(left_expr, right_expr), list(op = op, left_expr = left_expr, right_expr = right_expr)) + } + + formula_to_expression = function(formula) { + if (is.logical(formula)) return(c(formula)) + clause_exprs = lapply(as.CnfFormula(formula), function(clause) { + atom_exprs = lapply(clause, function(atom) { + substitute(symbol %among% values, list(symbol = as.name(atom$symbol), values = atom$values)) + }) + Reduce(function(x, y) substitute(x | y, list(x = x, y = y)), atom_exprs) + }) + Reduce(function(x, y) substitute(x & y, list(x = x, y = y)), clause_exprs) + } + + evaluate_expression = function(expression, assignment) { + substituted = do.call(substitute, list(expression, c(list("%among%" = quote(`%in%`)), assignment))) + eval(substituted, envir = baseenv()) + } + + expression_weight = function(expression) { + if (is.logical(expression)) return(0) + sum(all.names(expression) %in% c("|", "&")) + 1 + } + + + stats = list(depth = integer(0), expweight = numeric(0), simpweight = numeric(0), was_tautology = logical(0), was_contradiction = logical(0)) + set.seed(2) + for (depth_to_check in 2:11) { + for (repetition in seq_len(200)) { + if (depth_to_check == 10) { + expression = random_cnf_expression(10, TRUE, 4) + } else if (depth_to_check == 11) { + expression = random_cnf_expression(5, TRUE, 2) + } else { + expression = random_cnf_expression(depth_to_check) + } + simplified = formula_to_expression(eval(expression)) + stats$depth[[length(stats$depth) + 1]] = depth_to_check + stats$expweight[[length(stats$expweight) + 1]] = expression_weight(expression) + stats$simpweight[[length(stats$simpweight) + 1]] = expression_weight(simplified) + vars = intersect(names(u), all.names(expression)) + assignments = expand.grid(lapply(vars, function(var) u[[var]]), stringsAsFactors = FALSE) + colnames(assignments) = vars + + truevals = rep(NA, nrow(assignments)) + for (i in seq_len(nrow(assignments))) { + assignment = assignments[i, , drop = FALSE] + trueval = evaluate_expression(expression, assignment) + simpval = evaluate_expression(simplified, assignment) + if (trueval != simpval) break + truevals[[i]] = trueval + } + stats$was_tautology[[length(stats$was_tautology) + 1]] = all(truevals) + stats$was_contradiction[[length(stats$was_contradiction) + 1]] = all(!truevals) + expect_equal(trueval, simpval, + info = sprintf("Expression: %s\nAssignment:\n%s\nSimplified to: %s", + deparse1(expression), + paste(capture.output(print(assignment)), collapse = "\n"), + deparse1(simplified) + )) + } + } + dti <- as.data.table(stats) + dti[, .( + ew = mean(expweight), sw = mean(simpweight), + etriv = mean(expweight == 0), + striv = mean(simpweight == 0), + could_simplify = mean(expweight > simpweight), + was_tautology = mean(was_tautology), + was_contradiction = mean(was_contradiction), + tautologies_not_recognized = mean(was_tautology & simpweight > 0), + contradictions_not_recognized = mean(was_contradiction & simpweight > 0) + ), by = "depth"] + +}) From f93203989ff3733514fbd1e67c31ab297de42468 Mon Sep 17 00:00:00 2001 From: mb706 Date: Thu, 12 Sep 2024 05:26:02 +0200 Subject: [PATCH 29/87] did some experiments --- attic/expressionanalysis.R | 106 +++++++++++++++++++++++++++++++ tests/testthat/test_CnfFormula.R | 8 ++- 2 files changed, 113 insertions(+), 1 deletion(-) create mode 100644 attic/expressionanalysis.R diff --git a/attic/expressionanalysis.R b/attic/expressionanalysis.R new file mode 100644 index 000000000..7c1cf703a --- /dev/null +++ b/attic/expressionanalysis.R @@ -0,0 +1,106 @@ + + +u = CnfUniverse() +W = CnfSymbol(u, "W", c("p", "q", "r")) +X = CnfSymbol(u, "X", c("s", "t", "u")) +Y = CnfSymbol(u, "Y", c("v", "w", "x")) +Z = CnfSymbol(u, "Z", c("y", "z", "a")) + +random_atom_expression = function() { + symbol = sample(alist(W, X, Y, Z), 1)[[1]] + values = sample(u[[deparse(symbol)]], sample(2, 1)) + substitute(symbol %among% values, list(symbol = symbol, values = values)) +} + +random_cnf_expression = function(depth, do_cnf = FALSE, ddepth = 0) { + if (depth <= 1) { + # base case: return a random symbol expression call + return(random_atom_expression()) + } + # recursively build a random tree of expressions + if (do_cnf) { + op = if (depth <= ddepth) quote(`|`) else quote(`&`) + } else { + op = sample(alist(`&`, `|`), 1)[[1]] # randomly choose between AND and OR + } + left_expr = random_cnf_expression(depth - 1, do_cnf, ddepth) + right_expr = random_cnf_expression(depth - 1, do_cnf, ddepth) + + # create a call object for the expression: (left_expr op right_expr) + substitute(op(left_expr, right_expr), list(op = op, left_expr = left_expr, right_expr = right_expr)) +} + +formula_to_expression = function(formula) { + if (is.logical(formula)) return(c(formula)) + clause_exprs = lapply(as.CnfFormula(formula), function(clause) { + atom_exprs = lapply(clause, function(atom) { + substitute(symbol %among% values, list(symbol = as.name(atom$symbol), values = atom$values)) + }) + Reduce(function(x, y) substitute(x | y, list(x = x, y = y)), atom_exprs) + }) + Reduce(function(x, y) substitute(x & y, list(x = x, y = y)), clause_exprs) +} + +evaluate_expression = function(expression, assignment) { + substituted = do.call(substitute, list(expression, c(list("%among%" = quote(`%in%`)), assignment))) + eval(substituted, envir = baseenv()) +} + +expression_weight = function(expression) { + if (is.logical(expression)) return(0) + sum(all.names(expression) %in% c("|", "&")) + 1 +} + +dti_col <- parallel::mclapply(mc.cores = 16, 1:16, function(ss) { +stats = list(depth = integer(0), expweight = numeric(0), simpweight = numeric(0), was_tautology = logical(0), was_contradiction = logical(0)) +set.seed(3 + ss) +for (depth_to_check in 2:11) { + for (repetition in seq_len(2000)) { + if (depth_to_check == 10) { + expression = random_cnf_expression(10, TRUE, 4) + } else if (depth_to_check == 11) { + expression = random_cnf_expression(5, TRUE, 2) + } else { + expression = random_cnf_expression(depth_to_check) + } + simplified = formula_to_expression(eval(expression)) + stats$depth[[length(stats$depth) + 1]] = depth_to_check + stats$expweight[[length(stats$expweight) + 1]] = expression_weight(expression) + stats$simpweight[[length(stats$simpweight) + 1]] = expression_weight(simplified) + vars = intersect(names(u), all.names(expression)) + assignments = expand.grid(lapply(vars, function(var) u[[var]]), stringsAsFactors = FALSE) + colnames(assignments) = vars + + truevals = rep(NA, nrow(assignments)) + for (i in seq_len(nrow(assignments))) { + assignment = assignments[i, , drop = FALSE] + trueval = evaluate_expression(expression, assignment) + simpval = evaluate_expression(simplified, assignment) + if (trueval != simpval) break + truevals[[i]] = trueval + } + stats$was_tautology[[length(stats$was_tautology) + 1]] = all(truevals) + stats$was_contradiction[[length(stats$was_contradiction) + 1]] = all(!truevals) + expect_equal(trueval, simpval, + info = sprintf("Expression: %s\nAssignment:\n%s\nSimplified to: %s", + deparse1(expression), + paste(capture.output(print(assignment)), collapse = "\n"), + deparse1(simplified) + )) + } +} +dti <- as.data.table(stats) +}) + +dti <- rbindlist(dti_col, idcol = "seedoffset") + +dti[, .( + ew = mean(expweight), sw = mean(simpweight), + etriv = mean(expweight == 0), + striv = mean(simpweight == 0), + could_simplify = mean(expweight > simpweight), + was_tautology = mean(was_tautology), + was_contradiction = mean(was_contradiction), + tautologies_not_recognized = mean(was_tautology & simpweight > 0), + contradictions_not_recognized = mean(was_contradiction & simpweight > 0) + ), by = "depth"] diff --git a/tests/testthat/test_CnfFormula.R b/tests/testthat/test_CnfFormula.R index 082c886d8..9d2dc3c11 100644 --- a/tests/testthat/test_CnfFormula.R +++ b/tests/testthat/test_CnfFormula.R @@ -622,9 +622,11 @@ test_that("Brute-force test", { sum(all.names(expression) %in% c("|", "&")) + 1 } + ss = 0 + # dti_col <- parallel::mclapply(mc.cores = 16, 1:16, function(ss) { stats = list(depth = integer(0), expweight = numeric(0), simpweight = numeric(0), was_tautology = logical(0), was_contradiction = logical(0)) - set.seed(2) + set.seed(3 + ss) for (depth_to_check in 2:11) { for (repetition in seq_len(200)) { if (depth_to_check == 10) { @@ -661,6 +663,10 @@ test_that("Brute-force test", { } } dti <- as.data.table(stats) + # }) + + # dti <- rbindlist(dti_col, idcol = "seedoffset") + dti[, .( ew = mean(expweight), sw = mean(simpweight), etriv = mean(expweight == 0), From bb3babd497150c8e2d70c976cf2e42a090101c75 Mon Sep 17 00:00:00 2001 From: mb706 Date: Thu, 12 Sep 2024 14:51:22 +0200 Subject: [PATCH 30/87] compliance --- R/CnfClause.R | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/R/CnfClause.R b/R/CnfClause.R index 99d087f3a..4e8df0de4 100644 --- a/R/CnfClause.R +++ b/R/CnfClause.R @@ -188,7 +188,7 @@ as.CnfClause.CnfClause = function(x) { } #' @export -as.list.CnfClause = function(x) { +as.list.CnfClause = function(x, ...) { x_bare = c(x) if (isFALSE(x_bare)) return(list()) x = unclass(x) From 4ed1bba03b3a022379edb8247438246404f88a60 Mon Sep 17 00:00:00 2001 From: mb706 Date: Thu, 12 Sep 2024 15:06:23 +0200 Subject: [PATCH 31/87] some microoptimizations --- R/CnfClause.R | 19 +++++++++---------- R/CnfFormula.R | 20 ++++++++++---------- R/CnfSymbol.R | 4 ++-- attic/minibenchmarks.R | 26 ++++++++++++++++++++++++++ 4 files changed, 47 insertions(+), 22 deletions(-) diff --git a/R/CnfClause.R b/R/CnfClause.R index 4e8df0de4..b14befd01 100644 --- a/R/CnfClause.R +++ b/R/CnfClause.R @@ -91,7 +91,7 @@ CnfClause = function(atoms) { entries = list() universe = attr(atoms[[1]], "universe") for (a in atoms) { - a_bare = c(a) + a_bare = unclass(a) if (!identical(attr(a, "universe"), universe)) { stop("All symbols must be in the same universe.") } @@ -129,7 +129,7 @@ CnfClause = function(atoms) { #' @export print.CnfClause = function(x, ...) { - x_bare = c(x) + x_bare = unclass(x) if (isTRUE(x_bare)) { cat("CnfClause: TRUE\n") } else if (isFALSE(x_bare)) { @@ -146,7 +146,7 @@ print.CnfClause = function(x, ...) { #' @export format.CnfClause = function(x, ...) { - x_bare = c(x) + x_bare = unclass(x) if (isTRUE(x_bare)) { return("CnfClause: T") } else if (isFALSE(x_bare)) { @@ -189,12 +189,11 @@ as.CnfClause.CnfClause = function(x) { #' @export as.list.CnfClause = function(x, ...) { - x_bare = c(x) + x_bare = unclass(x) if (isFALSE(x_bare)) return(list()) - x = unclass(x) if (isTRUE(x_bare)) return(as.CnfAtom(x)) - lapply(names(x), function(sym) { - structure(list(symbol = sym, values = x[[sym]]), universe = attr(x, "universe"), class = "CnfAtom") + lapply(names(x_bare), function(sym) { + structure(list(symbol = sym, values = x_bare[[sym]]), universe = attr(x, "universe"), class = "CnfAtom") }) } @@ -210,7 +209,7 @@ as.logical.CnfClause = function(x, ...) { `[.CnfClause` = function(x, i) { if (missing(i)) return(x) assert_atomic(i) - i = c(i) + i = unclass(i) x_bare = unclass(x) true_length = if (isFALSE(x_bare)) 0 else length(x_bare) @@ -293,8 +292,8 @@ chooseOpsMethod.CnfClause <- function(x, y, mx, my, cl, reverse) TRUE # `|.CnfFormula` handles conversion return(`|.CnfFormula`(e1, e2)) } - e1_bare = c(e1) - e2_bare = c(e2) + e1_bare = unclass(e1) + e2_bare = unclass(e2) if (isFALSE(e1_bare) || isTRUE(e2_bare)) return(as.CnfClause(e2)) if (isFALSE(e2_bare) || isTRUE(e1_bare)) return(e1) CnfClause(list(e1, e2)) diff --git a/R/CnfFormula.R b/R/CnfFormula.R index ebd657085..434ec2e09 100644 --- a/R/CnfFormula.R +++ b/R/CnfFormula.R @@ -148,7 +148,7 @@ CnfFormula = function(clauses) { ## don't unclass() here, since we check the class in the next line! if (inherits(cl, "CnfClause")) { - entries[[length(entries) + 1]] = c(cl) + entries[[length(entries) + 1]] = cl_bare } else { # union with another CnfFormula object other_entries[[length(other_entries) + 1]] = cl @@ -162,7 +162,7 @@ CnfFormula = function(clauses) { #' @export print.CnfFormula = function(x, ...) { - x_bare = c(x) + x_bare = unclass(x) if (isTRUE(x_bare)) { cat("CnfFormula: TRUE\n") } else if (isFALSE(x_bare)) { @@ -183,7 +183,7 @@ print.CnfFormula = function(x, ...) { #' @export format.CnfFormula = function(x, ...) { - x_bare = c(x) + x_bare = unclass(x) if (isTRUE(x_bare)) { return("CnfFormula: T") } else if (isFALSE(x_bare)) { @@ -231,7 +231,7 @@ as.CnfFormula.CnfFormula = function(x) { #' @export as.list.CnfFormula = function(x, ...) { - x_bare = c(x) + x_bare = unclass(x) if (isTRUE(x_bare)) return(list()) lapply(x_bare, structure, class = "CnfClause", universe = attr(x, "universe")) } @@ -288,12 +288,12 @@ chooseOpsMethod.CnfFormula <- function(x, y, mx, my, cl, reverse) TRUE #' @export `&.CnfFormula` = function(e1, e2) { - e1_bare = c(e1) - e2_bare = c(e2) + e1_bare = unclass(e1) + e2_bare = unclass(e2) e1 = as.CnfFormula(e1) + if (isTRUE(e2_bare) || isFALSE(e1_bare)) return(e1) e2 = as.CnfFormula(e2) if (isTRUE(e1_bare) || isFALSE(e2_bare)) return(e2) - if (isTRUE(e2_bare) || isFALSE(e1_bare)) return(e1) if (!identical(attr(e1, "universe"), attr(e2, "universe"))) { stop("Both formulas must be in the same universe.") } @@ -302,12 +302,12 @@ chooseOpsMethod.CnfFormula <- function(x, y, mx, my, cl, reverse) TRUE #' @export `|.CnfFormula` = function(e1, e2) { - e1_bare = c(e1) - e2_bare = c(e2) + e1_bare = unclass(e1) + e2_bare = unclass(e2) e1 = as.CnfFormula(e1) + if (isFALSE(e2_bare) || isTRUE(e1_bare)) return(e1) e2 = as.CnfFormula(e2) if (isFALSE(e1_bare) || isTRUE(e2_bare)) return(e2) - if (isFALSE(e2_bare) || isTRUE(e1_bare)) return(e1) if (!identical(attr(e1, "universe"), attr(e2, "universe"))) { stop("Both formulas must be in the same universe.") } diff --git a/R/CnfSymbol.R b/R/CnfSymbol.R index aef77f005..03af939f9 100644 --- a/R/CnfSymbol.R +++ b/R/CnfSymbol.R @@ -54,11 +54,11 @@ CnfSymbol = function(universe, name, domain) { #' @export print.CnfSymbol = function(x, ...) { - cat(sprintf("CnfSymbol '%s' with domain {%s}.\n", c(x), paste(attr(x, "universe")[[x]], collapse = ", "))) + cat(sprintf("CnfSymbol '%s' with domain {%s}.\n", unclass(x), paste(attr(x, "universe")[[x]], collapse = ", "))) invisible(x) } #' @export format.CnfSymbol = function(x, ...) { - sprintf("CnfSymbol(%s)", c(x)) + sprintf("CnfSymbol(%s)", unclass(x)) } diff --git a/attic/minibenchmarks.R b/attic/minibenchmarks.R index be1345536..7bde0e33a 100644 --- a/attic/minibenchmarks.R +++ b/attic/minibenchmarks.R @@ -192,3 +192,29 @@ bm_create_list <- function() { bm_create_list() |> autoplot() # plain list is faster than creating an env first; setting the size of the env and making parent = emptyenv() makes a small difference! + + +remove_class_info <- function() { + sx <- structure( + list(a = 1, b = 2, c = 3), + class = "test", + attr = list(a = 1, b = 2, c = 3) + ) + + microbenchmark(times = 1000, + structure = structure(sx, class = NULL), + unclass = unclass(sx), + c = c(sx), + assign.class = { + class(sx) <- NULL + sx + }, + assign.attr = { + attr(sx, "class") <- NULL + sx + } + ) +} + +remove_class_info() |> autoplot() +# unclass() is MUCH faster than c(), which is better than the others From c7233a08a42c1c7eea0bb23891cd449abb56fed9 Mon Sep 17 00:00:00 2001 From: mb706 Date: Fri, 13 Sep 2024 03:17:58 +0200 Subject: [PATCH 32/87] not finishing this today :-/ --- R/CnfFormula_simplify2.R | 324 +++++++++++++++++++++++++++++++++++++++ attic/minibenchmarks.R | 254 ++++++++++++++++++++++++++++++ 2 files changed, 578 insertions(+) create mode 100644 R/CnfFormula_simplify2.R diff --git a/R/CnfFormula_simplify2.R b/R/CnfFormula_simplify2.R new file mode 100644 index 000000000..24e3d9196 --- /dev/null +++ b/R/CnfFormula_simplify2.R @@ -0,0 +1,324 @@ + + +simplify_cnf2 = function(entries, universe) { + # faster intersect that relies on x, y being characters with no duplicates + char_intersect = function(x, y) x[x %in% y] + + # construct the CnfFormula return object + return_entries = function(entries) { + structure( + if (!length(entries)) TRUE else entries, + universe = universe, + class = "CnfFormula" + ) + } + + if (is.logical(entries)) return(return_entries(entries)) + + entries = entries[order(lengths(entries))] + + is_unit = lengths(entries) == 1L + unit_queue = which(is_unit) + eliminated = logical(length(entries)) + + # maps symbol name -> the index of unit clauses + unit_registry = new.env(parent = emptyenv()) + + # maps symbol name -> their current domain + unit_domains = new.env(parent = emptyenv()) + + # maps symbol name -> the index of all non-unit clauses that refer to it + symbol_registry = new.env(parent = emptyenv()) + + is_not_subset_of = NULL # see further down + available_inverse = NULL # ditto + + register_unit <- function(unit_idx) { + unit = entries[[unit_idx]] + nu = names(unit) + ur = unit_registry[[nu]] + if (is.null(ur)) { + unit_registry[[nu]] = unit_idx # environment assignment + unit_domains[[nu]] = unit[[1L]] # environment assignment + is_unit[[unit_idx]] <<- TRUE + } else { + # two units refer to the same symbol + # -> we keep the one we saw before but update it to the intersection. + # the current one is eliminated + prev_unit = unit_domains[[nu]] + unit_isct = prev_unit[prev_unit %in% unit[[1L]]] + if (!length(unit_isct)) return(TRUE) # signal that we have a contradiction and can exit + entries[[ur]][[1L]] <<- (unit_domains[[nu]] = unit_isct) + eliminated[[unit_idx]] <<- TRUE + } + for (s in symbol_registry[[nu]]) { + if (apply_unit_propagation(sr, nu)) return(TRUE) # forward contradiction signal + } + FALSE # no contradiction + } + + apply_unit_propagation = function(clause_idx, symbol_s) { + for (symbol in symbol_s) { + clause = entries[[clause_idx]] + symbol_idx = match(symbol, names(clause)) + clause_symbol_length_before = length(clause[[symbol_idx]]) + clause[[symbol_idx]] = char_intersect(clause[[symbol_idx]], unit_domains[[symbol]]) + if (length(clause[[symbol_idx]]) == length(unit_domains[[symbol]])) { + # If the lengths match, then the clause is a superset of the unit (since they are equal) + # the clause is therefore subsumed by the unit + eliminated[[clause_idx]] <<- TRUE + for (s in names(clause)) { + sr = symbol_registry[[s]] + symbol_registry[[s]] = sr[sr != clause_idx] + } + break + } + if (!length(clause[[symbol_idx]])) { + esfc = eliminate_symbol_from_clause(clause_idx, symbol) + if (is.null(esfc)) { + break # don't iterate over other symbols for this clause + } else if (esfc) { + return(TRUE) # forward contradiction signal + } + } else if (length(clause[[symbol_idx]]) != clause_symbol_length_before) { + # clause was changed. We need to update the subset relations matrix + if (!is.null(is_not_subset_of)) { + meta_idx = available_inverse[[clause_idx]] + # meta_idx_outer is the index up to which we have built is_not_subset_of; if this is not TRUE, then we haven't seen the clause yet. + # we are not relying on the fact that as soon as is_not_subset_of is non-null, we will only get here for clauses for which + # this was built, because it could be cascading from a unit elimination. + if (meta_idx <= meta_idx_outer) { + available_inverse[symbol_registry[[symbol]]] + # we could now be a subset of things that we were not a subset of before, so we only need to check the TRUE entries and may be setting them to FALSE. + # We do not need to check other entries, since apply_unit_propagation happens to all clauses in a row, so the counter-side is updated in time. + # In particular, we do not need to worry that some other clause that was formerly our subset ceases to be our subset, since that other clause + # will also be restricted by the unit. + # We can only ever set those entries to FALSE for which the other clause is in the symbol registry for the current symbol + # Note: we cannot address is_not_subset_of by symbol_idx, since clauses may get shorter but is_not_subset_of stays the same! + rows_to_check = which(is_not_subset_of[[meta_idx]][, symbol] & available %in% symbol_registry[[symbol]] & available <= meta_idx_outer) + for (other_meta_idx in rows_to_check) { + # when we get here, that means that the symbol exists both in clause_idx and in other_ref_this symbol, *and* we have seen both clauses + # in the is_not_subset_of building process. + # If this were not the case, then we would not need to change anything. + other_clause_range = entries[[available[[other_meta_idx]]]][[symbol]] + if (all(clause[[symbol_idx]] %in% other_clause_range)) { + is_not_subset_of[[meta_idx]][other_meta_idx, symbol] <<- FALSE + } + rowsum = sum(is_not_subset_of[[meta_idx]][other_meta_idx, ]) + if (rowsum == 0) { + # subsumption elimination + eliminate_subsumption(available[[other_meta_idx]]) + next + } else if (rowsum == 1) { + # self-subsumption elimination + # TODO: self-subsumption elimination + # - here we don't need to limit ourselves to two symbols being complements, we can do unit-eliminiation-style restriction here. + # - also apply this further down in the meta_idx loop + # TODO: think harder about whether we can run in circles and end up eliminating something on the basis of something else that was also eliminated + } + } + } + } + entries[[clause_idx]] <<- clause + } + } + FALSE # no contradiction + } + + # returns 'NULL' for eliminated, 'TRUE' for contradiction, 'FALSE' for nothing happened + eliminate_symbol_from_clause = function(clause_idx, symbol) { + clause = entries[[clause_idx]] + clause[[symbol]] = NULL + if (!length(clause)) return(TRUE) # signal that we have a contradiction and can exit + # remove from symbol registry of the symbol that went to 0 + sr = symbol_registry[[symbol]] + symbol_registry[[symbol]] = sr[sr != clause_idx] + + if (length(clause) == 1) { + # new unit ahoy + # remove from symbol registry of the symbol that remains in the clause + # (since it is now a unit) + sr = symbol_registry[[names(clause)]] + symbol_registry[[names(clause)]] = sr[sr != clause_idx] + if (register_unit(clause_idx)) return(TRUE) # forward signal from register_unit: contradiction + entries[[clause_idx]] <<- clause + return(NULL) # clause was turned into a unit + } + # clause was not turned into a unit, so we need to fill in is_not_subset_of + if (!is.null(is_not_subset_of)) { # we started filling this one in + meta_idx = available_inverse[[clause_idx]] + # meta_idx_outer is the index up to which we have built is_not_subset_of; if this is not TRUE, then we haven't seen the clause yet. + # we are not relying on the fact that as soon as is_not_subset_of is non-null, we will only get here for clauses for which + # this was built, because it could be cascading from a unit elimination. + if (meta_idx <= meta_idx_outer) { + is_not_subset_of[[meta_idx]][, symbol] <<- FALSE + for (others_ref_this_symbol in available_inverse[sr]) { + if (others_ref_this_symbol <= meta_idx_outer) { # meta_idx_outer is the index up to which we have built is_not_subset_of + is_not_subset_of[[others_ref_this_symbol]][meta_idx, symbol] <<- TRUE + } + } + } + } + entries[[clause_idx]] <<- clause + FALSE + } + + eliminate_subsumption = function(clause_idx) { + eliminated[[clause_idx]] <<- TRUE + for (s in names(entries[[clause_idx]])) { + sr = symbol_registry[[s]] + symbol_registry[[s]] = sr[sr != clause_idx] + } + } + + # process units: + # - populate unit_domains + # - start populating symbol_registry; it gets finished later down with non-units + # - also reduce duplicate units and replace them with their intersection + for (unit_idx in unit_queue) { + if (register_unit(unit_idx)) return(return_entries(FALSE)) + } + + # if there were only units, we are done + if (length(unit_queue) == length(entries)) return(return_entries(entries[!eliminated])) + + # process non-units: + # - eliminate entries subsumed by units + # - populate symbol_registry + # we sorted clauses by length, so we can skip ahead by length(unit_queue) + for (clause_idx in seq.int(length(unit_queue) + 1L, length(entries))) { + clause = entries[[clause_idx]] + + # intersect with units and eliminate subsumed clauses + clause_symbol_isct = char_intersect(names(clause), names(unit_domains)) + # apply unit-propagation early, since we otherwise run the risk of adding the clause + # to lots of symbol registry entries, only to remove it again right away + if (apply_unit_propagation(clause_idx, clause_symbol_isct)) return(return_entries(FALSE)) + + if (eliminated[[clause_idx]]) next # could happen from unit propagation + + for (symbol in names(clause)) { + sr_entry = symbol_registry[[symbol]] + if (is.null(sr_entry)) { + symbol_registry[[symbol]] = clause_idx + } else { + symbol_registry[[symbol]][[length(sr_entry) + 1L]] = clause_idx + } + } + + } + + + # let's start with (self)-subsumption. + # this can also create new units etc. + + # we don't need to check for units, upon registration they are automatically removed, and they cannot help with self-subsumption or HLA + available = which(!(eliminated | is_unit)) + available_inverse = match(seq_along(entries), available) + + # record for each clause whether it is a subset of another clause. + # we record this for each symbol separately, so when a symbol gets self-subsumed, we can re-check others more quickly. + # Default is FALSE (not not a subset, i.e. it is a subset), this aligns with absent columns (which are subsets of everything) + is_not_subset_of = vector("list", length(available)) + + for (meta_idx_outer in seq_along(available)) { + clause_idx = available[[meta_idx_outer]] + clause = entries[[clause_idx]] + sc = names(clause) + # is_not_subset_of[[i]][j, k] records whether for symbol k, clause i is not a subset of clause j + # if k is not in clause i, then var(i, k) is trivially a subset of var(j, k), so this is interpreted as FALSE. + # if k is not in clause j but is in clause i, then var(i, k) is not a subset of var(j, k), so this is interpreted as TRUE. + # we initialize with TRUE and then search for instances where a symbol k is in both clauses i and j, and where var(i, k) *is* a subset of var(j, k). + is_not_subset_of[[meta_idx_outer]] = matrix( + TRUE, + ncol = length(available), # indexed by meta_idx! + nrow = length(clause), + dimnames = list(NULL, names(clause)) + ) + + for (meta_idx_inner in seq_len(meta_idx_outer - 1L)) { + clause_idx_inner = available[[meta_idx_inner]] + if (eliminated[[clause_idx_inner]] || is_unit[[clause_idx_inner]]) next + clause_inner = entries[[clause_idx_inner]] + # note we can *not* rely on clause_inner to have smaller or equal length than clause, + # since unit elimination can change the length of clauses + + + sci = names(clause_inner) + sci_sc_map = match(sci, sc, nomatch = 0L) + sci_names_in_common = which(sci != 0L) + all_symbols = unique(c(sci, sc)) + + # symbols that are not in common trivially get the matrix entry TRUE + # (they are subsets of their counterpart in the other clause, since the other ones are empty) + + for (symbol_idx_inner in sci_names_in_common) { + symbol_idx_outer = sci_sc_map[[symbol_idx_inner]] + symbol_inner = sci[[symbol_idx_inner]] + symbol_outer = sc[[symbol_idx_outer]] + range_inner = clause_inner[[symbol_inner]] + range_outer = clause[[symbol_outer]] + + inner_subset_of_outer = all(range_inner %in% range_outer) + outer_subset_of_inner = (inner_subset_of_outer && length(sc) == length(sci)) || all(range_outer %in% range_inner) + if (inner_subset_of_outer) { + # avoid assigning TRUE to matrix that is initialized with TRUE + is_not_subset_of[[meta_idx_inner]][meta_idx_outer, symbol_inner] = FALSE + } + if (outer_subset_of_inner) { + is_not_subset_of[[meta_idx_outer]][meta_idx_inner, symbol_outer] = FALSE + } + } + not_subset_sum_outer = sum(is_not_subset_of[[meta_idx_outer]][meta_idx_inner, ]) + if (not_subset_sum_outer == 0) { # subsumption elimination of outer + eliminate_subsumption(clause_idx_inner) + next + } + if (not_subset_sum_outer == 1) { # self-subsumption elimination + symbol_to_eliminate = which(is_not_subset_of[[meta_idx_outer]][meta_idx_inner, ]) + # update clause and sc! + } + not_subset_sum_inner = sum(is_not_subset_of[[meta_idx_inner]][meta_idx_outer, ]) + + + } + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) next # could happen if we eliminate or self-subsume in the inner loop + + } + + + + # Now for the big one: Asymmetric Hidden Literal Addition + + # copy of entries where we collect the clauses with hidden literals added + # We keep the original entries: these are the ones we will return, and + # we only ever need to compare each entries-clause against all entry_hla clauses, + # not against each other. + entry_hla = entries + + + for (clause_idx in seq.int(length(unit_queue) + 1L, length(entries))) { + clause = entries[[clause_idx]] + if (eliminated[[clause_idx]]) next + + # for each symbol in the clause, check if it is a hidden literal + # if it is, we add a new clause with the hidden literal removed + # and add it to entry_hla + for (symbol in names(clause)) { + if (length(symbol_registry[[symbol]]) == 1) { + # hidden literal found + hla_clause = clause + hla_clause[[symbol]] = NULL + if (!length(hla_clause)) return(return_entries(FALSE)) # signal that we have a contradiction and can exit + entry_hla[[length(entry_hla) + 1L]] = hla_clause + } + } + } + + + + + + + +} diff --git a/attic/minibenchmarks.R b/attic/minibenchmarks.R index 7bde0e33a..81905d412 100644 --- a/attic/minibenchmarks.R +++ b/attic/minibenchmarks.R @@ -59,6 +59,8 @@ matplot(bmrt[, -1], type = "b", pch = 1, xaxt = "n", ylab = "Values", xlab = "ex legend("bottomright", legend = colnames(bmrt)[-1], col = seq_along(bmrt[, -1]), pch = 1, lty = 1) axis(1, at = seq_along(bmrt$expr), labels = bmrt$expr, las = 2) +round(sweep(as.matrix(bmrt[, 2:4], rownames = bmrt[[1]]), 2, as.numeric(bmrt[1, 2:4]), "/"), 2) + # GET: (lst_bracket_int, env_bracket) is faster than lst_bracket, which is faster than # env_dollar, which is slightly faster than lst_indirect_(int), which is slightly faster than lst_dollar # HUGE difference to: env_get @@ -218,3 +220,255 @@ remove_class_info <- function() { remove_class_info() |> autoplot() # unclass() is MUCH faster than c(), which is better than the others + + + +fill_list = function() { + tofill = runif(10000) + env = new.env(parent = emptyenv()) + + microbenchmark(times = 100, + prealloc = { + v = numeric(length(tofill)) + for (i in seq_along(tofill)) { + v[[i]] = tofill[[i]] + } + }, + extend = { + v = numeric(0) + for (i in seq_along(tofill)) { + v[[i]] = tofill[[i]] + } + }, + extend_dynamic = { + v = numeric(0) + for (i in seq_along(tofill)) { + v[[length(v) + 1]] = tofill[[i]] + } + }, + in_env_prealloc = { + env[["v"]] = numeric(length(tofill)) + for (i in seq_along(tofill)) { + env[["v"]][[i]] = tofill[[i]] + } + }, + in_env_extend = { + env[["v"]] = numeric(0) + for (i in seq_along(tofill)) { + env[["v"]][[i]] = tofill[[i]] + } + }, + in_env_extend_dynamic = { + env[["v"]] = numeric(0) + for (i in seq_along(tofill)) { + env[["v"]][[length(env[["v"]]) + 1]] = tofill[[i]] + } + } + ) +} + +fill_list() |> autoplot() +# prealloc < extend (+8%) < extend_dynamic (+30%) +# (n_env_prealloc < in_env_extend ; approx 1.5x prealloc) << in_env_extend_dynamic (approx 2x prealloc) + +bmr <- fill_list() + +autoplot(bmr) + +bmrt <- as.data.table(bmr)[, .(mean = mean(time), median = median(time), mean_robust = mean(time, trim = 0.1)), by = expr][order(mean_robust)] + +par(mar = c(8, 4, 4, 2) + 0.1) +matplot(bmrt[, -1], type = "b", pch = 1, xaxt = "n", ylab = "Values", xlab = "expr", main = "List access benchmarks", col = seq_along(bmrt[, -1])) +legend("bottomright", legend = colnames(bmrt)[-1], col = seq_along(bmrt[, -1]), pch = 1, lty = 1) +axis(1, at = seq_along(bmrt$expr), labels = bmrt$expr, las = 2) + +round(sweep(as.matrix(bmrt[, 2:4], rownames = bmrt[[1]]), 2, as.numeric(bmrt[1, 2:4]), "/"), 2) + +local_globals = function() { + env <- new.env(parent = emptyenv()) + env$a <- 100000000 + env$b <- 100000000 + i <- 100000000 + j <- 100000000 + + funcall <- function() { } + + inc_i <- function() { + i <<- i + 1 + } + + inc_ij <- function() { + i <<- i + 1 + j <<- j + 1 + } + + inc_env <- function() { + env[["a"]] <- env[["a"]] + 1 + } + inc_env2 <- function() { + env[["a"]] <- env[["a"]] + 1 + env[["b"]] <- env[["b"]] + 1 + } + + microbenchmark(times = 1000, + funcall = { funcall() }, + inc_i = { inc_i() }, + inc_ij = { inc_ij() }, + inc_env = { inc_env() }, + inc_env2 = { inc_env2() }, + inc_i_direct = { i <- i + 1 }, + inc_ij_direct = { i <- i + 1; j <- j + 1 } + ) +} + +local_globals() |> autoplot() + +bmr <- local_globals() + +autoplot(bmr) + +bmrt <- as.data.table(bmr)[, .(mean = mean(time), median = median(time), mean_robust = mean(time, trim = 0.1)), by = expr][order(mean_robust)] + +par(mar = c(8, 4, 4, 2) + 0.1) +matplot(bmrt[, -1], type = "b", pch = 1, xaxt = "n", ylab = "Values", xlab = "expr", main = "List access benchmarks", col = seq_along(bmrt[, -1])) +legend("bottomright", legend = colnames(bmrt)[-1], col = seq_along(bmrt[, -1]), pch = 1, lty = 1) +axis(1, at = seq_along(bmrt$expr), labels = bmrt$expr, las = 2) + +round(sweep(as.matrix(bmrt[, 2:4], rownames = bmrt[[1]]), 2, as.numeric(bmrt[1, 2:4]), "/"), 2) +# accessing env is about 2x slower than direct access; <<- is not that bad actually, some part of it seems to be the function call itself + + +delete_vector_entry = function() { + vct = runif(20) + lst = as.list(vct) + microbenchmark(times = 1000, + set_null = { lst2 = lst ; lst2[[2]] <- NULL }, + neg_index_list = { lst2 = lst ; lst2 <- lst2[-2] }, + neg_index_vec = { vct2 = vct ; vct2 <- vct2[-2] } + ) +} + +bmr <- delete_vector_entry() + +bmrt <- as.data.table(bmr)[, .(mean = mean(time), median = median(time), mean_robust = mean(time, trim = 0.1)), by = expr][order(mean_robust)] + +par(mar = c(8, 4, 4, 2) + 0.1) +matplot(bmrt[, -1], type = "b", pch = 1, xaxt = "n", ylab = "Values", xlab = "expr", main = "List access benchmarks", col = seq_along(bmrt[, -1])) +legend("bottomright", legend = colnames(bmrt)[-1], col = seq_along(bmrt[, -1]), pch = 1, lty = 1) +axis(1, at = seq_along(bmrt$expr), labels = bmrt$expr, las = 2) + +round(sweep(as.matrix(bmrt[, 2:4], rownames = bmrt[[1]]), 2, as.numeric(bmrt[1, 2:4]), "/"), 2) + + +skip_loop = function() { + vct = runif(20) + skipped = c(FALSE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, TRUE, FALSE) + microbenchmark(times = 1000, + skip_entry = { + entries = c(1L, 3L, 5L, 7L, 9L, 11L, 13L, 15L, 17L, 19L) + result = 0 + for (i in entries) { + if (skipped[[i]]) { + next + } + result <- result + vct[[i]] + } + }, + delete_entry = { + entries = c(1L, 3L, 5L, 7L, 9L, 11L, 13L, 15L, 17L, 19L) + entries <- entries[-2] + entries <- entries[-5] + entries <- entries[-8] + result = 0 + for (i in entries) { + result <- result + vct[[i]] + } + }, + skip_entry_twice = { + entries = c(1L, 3L, 5L, 7L, 9L, 11L, 13L, 15L, 17L, 19L) + result = 0 + for (times in 1:2) { + for (i in entries) { + if (skipped[[i]]) { + next + } + result <- result + vct[[i]] + } + } + }, + delete_entry_twice = { + entries = c(1L, 3L, 5L, 7L, 9L, 11L, 13L, 15L, 17L, 19L) + entries <- entries[-2] + entries <- entries[-5] + entries <- entries[-8] + result = 0 + for (times in 1:2) { + for (i in entries) { + result <- result + vct[[i]] + } + } + } + ) +} + +bmr <- skip_loop() + +bmrt <- as.data.table(bmr)[, .(mean = mean(time), median = median(time), mean_robust = mean(time, trim = 0.1)), by = expr][order(mean_robust)] + +par(mar = c(8, 4, 4, 2) + 0.1) +matplot(bmrt[, -1], type = "b", pch = 1, xaxt = "n", ylab = "Values", xlab = "expr", main = "List access benchmarks", col = seq_along(bmrt[, -1])) +legend("bottomright", legend = colnames(bmrt)[-1], col = seq_along(bmrt[, -1]), pch = 1, lty = 1) +axis(1, at = seq_along(bmrt$expr), labels = bmrt$expr, las = 2) + +round(sweep(as.matrix(bmrt[, 2:4], rownames = bmrt[[1]]), 2, as.numeric(bmrt[1, 2:4]), "/"), 2) + +# deleting is faster than skipping, apparently + + +sum_all_any = function() { + vct1 = c(FALSE, FALSE, FALSE, FALSE, TRUE, FALSE, FALSE) + vct2 = c(FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE) + vct3 = c(TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE) + vct4 = c(TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE) + + int1 = as.integer(vct1) + int2 = as.integer(vct2) + int3 = as.integer(vct3) + int4 = as.integer(vct4) + + microbenchmark(times = 10000, + all_any = { + r1 = c(all(vct1), all(vct2), all(vct3), all(vct4)) + r2 = c(any(vct1), any(vct2), any(vct3), any(vct4)) + }, + sums = { + vs1 = c(sum(vct1), sum(vct2), sum(vct3), sum(vct4)) + r1 = vs1 == 7L + r2 = vs1 != 0L + }, + sums_int = { + vs1 = c(sum(int1), sum(int2), sum(int3), sum(int4)) + r = vs1 != 0L + }, + sums_any = { + vs1 = c(sum(vct1), sum(vct2), sum(vct3), sum(vct4)) + r = vs1 != 0L + }, + any = { + r = c(any(vct1), any(vct2), any(vct3), any(vct4)) + } + ) +} + +bmr <- sum_all_any() + +bmrt <- as.data.table(bmr)[, .(mean = mean(time), median = median(time), mean_robust = mean(time, trim = 0.1)), by = expr][order(mean_robust)] + +par(mar = c(8, 4, 4, 2) + 0.1) +matplot(bmrt[, -1], type = "b", pch = 1, xaxt = "n", ylab = "Values", xlab = "expr", main = "List access benchmarks", col = seq_along(bmrt[, -1])) +legend("bottomright", legend = colnames(bmrt)[-1], col = seq_along(bmrt[, -1]), pch = 1, lty = 1) +axis(1, at = seq_along(bmrt$expr), labels = bmrt$expr, las = 2) + +round(sweep(as.matrix(bmrt[, 2:4], rownames = bmrt[[1]]), 2, as.numeric(bmrt[1, 2:4]), "/"), 2) +# use all / any for when only requesting one, but when multiple are used use sums() +# sums don't make a difference between logical and integer vectors From e1ab8c7f475bd7462d0147c8f09a34b3ef843231 Mon Sep 17 00:00:00 2001 From: mb706 Date: Sat, 14 Sep 2024 19:19:57 +0200 Subject: [PATCH 33/87] small things --- R/CnfFormula_simplify2.R | 6 -- attic/expressionanalysis.R | 68 +++++++++++------------ attic/minibenchmarks.R | 110 +++++++++++++++++++++++++++++++++++++ 3 files changed, 144 insertions(+), 40 deletions(-) diff --git a/R/CnfFormula_simplify2.R b/R/CnfFormula_simplify2.R index 24e3d9196..1b886de16 100644 --- a/R/CnfFormula_simplify2.R +++ b/R/CnfFormula_simplify2.R @@ -315,10 +315,4 @@ simplify_cnf2 = function(entries, universe) { } } - - - - - - } diff --git a/attic/expressionanalysis.R b/attic/expressionanalysis.R index 7c1cf703a..107ef7c49 100644 --- a/attic/expressionanalysis.R +++ b/attic/expressionanalysis.R @@ -52,42 +52,42 @@ expression_weight = function(expression) { } dti_col <- parallel::mclapply(mc.cores = 16, 1:16, function(ss) { -stats = list(depth = integer(0), expweight = numeric(0), simpweight = numeric(0), was_tautology = logical(0), was_contradiction = logical(0)) -set.seed(3 + ss) -for (depth_to_check in 2:11) { - for (repetition in seq_len(2000)) { - if (depth_to_check == 10) { - expression = random_cnf_expression(10, TRUE, 4) - } else if (depth_to_check == 11) { - expression = random_cnf_expression(5, TRUE, 2) - } else { - expression = random_cnf_expression(depth_to_check) - } - simplified = formula_to_expression(eval(expression)) - stats$depth[[length(stats$depth) + 1]] = depth_to_check - stats$expweight[[length(stats$expweight) + 1]] = expression_weight(expression) - stats$simpweight[[length(stats$simpweight) + 1]] = expression_weight(simplified) - vars = intersect(names(u), all.names(expression)) - assignments = expand.grid(lapply(vars, function(var) u[[var]]), stringsAsFactors = FALSE) - colnames(assignments) = vars + stats = list(depth = integer(0), expweight = numeric(0), simpweight = numeric(0), was_tautology = logical(0), was_contradiction = logical(0)) + set.seed(3 + ss) + for (depth_to_check in 2:11) { + for (repetition in seq_len(2000)) { + if (depth_to_check == 10) { + expression = random_cnf_expression(10, TRUE, 4) + } else if (depth_to_check == 11) { + expression = random_cnf_expression(5, TRUE, 2) + } else { + expression = random_cnf_expression(depth_to_check) + } + simplified = formula_to_expression(eval(expression)) + stats$depth[[length(stats$depth) + 1]] = depth_to_check + stats$expweight[[length(stats$expweight) + 1]] = expression_weight(expression) + stats$simpweight[[length(stats$simpweight) + 1]] = expression_weight(simplified) + vars = intersect(names(u), all.names(expression)) + assignments = expand.grid(lapply(vars, function(var) u[[var]]), stringsAsFactors = FALSE) + colnames(assignments) = vars - truevals = rep(NA, nrow(assignments)) - for (i in seq_len(nrow(assignments))) { - assignment = assignments[i, , drop = FALSE] - trueval = evaluate_expression(expression, assignment) - simpval = evaluate_expression(simplified, assignment) - if (trueval != simpval) break - truevals[[i]] = trueval + truevals = rep(NA, nrow(assignments)) + for (i in seq_len(nrow(assignments))) { + assignment = assignments[i, , drop = FALSE] + trueval = evaluate_expression(expression, assignment) + simpval = evaluate_expression(simplified, assignment) + if (trueval != simpval) break + truevals[[i]] = trueval + } + stats$was_tautology[[length(stats$was_tautology) + 1]] = all(truevals) + stats$was_contradiction[[length(stats$was_contradiction) + 1]] = all(!truevals) + expect_equal(trueval, simpval, + info = sprintf("Expression: %s\nAssignment:\n%s\nSimplified to: %s", + deparse1(expression), + paste(capture.output(print(assignment)), collapse = "\n"), + deparse1(simplified) + )) } - stats$was_tautology[[length(stats$was_tautology) + 1]] = all(truevals) - stats$was_contradiction[[length(stats$was_contradiction) + 1]] = all(!truevals) - expect_equal(trueval, simpval, - info = sprintf("Expression: %s\nAssignment:\n%s\nSimplified to: %s", - deparse1(expression), - paste(capture.output(print(assignment)), collapse = "\n"), - deparse1(simplified) - )) - } } dti <- as.data.table(stats) }) diff --git a/attic/minibenchmarks.R b/attic/minibenchmarks.R index 81905d412..8f5b49911 100644 --- a/attic/minibenchmarks.R +++ b/attic/minibenchmarks.R @@ -472,3 +472,113 @@ axis(1, at = seq_along(bmrt$expr), labels = bmrt$expr, las = 2) round(sweep(as.matrix(bmrt[, 2:4], rownames = bmrt[[1]]), 2, as.numeric(bmrt[1, 2:4]), "/"), 2) # use all / any for when only requesting one, but when multiple are used use sums() # sums don't make a difference between logical and integer vectors + + +df_row_addition_benchmark = function() { + # Create an initial data frame + df = data.frame(a = 1:5, b = letters[1:5], c = rnorm(5)) + + # New row to be added + new_row = list(a = 6, b = "f", c = rnorm(1)) + + microbenchmark(times = 100, + rbind = { + df_new = df + for (i in 1:100) { + df_new = rbind(df_new, new_row) + } + }, + rbind_data_frame = { + df_new = df + for (i in 1:100) { + df_new = rbind(df_new, data.frame(new_row)) + } + }, + append_list = { + df_new = df + for (i in 1:100) { + df_new[nrow(df_new) + 1, ] = new_row + } + }, + append_unlist = { + df_new = df + for (i in 1:100) { + df_new[nrow(df_new) + 1, ] = unlist(new_row) + } + }, + bind_rows = { + df_new = df + for (i in 1:100) { + df_new = dplyr::bind_rows(df_new, new_row) + } + }, + rbindlist = { + new_rows_list = list() + for (i in 1:100) { + new_rows_list[[length(new_rows_list) + 1]] = new_row + } + df_new = data.table::rbindlist(c(list(df), new_rows_list)) + }, + rbind_200 = { + df_new = df + for (i in 1:200) { + df_new = rbind(df_new, new_row) + } + }, + rbind_data_frame_200 = { + df_new = df + for (i in 1:200) { + df_new = rbind(df_new, data.frame(new_row)) + } + }, + append_list_200 = { + df_new = df + for (i in 1:200) { + df_new[nrow(df_new) + 1, ] = new_row + } + }, + append_unlist_200 = { + df_new = df + for (i in 1:200) { + df_new[nrow(df_new) + 1, ] = unlist(new_row) + } + }, + bind_rows_200 = { + df_new = df + for (i in 1:200) { + df_new = dplyr::bind_rows(df_new, new_row) + } + }, + rbindlist_200 = { + new_rows_list = list() + for (i in 1:200) { + new_rows_list[[length(new_rows_list) + 1]] = new_row + } + df_new = data.table::rbindlist(c(list(df), new_rows_list)) + } + ) +} + +bmr_df_row <- df_row_addition_benchmark() + +bmrt_df_row <- as.data.table(bmr_df_row)[, .(mean = mean(time), median = median(time), mean_robust = mean(time, trim = 0.1)), by = expr][order(mean_robust)] + +par(mar = c(8, 4, 4, 2) + 0.1) +matplot(log10(bmrt_df_row[, -1]), type = "b", pch = 1, xaxt = "n", ylab = "Time (nanoseconds)", xlab = "Method", main = "Data Frame Row Addition Benchmarks (100 rows)", col = seq_along(bmrt_df_row[, -1])) +legend("topleft", legend = colnames(bmrt_df_row)[-1], col = seq_along(bmrt_df_row[, -1]), pch = 1, lty = 1) +axis(1, at = seq_along(bmrt_df_row$expr), labels = bmrt_df_row$expr, las = 2) + +print(round(sweep(as.matrix(bmrt_df_row[, 2:4], rownames = bmrt_df_row[[1]]), 2, as.numeric(bmrt_df_row[1, 2:4]), "/"), 2)) + + +((bmrt_df_row[, -"expr_base"] |> melt(id.vars = "expr"))[, basename := sub("_200$", "", expr)][, + is_divisor := grepl("_200$", expr)][, .(value = value[is_divisor] / value[!is_divisor]), by = c("basename", "variable")] |> dcast(basename ~ variable, value.var = "value"))[order(-mean_robust)] + +bmrt_df_row[, expr_base := sub("_200$", "", expr)] +bmrt_df_row_summary <- bmrt_df_row[, .( + mean_ratio = mean[grepl("_200$", expr)] / mean[!grepl("_200$", expr)], + median_ratio = median[grepl("_200$", expr)] / median[!grepl("_200$", expr)], + mean_robust_ratio = mean_robust[grepl("_200$", expr)] / mean_robust[!grepl("_200$", expr)] +), by = expr_base] + +bmrt_df_row_summary[order(-mean_robust_ratio)] From 8c894c4ebc2e8345c6872a4b60fa13a00a94e783 Mon Sep 17 00:00:00 2001 From: mb706 Date: Sun, 15 Sep 2024 20:13:20 +0200 Subject: [PATCH 34/87] format --- attic/expressionanalysis.R | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/attic/expressionanalysis.R b/attic/expressionanalysis.R index 107ef7c49..886955d74 100644 --- a/attic/expressionanalysis.R +++ b/attic/expressionanalysis.R @@ -1,5 +1,6 @@ + u = CnfUniverse() W = CnfSymbol(u, "W", c("p", "q", "r")) X = CnfSymbol(u, "X", c("s", "t", "u")) @@ -88,8 +89,8 @@ dti_col <- parallel::mclapply(mc.cores = 16, 1:16, function(ss) { deparse1(simplified) )) } -} -dti <- as.data.table(stats) + } + as.data.table(stats) }) dti <- rbindlist(dti_col, idcol = "seedoffset") From 4e2b8fbbf81dd6aa343421047ed6f9f8fed2f2e8 Mon Sep 17 00:00:00 2001 From: mb706 Date: Mon, 16 Sep 2024 18:44:01 +0200 Subject: [PATCH 35/87] going to try something --- R/CnfFormula_simplify2.R | 262 +++++++++++++++++++++++++++------------ 1 file changed, 181 insertions(+), 81 deletions(-) diff --git a/R/CnfFormula_simplify2.R b/R/CnfFormula_simplify2.R index 1b886de16..b587c3e1b 100644 --- a/R/CnfFormula_simplify2.R +++ b/R/CnfFormula_simplify2.R @@ -1,6 +1,31 @@ simplify_cnf2 = function(entries, universe) { + ################################# + # Some vocabulary: + # - `entries` is a list of `clauses`, which are named lists. + # - `clauses`' names are `symbols`, the values are the `ranges` of the symbols within that clause + # - `unit`: clause with single symbol + # Glossary of operations: + # - `unit propagation`: ranges of a symbol within a unit constitute the entire possible range of that symbol, + # so all clauses with that symbol are restricted to those values + # - `subsumption elimination`: if all ranges of all symbols within one clause are subsets of those ranges in another clause, + # then the other clause can be removed + # - `self-subsumption elimination`: if the ranges of all except one symbol within one clause are a subset of those ranges + # in another clause, then the remaining symbol in the latter clause can be intersected with the remaining symbol. + # - `hidden literal addition` (HLA): if the ranges of all except one symbol within one clause are a subset of those ranges + # in another clause, then the *complement* of the remaining symbol in the former clause can be added to the latter clause. + # This is basically the reverse of self-subsumption elimination. We do not use this to change clauses directly; + # the point here is that the resulting clause, even if applied repeatedly, is logically equivalent to the original clause within the formula: + # - `hidden subsumption elimination`: if applying HLA results in a clause that can be subsumed, the original clause can be removed. + # - `hidden tautology elimination`: if applying HLA results in a clause that is a tautology, the original clause can be removed. + # Note: 'Clause Elimination Procedures for CNF Formulas' by Marijn Heule et al. calls this "Asymmetric Hidden Literal Addition". + ################################# + + ######################## + ## Helper functions ## + ######################## + # faster intersect that relies on x, y being characters with no duplicates char_intersect = function(x, y) x[x %in% y] @@ -15,10 +40,13 @@ simplify_cnf2 = function(entries, universe) { if (is.logical(entries)) return(return_entries(entries)) + ######################## + ## Variable setup ## + ######################## + entries = entries[order(lengths(entries))] is_unit = lengths(entries) == 1L - unit_queue = which(is_unit) eliminated = logical(length(entries)) # maps symbol name -> the index of unit clauses @@ -33,6 +61,29 @@ simplify_cnf2 = function(entries, universe) { is_not_subset_of = NULL # see further down available_inverse = NULL # ditto + ################################## + ## Event-driven clause handling ## + ################################## + # The following functions process the CNF clauses in various ways, + # depending on the current state of the entries. + # The state of the entries is updated in-place. + # The functions are then called in a loop, but they may also call each other. + # It is therefore important that they make the global state consistent before + # calling other functions, and that they are aware of how the global state *can* + # have changed upon their return. + # - entries[[clause_idx]] should be updated if necessary before other fns are called + # - symbol_registry[[symbol]] could have been updated + # - eliminated[[clause_idx]] could have been set to TRUE + # Since functions can call each other in different ways, `eliminated` could have changed even for clauses + # for which the other functions were not called. + + # Register a clause as a unit: + # - check if there is already a unit for this symbol + # - if not, add it to the unit registry + # - otherwise, intersect unit domains (and exit on contradiction) + # - apply unit propagation + # - We do *not* update the sybmol registry here; if the clause is registered for a given symbol, + # it has to be removed from there *before* calling this function. register_unit <- function(unit_idx) { unit = entries[[unit_idx]] nu = names(unit) @@ -40,6 +91,7 @@ simplify_cnf2 = function(entries, universe) { if (is.null(ur)) { unit_registry[[nu]] = unit_idx # environment assignment unit_domains[[nu]] = unit[[1L]] # environment assignment + # this is init'd TRUE for those w/ length 1 at the start, we set it to TRUE for clauses where symbols were eliminated is_unit[[unit_idx]] <<- TRUE } else { # two units refer to the same symbol @@ -48,84 +100,91 @@ simplify_cnf2 = function(entries, universe) { prev_unit = unit_domains[[nu]] unit_isct = prev_unit[prev_unit %in% unit[[1L]]] if (!length(unit_isct)) return(TRUE) # signal that we have a contradiction and can exit - entries[[ur]][[1L]] <<- (unit_domains[[nu]] = unit_isct) + entries[[ur]][[1L]] <<- (unit_domains[[nu]] = unit_isct) # update the *old* unit and unit_domains in one go. unit_domains is updated by-reference (environment) eliminated[[unit_idx]] <<- TRUE } - for (s in symbol_registry[[nu]]) { - if (apply_unit_propagation(sr, nu)) return(TRUE) # forward contradiction signal + # The symbol registry is empty at the start, this happens when new units are added later + for (s_clause_idx in symbol_registry[[nu]]) { + if (eliminated[[s_clause_idx]]) next # could have been eliminated by subsumption elimination during unit propagation of another clause + if (apply_unit_propagation(s_clause_idx, nu)) return(TRUE) # forward contradiction signal } FALSE # no contradiction } + # restrict the clause to the unit domains of the given symbols + # - clause_idx: index in entries + # - symbol_s: character vector of symbols + # we assume without checking that the clause does contain the symbol apply_unit_propagation = function(clause_idx, symbol_s) { - for (symbol in symbol_s) { - clause = entries[[clause_idx]] - symbol_idx = match(symbol, names(clause)) + clause = entries[[clause_idx]] + symbol_idx_s = match(symbol_s, names(clause)) + for (symbol_idx in symbol_idx_s) { + symbol = names(clause)[[symbol_idx]] clause_symbol_length_before = length(clause[[symbol_idx]]) clause[[symbol_idx]] = char_intersect(clause[[symbol_idx]], unit_domains[[symbol]]) if (length(clause[[symbol_idx]]) == length(unit_domains[[symbol]])) { # If the lengths match, then the clause is a superset of the unit (since they are equal) # the clause is therefore subsumed by the unit - eliminated[[clause_idx]] <<- TRUE - for (s in names(clause)) { - sr = symbol_registry[[s]] - symbol_registry[[s]] = sr[sr != clause_idx] - } + eliminate_subsumption(clause_idx) break } + # clause was not changed + if (length(clause[[symbol_idx]]) == clause_symbol_length_before) next + # clause was changed. + entries[[clause_idx]] <<- clause if (!length(clause[[symbol_idx]])) { + # the symbol is not in the clause anymore esfc = eliminate_symbol_from_clause(clause_idx, symbol) if (is.null(esfc)) { - break # don't iterate over other symbols for this clause + break # clause was turned into a unit, don't iterate over other symbols for this clause } else if (esfc) { return(TRUE) # forward contradiction signal } - } else if (length(clause[[symbol_idx]]) != clause_symbol_length_before) { - # clause was changed. We need to update the subset relations matrix - if (!is.null(is_not_subset_of)) { - meta_idx = available_inverse[[clause_idx]] - # meta_idx_outer is the index up to which we have built is_not_subset_of; if this is not TRUE, then we haven't seen the clause yet. - # we are not relying on the fact that as soon as is_not_subset_of is non-null, we will only get here for clauses for which - # this was built, because it could be cascading from a unit elimination. - if (meta_idx <= meta_idx_outer) { - available_inverse[symbol_registry[[symbol]]] - # we could now be a subset of things that we were not a subset of before, so we only need to check the TRUE entries and may be setting them to FALSE. - # We do not need to check other entries, since apply_unit_propagation happens to all clauses in a row, so the counter-side is updated in time. - # In particular, we do not need to worry that some other clause that was formerly our subset ceases to be our subset, since that other clause - # will also be restricted by the unit. - # We can only ever set those entries to FALSE for which the other clause is in the symbol registry for the current symbol - # Note: we cannot address is_not_subset_of by symbol_idx, since clauses may get shorter but is_not_subset_of stays the same! - rows_to_check = which(is_not_subset_of[[meta_idx]][, symbol] & available %in% symbol_registry[[symbol]] & available <= meta_idx_outer) - for (other_meta_idx in rows_to_check) { - # when we get here, that means that the symbol exists both in clause_idx and in other_ref_this symbol, *and* we have seen both clauses - # in the is_not_subset_of building process. - # If this were not the case, then we would not need to change anything. - other_clause_range = entries[[available[[other_meta_idx]]]][[symbol]] - if (all(clause[[symbol_idx]] %in% other_clause_range)) { - is_not_subset_of[[meta_idx]][other_meta_idx, symbol] <<- FALSE - } - rowsum = sum(is_not_subset_of[[meta_idx]][other_meta_idx, ]) - if (rowsum == 0) { - # subsumption elimination - eliminate_subsumption(available[[other_meta_idx]]) - next - } else if (rowsum == 1) { - # self-subsumption elimination - # TODO: self-subsumption elimination - # - here we don't need to limit ourselves to two symbols being complements, we can do unit-eliminiation-style restriction here. - # - also apply this further down in the meta_idx loop - # TODO: think harder about whether we can run in circles and end up eliminating something on the basis of something else that was also eliminated - } - } - } - } - entries[[clause_idx]] <<- clause + next + } + # We need to update the subset relations matrix, if it exists + if (is.null(is_not_subset_of)) next + + meta_idx = available_inverse[[clause_idx]] + # meta_idx_outer is the index up to which we have built is_not_subset_of; if meta_idx > meta_idx_outer, then we haven't seen the clause yet. + # we are not relying on the fact that as soon as is_not_subset_of is non-null, we will only get here for clauses for which + # is_not_subset_of was built, because unit-propagation could be cascading from a unit elimination. + if (meta_idx > meta_idx_outer) next + + is_not_subset_of_col = match(symbol, colnames(is_not_subset_of[[meta_idx]])) + # * We could now be a subset of things that we were not a subset of before, so we only need to check the TRUE entries and may be setting them to FALSE. + # --> hence `is_not_subset_of[meta_idx][is_not_subset_of[meta_idx]` + # Note: we cannot address is_not_subset_of by symbol_idx, since clauses may get shorter but is_not_subset_of stays the same! + # * We do not need to check other entries, since apply_unit_propagation happens to all clauses in a row, so the counter-side is updated in time. + # In particular, we do not need to worry that some other clause that was formerly our subset ceases to be our subset, since that other clause + # will also be restricted by the unit. + # * We can only ever set those entries to FALSE for which the other clause is in the symbol registry for the current symbol + # --> hence `available %in% symbol_registry[[symbol]]` + # * We only need to check up to the point where we have built is_not_subset_of + # --> hence `available <= meta_idx_outer` + rows_to_check = which(is_not_subset_of[[meta_idx]][, is_not_subset_of_col] & available %in% symbol_registry[[symbol]] & available <= meta_idx_outer) + for (other_meta_idx in rows_to_check) { + # when we get here, that means that the symbol exists both in clause_idx and in other_ref_this symbol, *and* we have seen both clauses + # in the is_not_subset_of building process. + # If this were not the case, then we would not need to change anything. + other_clause_range = entries[[available[[other_meta_idx]]]][[symbol]] + if (!all(clause[[symbol_idx]] %in% other_clause_range)) next + + # we are now a subset (and most likely were not before) + # ("most likely" because it could probably happen that we re-enter this part through some cascading elimination / propagation) + is_not_subset_of[[meta_idx]][other_meta_idx, is_not_subset_of_col] <<- FALSE + ousr = on_updated_subset_relations(meta_idx, other_meta_idx) + if (isTRUE(ousr)) return(TRUE) # forward contradiction signal } } FALSE # no contradiction } - # returns 'NULL' for eliminated, 'TRUE' for contradiction, 'FALSE' for nothing happened + + + + # eliminate `symbol` from `clause_idx` + # returns 'NULL' for turned into a unit, 'TRUE' for contradiction, 'FALSE' for nothing happened eliminate_symbol_from_clause = function(clause_idx, symbol) { clause = entries[[clause_idx]] clause[[symbol]] = NULL @@ -134,6 +193,7 @@ simplify_cnf2 = function(entries, universe) { sr = symbol_registry[[symbol]] symbol_registry[[symbol]] = sr[sr != clause_idx] + entries[[clause_idx]] <<- clause if (length(clause) == 1) { # new unit ahoy # remove from symbol registry of the symbol that remains in the clause @@ -141,28 +201,62 @@ simplify_cnf2 = function(entries, universe) { sr = symbol_registry[[names(clause)]] symbol_registry[[names(clause)]] = sr[sr != clause_idx] if (register_unit(clause_idx)) return(TRUE) # forward signal from register_unit: contradiction - entries[[clause_idx]] <<- clause return(NULL) # clause was turned into a unit } # clause was not turned into a unit, so we need to fill in is_not_subset_of - if (!is.null(is_not_subset_of)) { # we started filling this one in - meta_idx = available_inverse[[clause_idx]] - # meta_idx_outer is the index up to which we have built is_not_subset_of; if this is not TRUE, then we haven't seen the clause yet. - # we are not relying on the fact that as soon as is_not_subset_of is non-null, we will only get here for clauses for which - # this was built, because it could be cascading from a unit elimination. - if (meta_idx <= meta_idx_outer) { - is_not_subset_of[[meta_idx]][, symbol] <<- FALSE - for (others_ref_this_symbol in available_inverse[sr]) { - if (others_ref_this_symbol <= meta_idx_outer) { # meta_idx_outer is the index up to which we have built is_not_subset_of - is_not_subset_of[[others_ref_this_symbol]][meta_idx, symbol] <<- TRUE - } - } + if (is.null(is_not_subset_of)) return(FALSE) # we have not started filling this one in + + meta_idx = available_inverse[[clause_idx]] + # meta_idx_outer is the index up to which we have built is_not_subset_of; if meta_idx > meta_idx_outer, then we haven't seen the clause yet. + # we are not relying on the fact that as soon as is_not_subset_of is non-null, we will only get here for clauses for which + # this was built, because it could be cascading from a unit elimination. + if (meta_idx > meta_idx_outer) return(FALSE) + + is_not_subset_of_col = match(symbol, colnames(is_not_subset_of[[meta_idx]])) + rows_changed = which(is_not_subset_of[[meta_idx]][, is_not_subset_of_col]) + is_not_subset_of[[meta_idx]][, is_not_subset_of_col] <<- FALSE + for (others_ref_this_symbol in available_inverse[sr]) { + if (others_ref_this_symbol <= meta_idx_outer) { # meta_idx_outer is the index up to which we have built is_not_subset_of + is_not_subset_of[[others_ref_this_symbol]][meta_idx, is_not_subset_of_col] <<- TRUE } } - entries[[clause_idx]] <<- clause + for (meta_idx_other in rows_changed) { + # We have to do this *after* we set the corresponding values to TRUE for others_ref_this_symbol, + # since calling this could realistically change the symbol registry (e.g. if it leads to a symbol + # being eliminated from other clauses). + if (isTRUE(on_updated_subset_relations(meta_idx, meta_idx_other))) break + # on_updated_subset_relations could cascade down to eliminating meta_idx (i.e. clause_idx) + if (eliminated[[clause_idx]]) break + } FALSE } + # returns 'NULL' when meta_idx_other was eliminated (or possibly turned into a unit), + # 'TRUE' for contradiction, 'FALSE' for nothing changed + on_updated_subset_relations = function(meta_idx, meta_idx_other) { + # the row `meta_idx_other` of `is_not_subset_of[[meta_idx]]` has been updated. + # we now check whether we can apply subsumption elimination, or at least self-subsumption elimination, on `meta_idx`. + rowsum = sum(is_not_subset_of[[meta_idx]][meta_idx_other, ]) + if (rowsum > 1) return(FALSE) # nothing to do + if (rowsum == 0) { + eliminate_subsumption(available[[meta_idx]]) + return(NULL) + } + # rowsum == 1 + symbol_to_restrict = which(is_not_subset_of[[meta_idx]][meta_idx_other, ]) + # update clause and sc! + + + # self-subsumption elimination + # TODO: self-subsumption elimination + # - here we don't need to limit ourselves to two symbols being complements, we can do unit-eliminiation-style restriction here. + # - also apply this further down in the meta_idx loop + # TODO: think harder about whether we can run in circles and end up eliminating something on the basis of something else that was also eliminated + + } + + # mark a clause as eliminated and update symbol registry + # This is relatively safe to call, since it does not modify any other clauses and does not create new units or subset relationships. eliminate_subsumption = function(clause_idx) { eliminated[[clause_idx]] <<- TRUE for (s in names(entries[[clause_idx]])) { @@ -175,6 +269,7 @@ simplify_cnf2 = function(entries, universe) { # - populate unit_domains # - start populating symbol_registry; it gets finished later down with non-units # - also reduce duplicate units and replace them with their intersection + unit_queue = which(is_unit) for (unit_idx in unit_queue) { if (register_unit(unit_idx)) return(return_entries(FALSE)) } @@ -186,6 +281,8 @@ simplify_cnf2 = function(entries, universe) { # - eliminate entries subsumed by units # - populate symbol_registry # we sorted clauses by length, so we can skip ahead by length(unit_queue) + # At this point, everything after the unit_queue is not (yet) a unit. + # The seq.int here is "dangerous" and only allowed because we checked for length(unit_queue) == length(entries) above. for (clause_idx in seq.int(length(unit_queue) + 1L, length(entries))) { clause = entries[[clause_idx]] @@ -205,7 +302,6 @@ simplify_cnf2 = function(entries, universe) { symbol_registry[[symbol]][[length(sr_entry) + 1L]] = clause_idx } } - } @@ -219,6 +315,8 @@ simplify_cnf2 = function(entries, universe) { # record for each clause whether it is a subset of another clause. # we record this for each symbol separately, so when a symbol gets self-subsumed, we can re-check others more quickly. # Default is FALSE (not not a subset, i.e. it is a subset), this aligns with absent columns (which are subsets of everything) + # + # note that as soon as is_not_subset_of is non-null, some other functions assume that meta_idx_outer is also defined. is_not_subset_of = vector("list", length(available)) for (meta_idx_outer in seq_along(available)) { @@ -226,9 +324,10 @@ simplify_cnf2 = function(entries, universe) { clause = entries[[clause_idx]] sc = names(clause) # is_not_subset_of[[i]][j, k] records whether for symbol k, clause i is not a subset of clause j - # if k is not in clause i, then var(i, k) is trivially a subset of var(j, k), so this is interpreted as FALSE. - # if k is not in clause j but is in clause i, then var(i, k) is not a subset of var(j, k), so this is interpreted as TRUE. - # we initialize with TRUE and then search for instances where a symbol k is in both clauses i and j, and where var(i, k) *is* a subset of var(j, k). + # If k is not in clause i, then var(i, k) is trivially a subset of var(j, k), so this is interpreted as FALSE. + # If k is not in clause j but is in clause i, then var(i, k) is not a subset of var(j, k), so this is interpreted as TRUE. + # We initialize with TRUE and then search for instances where a symbol k is in both clauses i and j, and where var(i, k) *is* a subset of var(j, k). + # In that case, we set the entry to FALSE. is_not_subset_of[[meta_idx_outer]] = matrix( TRUE, ncol = length(available), # indexed by meta_idx! @@ -240,29 +339,30 @@ simplify_cnf2 = function(entries, universe) { clause_idx_inner = available[[meta_idx_inner]] if (eliminated[[clause_idx_inner]] || is_unit[[clause_idx_inner]]) next clause_inner = entries[[clause_idx_inner]] - # note we can *not* rely on clause_inner to have smaller or equal length than clause, + # note that even though we sort entries at the beginning, we can *not* rely on clause_inner to have smaller or equal length than clause, # since unit elimination can change the length of clauses - sci = names(clause_inner) sci_sc_map = match(sci, sc, nomatch = 0L) - sci_names_in_common = which(sci != 0L) - all_symbols = unique(c(sci, sc)) + sci_names_in_common = which(sci_sc_map != 0L) + # all_symbols = unique(c(sci, sc)) # TODO: is this needed? it can be gotten cheaper by using sci_names_in_common # symbols that are not in common trivially get the matrix entry TRUE - # (they are subsets of their counterpart in the other clause, since the other ones are empty) + # (they are not subsets of their counterpart in the other clause, since the other ones are empty) for (symbol_idx_inner in sci_names_in_common) { symbol_idx_outer = sci_sc_map[[symbol_idx_inner]] symbol_inner = sci[[symbol_idx_inner]] symbol_outer = sc[[symbol_idx_outer]] - range_inner = clause_inner[[symbol_inner]] - range_outer = clause[[symbol_outer]] + range_inner = clause_inner[[symbol_idx_inner]] + range_outer = clause[[symbol_idx_outer]] inner_subset_of_outer = all(range_inner %in% range_outer) outer_subset_of_inner = (inner_subset_of_outer && length(sc) == length(sci)) || all(range_outer %in% range_inner) if (inner_subset_of_outer) { - # avoid assigning TRUE to matrix that is initialized with TRUE + # Avoid assigning TRUE to matrix that is initialized with TRUE. + # We index by column name here, since it is possible that clauses were shortened by + # unit propagation or self subsumption elimination somewhere on the way here is_not_subset_of[[meta_idx_inner]][meta_idx_outer, symbol_inner] = FALSE } if (outer_subset_of_inner) { @@ -271,7 +371,7 @@ simplify_cnf2 = function(entries, universe) { } not_subset_sum_outer = sum(is_not_subset_of[[meta_idx_outer]][meta_idx_inner, ]) if (not_subset_sum_outer == 0) { # subsumption elimination of outer - eliminate_subsumption(clause_idx_inner) + eliminate_subsumption(clause_idx_inner) # can not lead to new units etc., so can not indirectly change the outer clause next } if (not_subset_sum_outer == 1) { # self-subsumption elimination From 34a31a854dc7d2b57ab6f51db2083fd882607c60 Mon Sep 17 00:00:00 2001 From: mb706 Date: Mon, 16 Sep 2024 19:27:42 +0200 Subject: [PATCH 36/87] everything except HLA should be done --- R/CnfFormula_simplify2.R | 175 +++++++++++++++++++-------------------- 1 file changed, 87 insertions(+), 88 deletions(-) diff --git a/R/CnfFormula_simplify2.R b/R/CnfFormula_simplify2.R index b587c3e1b..9d2ae9d9c 100644 --- a/R/CnfFormula_simplify2.R +++ b/R/CnfFormula_simplify2.R @@ -84,7 +84,7 @@ simplify_cnf2 = function(entries, universe) { # - apply unit propagation # - We do *not* update the sybmol registry here; if the clause is registered for a given symbol, # it has to be removed from there *before* calling this function. - register_unit <- function(unit_idx) { + register_unit = function(unit_idx) { unit = entries[[unit_idx]] nu = names(unit) ur = unit_registry[[nu]] @@ -106,76 +106,72 @@ simplify_cnf2 = function(entries, universe) { # The symbol registry is empty at the start, this happens when new units are added later for (s_clause_idx in symbol_registry[[nu]]) { if (eliminated[[s_clause_idx]]) next # could have been eliminated by subsumption elimination during unit propagation of another clause - if (apply_unit_propagation(s_clause_idx, nu)) return(TRUE) # forward contradiction signal + adr = apply_domain_restriction(s_clause_idx, nu, unit_domains[[nu]]) + if (identical(adr, TRUE)) return(TRUE) # forward contradiction signal } FALSE # no contradiction } - # restrict the clause to the unit domains of the given symbols + # restrict the symbol in the clause to a given domain, e.g. a unit # - clause_idx: index in entries - # - symbol_s: character vector of symbols - # we assume without checking that the clause does contain the symbol - apply_unit_propagation = function(clause_idx, symbol_s) { + # - symbol: name of symbol to restrict + # - restringent: domain to restrict to + # returns TRUE if a contradiction was detected, NULL if the clause was eliminated + apply_domain_restriction = function(clause_idx, symbol, restringent) { clause = entries[[clause_idx]] - symbol_idx_s = match(symbol_s, names(clause)) - for (symbol_idx in symbol_idx_s) { - symbol = names(clause)[[symbol_idx]] - clause_symbol_length_before = length(clause[[symbol_idx]]) - clause[[symbol_idx]] = char_intersect(clause[[symbol_idx]], unit_domains[[symbol]]) - if (length(clause[[symbol_idx]]) == length(unit_domains[[symbol]])) { - # If the lengths match, then the clause is a superset of the unit (since they are equal) - # the clause is therefore subsumed by the unit - eliminate_subsumption(clause_idx) - break - } - # clause was not changed - if (length(clause[[symbol_idx]]) == clause_symbol_length_before) next - # clause was changed. - entries[[clause_idx]] <<- clause - if (!length(clause[[symbol_idx]])) { - # the symbol is not in the clause anymore - esfc = eliminate_symbol_from_clause(clause_idx, symbol) - if (is.null(esfc)) { - break # clause was turned into a unit, don't iterate over other symbols for this clause - } else if (esfc) { - return(TRUE) # forward contradiction signal - } - next - } - # We need to update the subset relations matrix, if it exists - if (is.null(is_not_subset_of)) next - - meta_idx = available_inverse[[clause_idx]] - # meta_idx_outer is the index up to which we have built is_not_subset_of; if meta_idx > meta_idx_outer, then we haven't seen the clause yet. - # we are not relying on the fact that as soon as is_not_subset_of is non-null, we will only get here for clauses for which - # is_not_subset_of was built, because unit-propagation could be cascading from a unit elimination. - if (meta_idx > meta_idx_outer) next - - is_not_subset_of_col = match(symbol, colnames(is_not_subset_of[[meta_idx]])) - # * We could now be a subset of things that we were not a subset of before, so we only need to check the TRUE entries and may be setting them to FALSE. - # --> hence `is_not_subset_of[meta_idx][is_not_subset_of[meta_idx]` - # Note: we cannot address is_not_subset_of by symbol_idx, since clauses may get shorter but is_not_subset_of stays the same! - # * We do not need to check other entries, since apply_unit_propagation happens to all clauses in a row, so the counter-side is updated in time. - # In particular, we do not need to worry that some other clause that was formerly our subset ceases to be our subset, since that other clause - # will also be restricted by the unit. - # * We can only ever set those entries to FALSE for which the other clause is in the symbol registry for the current symbol - # --> hence `available %in% symbol_registry[[symbol]]` - # * We only need to check up to the point where we have built is_not_subset_of - # --> hence `available <= meta_idx_outer` - rows_to_check = which(is_not_subset_of[[meta_idx]][, is_not_subset_of_col] & available %in% symbol_registry[[symbol]] & available <= meta_idx_outer) - for (other_meta_idx in rows_to_check) { - # when we get here, that means that the symbol exists both in clause_idx and in other_ref_this symbol, *and* we have seen both clauses - # in the is_not_subset_of building process. - # If this were not the case, then we would not need to change anything. - other_clause_range = entries[[available[[other_meta_idx]]]][[symbol]] - if (!all(clause[[symbol_idx]] %in% other_clause_range)) next - - # we are now a subset (and most likely were not before) - # ("most likely" because it could probably happen that we re-enter this part through some cascading elimination / propagation) - is_not_subset_of[[meta_idx]][other_meta_idx, is_not_subset_of_col] <<- FALSE - ousr = on_updated_subset_relations(meta_idx, other_meta_idx) - if (isTRUE(ousr)) return(TRUE) # forward contradiction signal - } + symbol_idx = match(symbol, names(clause)) + if (is.na(symbol_idx)) return(FALSE) + + clause_symbol_length_before = length(clause[[symbol_idx]]) + clause[[symbol_idx]] = char_intersect(clause[[symbol_idx]], restringent) + if (length(clause[[symbol_idx]]) == length(restringent)) { + # If the lengths match, then the clause is a superset of the unit (since the intersections are equal) + # the clause is therefore subsumed by the unit + eliminate_subsumption(clause_idx) + return(NULL) + } + # clause was not changed + if (length(clause[[symbol_idx]]) == clause_symbol_length_before) next + # clause was changed. + entries[[clause_idx]] <<- clause + if (!length(clause[[symbol_idx]])) { + # the symbol is not in the clause anymore + return(eliminate_symbol_from_clause(clause_idx, symbol)) + } + # We need to update the subset relations matrix, if it exists + if (is.null(is_not_subset_of)) return(FALSE) + + meta_idx = available_inverse[[clause_idx]] + # meta_idx_outer is the index up to which we have built is_not_subset_of; if meta_idx > meta_idx_outer, then we haven't seen the clause yet. + # we are not relying on the fact that as soon as is_not_subset_of is non-null, we will only get here for clauses for which + # is_not_subset_of was built, because unit-propagation could be cascading from a unit elimination. + if (meta_idx > meta_idx_outer) return(FALSE) + + is_not_subset_of_col = match(symbol, colnames(is_not_subset_of[[meta_idx]])) + # * We could now be a subset of things that we were not a subset of before, so we only need to check the TRUE entries and may be setting them to FALSE. + # --> hence `is_not_subset_of[meta_idx][is_not_subset_of[meta_idx]` + # Note: we cannot address is_not_subset_of by symbol_idx, since clauses may get shorter but is_not_subset_of stays the same! + # * We do not need to check other entries, since apply_domain_restriction happens to all clauses in a row, so the counter-side is updated in time. + # In particular, we do not need to worry that some other clause that was formerly our subset ceases to be our subset, since that other clause + # will also be restricted by the unit. + # * We can only ever set those entries to FALSE for which the other clause is in the symbol registry for the current symbol + # --> hence `available %in% symbol_registry[[symbol]]` + # * We only need to check up to the point where we have built is_not_subset_of + # --> hence `available <= meta_idx_outer` + rows_to_check = which(is_not_subset_of[[meta_idx]][, is_not_subset_of_col] & available %in% symbol_registry[[symbol]] & available <= meta_idx_outer) + for (other_meta_idx in rows_to_check) { + # when we get here, that means that the symbol exists both in clause_idx and in other_ref_this symbol, *and* we have seen both clauses + # in the is_not_subset_of building process. + # If this were not the case, then we would not need to change anything. + other_clause_range = entries[[available[[other_meta_idx]]]][[symbol]] + if (!all(clause[[symbol_idx]] %in% other_clause_range)) next + + # we are now a subset (and most likely were not before) + # ("most likely" because it could probably happen that we re-enter this part through some cascading elimination / propagation) + is_not_subset_of[[meta_idx]][other_meta_idx, is_not_subset_of_col] <<- FALSE + ousr = on_updated_subset_relations(meta_idx, other_meta_idx) + if (identical(ousr, TRUE)) return(TRUE) # forward contradiction signal. We don't care if other_meta_idx was eliminated. + if (eliminated[[clause_idx]]) return(NULL) # need to check more directly if things escalated somehow and clause_idx was eliminated indirectly } FALSE # no contradiction } @@ -184,7 +180,7 @@ simplify_cnf2 = function(entries, universe) { # eliminate `symbol` from `clause_idx` - # returns 'NULL' for turned into a unit, 'TRUE' for contradiction, 'FALSE' for nothing happened + # returns 'NULL' for turned into a unit or eliminated, 'TRUE' for contradiction, 'FALSE' for nothing happened eliminate_symbol_from_clause = function(clause_idx, symbol) { clause = entries[[clause_idx]] clause[[symbol]] = NULL @@ -224,9 +220,10 @@ simplify_cnf2 = function(entries, universe) { # We have to do this *after* we set the corresponding values to TRUE for others_ref_this_symbol, # since calling this could realistically change the symbol registry (e.g. if it leads to a symbol # being eliminated from other clauses). - if (isTRUE(on_updated_subset_relations(meta_idx, meta_idx_other))) break + ousr = on_updated_subset_relations(meta_idx, meta_idx_other) + if (identical(ousr, TRUE)) return(TRUE) # on_updated_subset_relations could cascade down to eliminating meta_idx (i.e. clause_idx) - if (eliminated[[clause_idx]]) break + if (eliminated[[clause_idx]]) return(NULL) } FALSE } @@ -243,14 +240,15 @@ simplify_cnf2 = function(entries, universe) { return(NULL) } # rowsum == 1 - symbol_to_restrict = which(is_not_subset_of[[meta_idx]][meta_idx_other, ]) + symbol_to_restrict = colnames(is_not_subset_of[[meta_idx]])[is_not_subset_of[[meta_idx]][meta_idx_other, ]] # update clause and sc! + # note we update meta_idx_other: we are currently subset of that other clause w/r/t all except one symbol. + # we can therefore intersect that last symbol in the other clause with the range of that symbol in the current clause. + # apply_domain_restriction will take care of eliminating the symbol if the range becomes empty. + # It could in theory even do subsumption, but we have already taken care of that above. + apply_domain_restriction(available[[meta_idx_other]], symbol_to_restrict, entries[[available[[meta_idx]]]][[symbol_to_restrict]]) - # self-subsumption elimination - # TODO: self-subsumption elimination - # - here we don't need to limit ourselves to two symbols being complements, we can do unit-eliminiation-style restriction here. - # - also apply this further down in the meta_idx loop # TODO: think harder about whether we can run in circles and end up eliminating something on the basis of something else that was also eliminated } @@ -290,7 +288,11 @@ simplify_cnf2 = function(entries, universe) { clause_symbol_isct = char_intersect(names(clause), names(unit_domains)) # apply unit-propagation early, since we otherwise run the risk of adding the clause # to lots of symbol registry entries, only to remove it again right away - if (apply_unit_propagation(clause_idx, clause_symbol_isct)) return(return_entries(FALSE)) + for (symbol in clause_symbol_isct) { + adr = apply_domain_restriction(clause_idx, symbol, unit_domains[[symbol]]) + if (is.null(adr)) break + if (adr) return(return_entries(FALSE)) + } if (eliminated[[clause_idx]]) next # could happen from unit propagation @@ -345,7 +347,6 @@ simplify_cnf2 = function(entries, universe) { sci = names(clause_inner) sci_sc_map = match(sci, sc, nomatch = 0L) sci_names_in_common = which(sci_sc_map != 0L) - # all_symbols = unique(c(sci, sc)) # TODO: is this needed? it can be gotten cheaper by using sci_names_in_common # symbols that are not in common trivially get the matrix entry TRUE # (they are not subsets of their counterpart in the other clause, since the other ones are empty) @@ -369,25 +370,23 @@ simplify_cnf2 = function(entries, universe) { is_not_subset_of[[meta_idx_outer]][meta_idx_inner, symbol_outer] = FALSE } } - not_subset_sum_outer = sum(is_not_subset_of[[meta_idx_outer]][meta_idx_inner, ]) - if (not_subset_sum_outer == 0) { # subsumption elimination of outer - eliminate_subsumption(clause_idx_inner) # can not lead to new units etc., so can not indirectly change the outer clause - next - } - if (not_subset_sum_outer == 1) { # self-subsumption elimination - symbol_to_eliminate = which(is_not_subset_of[[meta_idx_outer]][meta_idx_inner, ]) - # update clause and sc! - } - not_subset_sum_inner = sum(is_not_subset_of[[meta_idx_inner]][meta_idx_outer, ]) + # prefer to eliminate the outer loopo clause first, since we have already + # done more work for the inner loop clause (which comes earlier in 'entries') + ousr = on_updated_subset_relations(meta_idx_inner, meta_idx_outer) + if (is.null(ousr)) break + if (!ousr) return(return_entries(FALSE)) + ousr = on_updated_subset_relations(meta_idx_outer, meta_idx_inner) + if (is.null(ousr)) next + if (!ousr) return(return_entries(FALSE)) } - if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) next # could happen if we eliminate or self-subsume in the inner loop + # not necessary, since the only place where this could happen is on_update_subset_relations, + # and we do check the return value of that one: + # > if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) next } - - # Now for the big one: Asymmetric Hidden Literal Addition # copy of entries where we collect the clauses with hidden literals added From 24166628ae06c2bc101796889d56954e76381d87 Mon Sep 17 00:00:00 2001 From: mb706 Date: Mon, 16 Sep 2024 22:22:43 +0200 Subject: [PATCH 37/87] feature complete simplify2 --- R/CnfFormula_simplify2.R | 78 ++++++++++++++++++++++++++-------------- 1 file changed, 51 insertions(+), 27 deletions(-) diff --git a/R/CnfFormula_simplify2.R b/R/CnfFormula_simplify2.R index 9d2ae9d9c..ec1772baf 100644 --- a/R/CnfFormula_simplify2.R +++ b/R/CnfFormula_simplify2.R @@ -26,8 +26,9 @@ simplify_cnf2 = function(entries, universe) { ## Helper functions ## ######################## - # faster intersect that relies on x, y being characters with no duplicates + # faster intersect, setdiff etc. that rely on x, y being characters with no duplicates char_intersect = function(x, y) x[x %in% y] + char_setdiff = function(x, y) x[!x %in% y] # construct the CnfFormula return object return_entries = function(entries) { @@ -127,7 +128,7 @@ simplify_cnf2 = function(entries, universe) { if (length(clause[[symbol_idx]]) == length(restringent)) { # If the lengths match, then the clause is a superset of the unit (since the intersections are equal) # the clause is therefore subsumed by the unit - eliminate_subsumption(clause_idx) + eliminate_clause_update_sr(clause_idx) return(NULL) } # clause was not changed @@ -236,7 +237,7 @@ simplify_cnf2 = function(entries, universe) { rowsum = sum(is_not_subset_of[[meta_idx]][meta_idx_other, ]) if (rowsum > 1) return(FALSE) # nothing to do if (rowsum == 0) { - eliminate_subsumption(available[[meta_idx]]) + eliminate_clause_update_sr(available[[meta_idx]]) return(NULL) } # rowsum == 1 @@ -249,13 +250,11 @@ simplify_cnf2 = function(entries, universe) { # It could in theory even do subsumption, but we have already taken care of that above. apply_domain_restriction(available[[meta_idx_other]], symbol_to_restrict, entries[[available[[meta_idx]]]][[symbol_to_restrict]]) - # TODO: think harder about whether we can run in circles and end up eliminating something on the basis of something else that was also eliminated - } # mark a clause as eliminated and update symbol registry # This is relatively safe to call, since it does not modify any other clauses and does not create new units or subset relationships. - eliminate_subsumption = function(clause_idx) { + eliminate_clause_update_sr = function(clause_idx) { eliminated[[clause_idx]] <<- TRUE for (s in names(entries[[clause_idx]])) { sr = symbol_registry[[s]] @@ -389,29 +388,54 @@ simplify_cnf2 = function(entries, universe) { # Now for the big one: Asymmetric Hidden Literal Addition - # copy of entries where we collect the clauses with hidden literals added - # We keep the original entries: these are the ones we will return, and - # we only ever need to compare each entries-clause against all entry_hla clauses, - # not against each other. - entry_hla = entries - - - for (clause_idx in seq.int(length(unit_queue) + 1L, length(entries))) { + # we only loop over the entries that have not been eliminated yet. + # We update `remaining_entries` inside the loop whenever a clause is eliminated. + # This will not affect the outer loop, but the inner loop gets to be shorter. + remaining_entries = which(!eliminated)[order(lengths(entries[!eliminated]), decreasing = TRUE)] + for (clause_idx in remaining_entries) { clause = entries[[clause_idx]] - if (eliminated[[clause_idx]]) next - - # for each symbol in the clause, check if it is a hidden literal - # if it is, we add a new clause with the hidden literal removed - # and add it to entry_hla - for (symbol in names(clause)) { - if (length(symbol_registry[[symbol]]) == 1) { - # hidden literal found - hla_clause = clause - hla_clause[[symbol]] = NULL - if (!length(hla_clause)) return(return_entries(FALSE)) # signal that we have a contradiction and can exit - entry_hla[[length(entry_hla) + 1L]] = hla_clause + if (length(clause) == 1) break # only units remaining + meta_idx = available_inverse[[clause_idx]] + remaining_other_entries = remaining_entries[remaining_entries != clause_idx] + + not_subset_count = integer(length(remaining_other_entries)) + was_used = logical(length(remaining_other_entries)) # we keep track of which clauses were used for HLA, since every other clause can only do that once. + for (roe_idx in seq_along(remaining_other_entries)) { + other_clause_idx = remaining_other_entries[[roe_idx]] + meta_idx_other = available_inverse[[other_clause_idx]] + not_subset_count[[roe_idx]] = sum(is_not_subset_of[[meta_idx_other]][meta_idx, ]) + } + repeat { + hla_clause_idx = match(TRUE, not_subset_count == 1 & !was_used) + if (is.na(hla_clause_idx)) break + clause_other = remaining_other_entries[[hla_clause_idx]] + meta_idx_other = available_inverse[[clause_other]] + symbol = colnames(is_not_subset_of[[meta_idx_other]])[is_not_subset_of[[meta_idx_other]][meta_idx, ]] + range_old = clause[[symbol]] + range_new = c(range_old, char_setdiff(universe[[symbol]], c(range_old, entries[[clause_other]][[symbol]]))) + if (length(range_new) == length(universe[[symbol]])) { + # hidden tautology elimination + eliminate_clause_update_sr(clause_idx) + remaining_entries = remaining_other_entries + break + } + was_used[[hla_clause_idx]] = TRUE + for (updating_clause_idx in available_inverse[symbol_registry[[symbol]]]) { + # we don't want to skip 'was_used' here, since we might still do hidden subsumption elimination with them. + if (is_not_subset_of[[updating_clause_idx]][meta_idx, symbol] && + all(entries[[available[[updating_clause_idx]]]][[symbol]] %in% range_new)) { + is_not_subset_of[[updating_clause_idx]][meta_idx, symbol] = FALSE + roe_idx = match(updating_clause_idx, remaining_other_entries) # I wished I didn't have to do this + not_subset_count[[roe_idx]] = not_subset_count[[roe_idx]] - 1L + if (not_subset_count[[roe_idx]] == 0) { + # hidden subsumption elimination + eliminate_clause_update_sr(available[[updating_clause_idx]]) + remaining_entries = remaining_other_entries + break + } + } } } } - + return_entries(entries[!eliminated]) } From 39e9f9282c603dab99f8c81462c123dfaccb80f6 Mon Sep 17 00:00:00 2001 From: mb706 Date: Tue, 17 Sep 2024 00:52:53 +0200 Subject: [PATCH 38/87] simple tests pass now --- R/CnfFormula_simplify.R | 2 +- R/CnfFormula_simplify2.R | 123 ++++++++++++++++++++++--------- tests/testthat/test_CnfFormula.R | 2 + 3 files changed, 92 insertions(+), 35 deletions(-) diff --git a/R/CnfFormula_simplify.R b/R/CnfFormula_simplify.R index 52ebb3097..c422c7d4e 100644 --- a/R/CnfFormula_simplify.R +++ b/R/CnfFormula_simplify.R @@ -3,7 +3,7 @@ -simplify_cnf = function(entries, universe) { +simplify_cnf_old = function(entries, universe) { return_false = structure( FALSE, universe = universe, diff --git a/R/CnfFormula_simplify2.R b/R/CnfFormula_simplify2.R index ec1772baf..e4d2f5372 100644 --- a/R/CnfFormula_simplify2.R +++ b/R/CnfFormula_simplify2.R @@ -1,6 +1,6 @@ -simplify_cnf2 = function(entries, universe) { +simplify_cnf = function(entries, universe) { ################################# # Some vocabulary: # - `entries` is a list of `clauses`, which are named lists. @@ -132,7 +132,7 @@ simplify_cnf2 = function(entries, universe) { return(NULL) } # clause was not changed - if (length(clause[[symbol_idx]]) == clause_symbol_length_before) next + if (length(clause[[symbol_idx]]) == clause_symbol_length_before) return(FALSE) # clause was changed. entries[[clause_idx]] <<- clause if (!length(clause[[symbol_idx]])) { @@ -237,7 +237,7 @@ simplify_cnf2 = function(entries, universe) { rowsum = sum(is_not_subset_of[[meta_idx]][meta_idx_other, ]) if (rowsum > 1) return(FALSE) # nothing to do if (rowsum == 0) { - eliminate_clause_update_sr(available[[meta_idx]]) + eliminate_clause_update_sr(available[[meta_idx_other]]) return(NULL) } # rowsum == 1 @@ -322,6 +322,7 @@ simplify_cnf2 = function(entries, universe) { for (meta_idx_outer in seq_along(available)) { clause_idx = available[[meta_idx_outer]] + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) break # may happen if we somehow turn something into a unit that eliminates a later clause clause = entries[[clause_idx]] sc = names(clause) # is_not_subset_of[[i]][j, k] records whether for symbol k, clause i is not a subset of clause j @@ -331,10 +332,13 @@ simplify_cnf2 = function(entries, universe) { # In that case, we set the entry to FALSE. is_not_subset_of[[meta_idx_outer]] = matrix( TRUE, - ncol = length(available), # indexed by meta_idx! - nrow = length(clause), + nrow = length(available), # indexed by meta_idx! + ncol = length(clause), dimnames = list(NULL, names(clause)) ) + # we are not a subset of ourselves + # (this prevents us from checking this later in on_updated_subset_relations; if we do check it there, we would eliminate the clause from itself) + is_not_subset_of[[meta_idx_outer]][meta_idx_outer, ] = FALSE for (meta_idx_inner in seq_len(meta_idx_outer - 1L)) { clause_idx_inner = available[[meta_idx_inner]] @@ -352,51 +356,47 @@ simplify_cnf2 = function(entries, universe) { for (symbol_idx_inner in sci_names_in_common) { symbol_idx_outer = sci_sc_map[[symbol_idx_inner]] - symbol_inner = sci[[symbol_idx_inner]] - symbol_outer = sc[[symbol_idx_outer]] + symbol = sci[[symbol_idx_inner]] + range_inner = clause_inner[[symbol_idx_inner]] range_outer = clause[[symbol_idx_outer]] inner_subset_of_outer = all(range_inner %in% range_outer) - outer_subset_of_inner = (inner_subset_of_outer && length(sc) == length(sci)) || all(range_outer %in% range_inner) + outer_subset_of_inner = (inner_subset_of_outer && length(range_outer) == length(range_inner)) || all(range_outer %in% range_inner) if (inner_subset_of_outer) { # Avoid assigning TRUE to matrix that is initialized with TRUE. # We index by column name here, since it is possible that clauses were shortened by # unit propagation or self subsumption elimination somewhere on the way here - is_not_subset_of[[meta_idx_inner]][meta_idx_outer, symbol_inner] = FALSE + is_not_subset_of[[meta_idx_inner]][meta_idx_outer, symbol] = FALSE } if (outer_subset_of_inner) { - is_not_subset_of[[meta_idx_outer]][meta_idx_inner, symbol_outer] = FALSE + is_not_subset_of[[meta_idx_outer]][meta_idx_inner, symbol] = FALSE } } # prefer to eliminate the outer loopo clause first, since we have already # done more work for the inner loop clause (which comes earlier in 'entries') ousr = on_updated_subset_relations(meta_idx_inner, meta_idx_outer) if (is.null(ousr)) break - if (!ousr) return(return_entries(FALSE)) + if (ousr) return(return_entries(FALSE)) ousr = on_updated_subset_relations(meta_idx_outer, meta_idx_inner) + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) break # honestly not sure if this could happen here if (is.null(ousr)) next - if (!ousr) return(return_entries(FALSE)) - + if (ousr) return(return_entries(FALSE)) } - # not necessary, since the only place where this could happen is on_update_subset_relations, - # and we do check the return value of that one: - # > if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) next - } # Now for the big one: Asymmetric Hidden Literal Addition # we only loop over the entries that have not been eliminated yet. - # We update `remaining_entries` inside the loop whenever a clause is eliminated. - # This will not affect the outer loop, but the inner loop gets to be shorter. + # We update `remaining_nonunit_entries` inside the loop whenever a clause is eliminated. remaining_entries = which(!eliminated)[order(lengths(entries[!eliminated]), decreasing = TRUE)] - for (clause_idx in remaining_entries) { + remaining_nonunit_entries = remaining_entries[seq_len(length(remaining_entries) - length(unit_domains))] + remaining_unit_entries = if (length(unit_domains)) remaining_entries[seq.int(length(remaining_entries) - length(unit_domains) + 1L, length(remaining_entries))] + for (clause_idx in remaining_nonunit_entries) { clause = entries[[clause_idx]] - if (length(clause) == 1) break # only units remaining meta_idx = available_inverse[[clause_idx]] - remaining_other_entries = remaining_entries[remaining_entries != clause_idx] + remaining_other_entries = remaining_nonunit_entries[remaining_nonunit_entries != clause_idx] not_subset_count = integer(length(remaining_other_entries)) was_used = logical(length(remaining_other_entries)) # we keep track of which clauses were used for HLA, since every other clause can only do that once. @@ -408,34 +408,89 @@ simplify_cnf2 = function(entries, universe) { repeat { hla_clause_idx = match(TRUE, not_subset_count == 1 & !was_used) if (is.na(hla_clause_idx)) break - clause_other = remaining_other_entries[[hla_clause_idx]] - meta_idx_other = available_inverse[[clause_other]] + clause_idx_other = remaining_other_entries[[hla_clause_idx]] + meta_idx_other = available_inverse[[clause_idx_other]] symbol = colnames(is_not_subset_of[[meta_idx_other]])[is_not_subset_of[[meta_idx_other]][meta_idx, ]] range_old = clause[[symbol]] - range_new = c(range_old, char_setdiff(universe[[symbol]], c(range_old, entries[[clause_other]][[symbol]]))) + range_new = c(range_old, char_setdiff(universe[[symbol]], c(range_old, entries[[clause_idx_other]][[symbol]]))) if (length(range_new) == length(universe[[symbol]])) { # hidden tautology elimination eliminate_clause_update_sr(clause_idx) - remaining_entries = remaining_other_entries + remaining_nonunit_entries = remaining_other_entries break } - was_used[[hla_clause_idx]] = TRUE - for (updating_clause_idx in available_inverse[symbol_registry[[symbol]]]) { + for (updating_clause_meta_idx in available_inverse[symbol_registry[[symbol]]]) { # we don't want to skip 'was_used' here, since we might still do hidden subsumption elimination with them. - if (is_not_subset_of[[updating_clause_idx]][meta_idx, symbol] && - all(entries[[available[[updating_clause_idx]]]][[symbol]] %in% range_new)) { - is_not_subset_of[[updating_clause_idx]][meta_idx, symbol] = FALSE - roe_idx = match(updating_clause_idx, remaining_other_entries) # I wished I didn't have to do this + if (is_not_subset_of[[updating_clause_meta_idx]][meta_idx, symbol] && + all(entries[[available[[updating_clause_meta_idx]]]][[symbol]] %in% range_new)) { + is_not_subset_of[[updating_clause_meta_idx]][meta_idx, symbol] = FALSE + roe_idx = match(updating_clause_meta_idx, remaining_other_entries) # I wished I didn't have to do this not_subset_count[[roe_idx]] = not_subset_count[[roe_idx]] - 1L if (not_subset_count[[roe_idx]] == 0) { # hidden subsumption elimination - eliminate_clause_update_sr(available[[updating_clause_idx]]) - remaining_entries = remaining_other_entries + eliminate_clause_update_sr(clause_idx) + remaining_nonunit_entries = remaining_other_entries + break + } + } + } + if (eliminated[[clause_idx]]) break # the break inside the for-loop above will not break the repeat loop + was_used[[hla_clause_idx]] = TRUE + clause[[symbol]] = range_new + } + } + + delayedAssign("roe_inverse", match(seq_along(entries), remaining_nonunit_entries)) + for (clause_idx in remaining_unit_entries) { + clause = entries[[clause_idx]] + unitsymbol = names(clause) + was_used = logical(length(remaining_nonunit_entries)) + # every clause that is not yet eliminated is a proper subset of the current unit. + # If it is length N and contains the unit symbol, then N - 1 of its symbols are not subsets; + # otherwise (if it does not contain the unit symbol), all N symbols are not subsets. + not_subset_count = lengths(entries[remaining_nonunit_entries]) - (remaining_nonunit_entries %in% symbol_registry[[unitsymbol]]) + + is_not_subset_of_unit = vector("list", length(remaining_nonunit_entries)) + repeat { + hla_clause_idx = match(TRUE, not_subset_count == 1 & !was_used) + if (is.na(hla_clause_idx)) break + clause_idx_other = remaining_nonunit_entries[[hla_clause_idx]] + clause_other = entries[[clause_idx_other]] + if (is.null(is_not_subset_of_unit[[hla_clause_idx]])) { + is_not_subset_of_unit[[hla_clause_idx]] = structure(names(clause_other) != unitsymbol, names = names(clause_other)) + } + is_not_subset_entry = is_not_subset_of_unit[[hla_clause_idx]] + symbol = names(is_not_subset_entry)[is_not_subset_entry] + range_old = clause[[symbol]] + range_new = c(range_old, char_setdiff(universe[[symbol]], c(range_old, clause_other[[symbol]]))) + if (length(range_new) == length(universe[[symbol]])) { + # hidden tautology elimination + # no more need to update unit registry etc. + eliminated[[clause_idx]] = TRUE + break + } + for (updating_clause_idx in symbol_registry[[symbol]]) { + updating_hla_clause_idx = roe_inverse[[updating_clause_idx]] + if (is.null(is_not_subset_of_unit[[updating_hla_clause_idx]])) { + updating_clause = entries[[updating_clause_idx]] + is_not_subset_of_unit[[updating_hla_clause_idx]] = structure(names(updating_clause) != unitsymbol, names = names(updating_clause)) + } + if (is_not_subset_of_unit[[updating_hla_clause_idx]][[symbol]] && + all(entries[[updating_clause_idx]][[symbol]] %in% range_new)) { + is_not_subset_of_unit[[updating_hla_clause_idx]][[symbol]] = FALSE + not_subset_count[[updating_hla_clause_idx]] = not_subset_count[[updating_hla_clause_idx]] - 1L + if (not_subset_count[[updating_hla_clause_idx]] == 0) { + # hidden subsumption elimination + eliminated[[clause_idx]] = TRUE break } } } + if (eliminated[[clause_idx]]) break # the break inside the for-loop above will not break the repeat loop + was_used[[hla_clause_idx]] = TRUE + clause[[symbol]] = range_new } } + return_entries(entries[!eliminated]) } diff --git a/tests/testthat/test_CnfFormula.R b/tests/testthat/test_CnfFormula.R index 9d2dc3c11..3d240cda6 100644 --- a/tests/testthat/test_CnfFormula.R +++ b/tests/testthat/test_CnfFormula.R @@ -570,6 +570,7 @@ test_that("CnfFormula performs all simplifications in a complex formula", { test_that("Brute-force test", { skip_on_cran() + skip() u = CnfUniverse() W = CnfSymbol(u, "W", c("p", "q", "r")) @@ -679,3 +680,4 @@ test_that("Brute-force test", { ), by = "depth"] }) + From 005a9739d7ae4822848c456282b2353e3905e8bb Mon Sep 17 00:00:00 2001 From: mb706 Date: Tue, 17 Sep 2024 04:22:47 +0200 Subject: [PATCH 39/87] quite a few bugfixes --- R/CnfFormula_simplify2.R | 50 +++++++++++++++++++++----------- attic/mvsat.mv | 1 + tests/testthat/test_CnfFormula.R | 1 - 3 files changed, 34 insertions(+), 18 deletions(-) diff --git a/R/CnfFormula_simplify2.R b/R/CnfFormula_simplify2.R index e4d2f5372..0d4419b8a 100644 --- a/R/CnfFormula_simplify2.R +++ b/R/CnfFormula_simplify2.R @@ -107,7 +107,7 @@ simplify_cnf = function(entries, universe) { # The symbol registry is empty at the start, this happens when new units are added later for (s_clause_idx in symbol_registry[[nu]]) { if (eliminated[[s_clause_idx]]) next # could have been eliminated by subsumption elimination during unit propagation of another clause - adr = apply_domain_restriction(s_clause_idx, nu, unit_domains[[nu]]) + adr = apply_domain_restriction(s_clause_idx, nu, unit_domains[[nu]], TRUE) if (identical(adr, TRUE)) return(TRUE) # forward contradiction signal } FALSE # no contradiction @@ -118,7 +118,7 @@ simplify_cnf = function(entries, universe) { # - symbol: name of symbol to restrict # - restringent: domain to restrict to # returns TRUE if a contradiction was detected, NULL if the clause was eliminated - apply_domain_restriction = function(clause_idx, symbol, restringent) { + apply_domain_restriction = function(clause_idx, symbol, restringent, is_unit_propagation) { clause = entries[[clause_idx]] symbol_idx = match(symbol, names(clause)) if (is.na(symbol_idx)) return(FALSE) @@ -133,12 +133,14 @@ simplify_cnf = function(entries, universe) { } # clause was not changed if (length(clause[[symbol_idx]]) == clause_symbol_length_before) return(FALSE) - # clause was changed. - entries[[clause_idx]] <<- clause if (!length(clause[[symbol_idx]])) { # the symbol is not in the clause anymore return(eliminate_symbol_from_clause(clause_idx, symbol)) } + # clause was changed. + # We don't need to do this when we go the eliminate_symbol_from_clause route, since that will update the clause in any case. + entries[[clause_idx]] <<- clause + # We need to update the subset relations matrix, if it exists if (is.null(is_not_subset_of)) return(FALSE) @@ -152,7 +154,7 @@ simplify_cnf = function(entries, universe) { # * We could now be a subset of things that we were not a subset of before, so we only need to check the TRUE entries and may be setting them to FALSE. # --> hence `is_not_subset_of[meta_idx][is_not_subset_of[meta_idx]` # Note: we cannot address is_not_subset_of by symbol_idx, since clauses may get shorter but is_not_subset_of stays the same! - # * We do not need to check other entries, since apply_domain_restriction happens to all clauses in a row, so the counter-side is updated in time. + # * If this is unit propagation, we do not need to check other entries, since apply_domain_restriction happens to all clauses in a row, so the counter-side is updated in time. # In particular, we do not need to worry that some other clause that was formerly our subset ceases to be our subset, since that other clause # will also be restricted by the unit. # * We can only ever set those entries to FALSE for which the other clause is in the symbol registry for the current symbol @@ -165,7 +167,7 @@ simplify_cnf = function(entries, universe) { # in the is_not_subset_of building process. # If this were not the case, then we would not need to change anything. other_clause_range = entries[[available[[other_meta_idx]]]][[symbol]] - if (!all(clause[[symbol_idx]] %in% other_clause_range)) next + if (!all(entries[[clause_idx]][[symbol]] %in% other_clause_range)) next # we are now a subset (and most likely were not before) # ("most likely" because it could probably happen that we re-enter this part through some cascading elimination / propagation) @@ -174,6 +176,17 @@ simplify_cnf = function(entries, universe) { if (identical(ousr, TRUE)) return(TRUE) # forward contradiction signal. We don't care if other_meta_idx was eliminated. if (eliminated[[clause_idx]]) return(NULL) # need to check more directly if things escalated somehow and clause_idx was eliminated indirectly } + if (!is_unit_propagation) { + # we are not propagating units, so we need to update the subset relations in the other direction as well + idx_to_check = which(available %in% symbol_registry[[symbol]] & available <= meta_idx_outer) + for (other_meta_idx in idx_to_check) { + # was the other a subset of us before? that could have changed now. + if (!is_not_subset_of[[other_meta_idx]][meta_idx, symbol] && !all(entries[[available[[other_meta_idx]]]][[symbol]] %in% entries[[clause_idx]][[symbol]])) { + is_not_subset_of[[other_meta_idx]][meta_idx, symbol] <<- TRUE + # no need to call on_updated_subset_relations, since we are increasing rowsums, not decreasing them + } + } + } FALSE # no contradiction } @@ -214,7 +227,7 @@ simplify_cnf = function(entries, universe) { is_not_subset_of[[meta_idx]][, is_not_subset_of_col] <<- FALSE for (others_ref_this_symbol in available_inverse[sr]) { if (others_ref_this_symbol <= meta_idx_outer) { # meta_idx_outer is the index up to which we have built is_not_subset_of - is_not_subset_of[[others_ref_this_symbol]][meta_idx, is_not_subset_of_col] <<- TRUE + is_not_subset_of[[others_ref_this_symbol]][meta_idx, symbol] <<- TRUE } } for (meta_idx_other in rows_changed) { @@ -248,7 +261,7 @@ simplify_cnf = function(entries, universe) { # we can therefore intersect that last symbol in the other clause with the range of that symbol in the current clause. # apply_domain_restriction will take care of eliminating the symbol if the range becomes empty. # It could in theory even do subsumption, but we have already taken care of that above. - apply_domain_restriction(available[[meta_idx_other]], symbol_to_restrict, entries[[available[[meta_idx]]]][[symbol_to_restrict]]) + apply_domain_restriction(available[[meta_idx_other]], symbol_to_restrict, entries[[available[[meta_idx]]]][[symbol_to_restrict]], FALSE) } @@ -281,21 +294,22 @@ simplify_cnf = function(entries, universe) { # At this point, everything after the unit_queue is not (yet) a unit. # The seq.int here is "dangerous" and only allowed because we checked for length(unit_queue) == length(entries) above. for (clause_idx in seq.int(length(unit_queue) + 1L, length(entries))) { - clause = entries[[clause_idx]] # intersect with units and eliminate subsumed clauses - clause_symbol_isct = char_intersect(names(clause), names(unit_domains)) + clause_symbol_isct = char_intersect(names(entries[[clause_idx]]), names(unit_domains)) # apply unit-propagation early, since we otherwise run the risk of adding the clause # to lots of symbol registry entries, only to remove it again right away for (symbol in clause_symbol_isct) { - adr = apply_domain_restriction(clause_idx, symbol, unit_domains[[symbol]]) + adr = apply_domain_restriction(clause_idx, symbol, unit_domains[[symbol]], TRUE) if (is.null(adr)) break if (adr) return(return_entries(FALSE)) } - if (eliminated[[clause_idx]]) next # could happen from unit propagation + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) next # could happen from unit propagation - for (symbol in names(clause)) { + # do cache `clause = entries[[clause_idx]]` and refer to names(clause) here, + # since apply_domain_restriction might have removed symbols from the clause + for (symbol in names(entries[[clause_idx]])) { sr_entry = symbol_registry[[symbol]] if (is.null(sr_entry)) { symbol_registry[[symbol]] = clause_idx @@ -322,9 +336,9 @@ simplify_cnf = function(entries, universe) { for (meta_idx_outer in seq_along(available)) { clause_idx = available[[meta_idx_outer]] - if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) break # may happen if we somehow turn something into a unit that eliminates a later clause + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) next # may happen if we somehow turn something into a unit that eliminates a later clause clause = entries[[clause_idx]] - sc = names(clause) + # is_not_subset_of[[i]][j, k] records whether for symbol k, clause i is not a subset of clause j # If k is not in clause i, then var(i, k) is trivially a subset of var(j, k), so this is interpreted as FALSE. # If k is not in clause j but is in clause i, then var(i, k) is not a subset of var(j, k), so this is interpreted as TRUE. @@ -341,6 +355,8 @@ simplify_cnf = function(entries, universe) { is_not_subset_of[[meta_idx_outer]][meta_idx_outer, ] = FALSE for (meta_idx_inner in seq_len(meta_idx_outer - 1L)) { + ## need to refresh clause here, since it might have been shortened by unit propagation in an earlier iteration + clause = entries[[clause_idx]] clause_idx_inner = available[[meta_idx_inner]] if (eliminated[[clause_idx_inner]] || is_unit[[clause_idx_inner]]) next clause_inner = entries[[clause_idx_inner]] @@ -348,7 +364,7 @@ simplify_cnf = function(entries, universe) { # since unit elimination can change the length of clauses sci = names(clause_inner) - sci_sc_map = match(sci, sc, nomatch = 0L) + sci_sc_map = match(sci, names(clause), nomatch = 0L) sci_names_in_common = which(sci_sc_map != 0L) # symbols that are not in common trivially get the matrix entry TRUE @@ -424,7 +440,7 @@ simplify_cnf = function(entries, universe) { if (is_not_subset_of[[updating_clause_meta_idx]][meta_idx, symbol] && all(entries[[available[[updating_clause_meta_idx]]]][[symbol]] %in% range_new)) { is_not_subset_of[[updating_clause_meta_idx]][meta_idx, symbol] = FALSE - roe_idx = match(updating_clause_meta_idx, remaining_other_entries) # I wished I didn't have to do this + roe_idx = match(available[[updating_clause_meta_idx]], remaining_other_entries) # I wished I didn't have to do this not_subset_count[[roe_idx]] = not_subset_count[[roe_idx]] - 1L if (not_subset_count[[roe_idx]] == 0) { # hidden subsumption elimination diff --git a/attic/mvsat.mv b/attic/mvsat.mv index 46e7105c0..27fcdcd26 100644 --- a/attic/mvsat.mv +++ b/attic/mvsat.mv @@ -109,3 +109,4 @@ # This is because we don't eliminate (C | A) & (!C | B) & (B | A) by removing (B | A) # so, if clause X and clause Y have a symbol in common where the values are disjoint, the disjunction of the rest is implied? + diff --git a/tests/testthat/test_CnfFormula.R b/tests/testthat/test_CnfFormula.R index 3d240cda6..43bbc5b91 100644 --- a/tests/testthat/test_CnfFormula.R +++ b/tests/testthat/test_CnfFormula.R @@ -570,7 +570,6 @@ test_that("CnfFormula performs all simplifications in a complex formula", { test_that("Brute-force test", { skip_on_cran() - skip() u = CnfUniverse() W = CnfSymbol(u, "W", c("p", "q", "r")) From 158a54ac1d6179f796f674bd0e1aefc730f235ad Mon Sep 17 00:00:00 2001 From: mb706 Date: Tue, 17 Sep 2024 05:52:08 +0200 Subject: [PATCH 40/87] experiments --- attic/expression_experiments.R | 111 +++++++++++++++++++++++++++++++++ 1 file changed, 111 insertions(+) create mode 100644 attic/expression_experiments.R diff --git a/attic/expression_experiments.R b/attic/expression_experiments.R new file mode 100644 index 000000000..72031b0b9 --- /dev/null +++ b/attic/expression_experiments.R @@ -0,0 +1,111 @@ + +# Get 'ss' from command line arguments +args <- commandArgs(trailingOnly = TRUE) +checkmate::assert_integer(ss <- as.integer(args[1]), lower = 1, len = 1, any.missing = FALSE) + +library("mlr3pipelines") +library("testthat") +library("data.table") + +u = CnfUniverse() +W = CnfSymbol(u, "W", c("p", "q", "r")) +X = CnfSymbol(u, "X", c("s", "t", "u")) +Y = CnfSymbol(u, "Y", c("v", "w", "x")) +Z = CnfSymbol(u, "Z", c("y", "z", "a")) + +random_atom_expression = function() { + symbol = sample(alist(W, X, Y, Z), 1)[[1]] + values = sample(u[[deparse(symbol)]], sample(2, 1)) + substitute(symbol %among% values, list(symbol = symbol, values = values)) +} + +random_cnf_expression = function(depth, do_cnf = FALSE, ddepth = 0) { + if (depth <= 1) { + # base case: return a random symbol expression call + return(random_atom_expression()) + } + # recursively build a random tree of expressions + if (do_cnf) { + op = if (depth <= ddepth) quote(`|`) else quote(`&`) + } else { + op = sample(alist(`&`, `|`), 1)[[1]] # randomly choose between AND and OR + } + left_expr = random_cnf_expression(depth - 1, do_cnf, ddepth) + right_expr = random_cnf_expression(depth - 1, do_cnf, ddepth) + + # create a call object for the expression: (left_expr op right_expr) + substitute(op(left_expr, right_expr), list(op = op, left_expr = left_expr, right_expr = right_expr)) +} + +formula_to_expression = function(formula) { + if (is.logical(formula)) return(c(formula)) + clause_exprs = lapply(as.CnfFormula(formula), function(clause) { + atom_exprs = lapply(clause, function(atom) { + substitute(symbol %among% values, list(symbol = as.name(atom$symbol), values = atom$values)) + }) + Reduce(function(x, y) substitute(x | y, list(x = x, y = y)), atom_exprs) + }) + Reduce(function(x, y) substitute(x & y, list(x = x, y = y)), clause_exprs) +} + +evaluate_expression = function(expression, assignment) { + substituted = do.call(substitute, list(expression, c(list("%among%" = quote(`%in%`)), assignment))) + eval(substituted, envir = baseenv()) +} + +expression_weight = function(expression) { + if (is.logical(expression)) return(0) + sum(all.names(expression) %in% c("|", "&")) + 1 +} + + stats = list(depth = integer(0), expweight = numeric(0), simpweight = numeric(0), was_tautology = logical(0), was_contradiction = logical(0)) + set.seed(3 + ss) + for (depth_to_check in 2:12) { + for (repetition in seq_len(2000)) { + if (depth_to_check == 11) { + expression = random_cnf_expression(10, TRUE, 4) + } else if (depth_to_check == 12) { + expression = random_cnf_expression(5, TRUE, 2) + } else { + expression = random_cnf_expression(depth_to_check) + } + simplified = formula_to_expression(eval(expression)) + stats$depth[[length(stats$depth) + 1]] = depth_to_check + stats$expweight[[length(stats$expweight) + 1]] = expression_weight(expression) + stats$simpweight[[length(stats$simpweight) + 1]] = expression_weight(simplified) + vars = intersect(names(u), all.names(expression)) + assignments = expand.grid(lapply(vars, function(var) u[[var]]), stringsAsFactors = FALSE) + colnames(assignments) = vars + + truevals = rep(NA, nrow(assignments)) + for (i in seq_len(nrow(assignments))) { + assignment = assignments[i, , drop = FALSE] + trueval = evaluate_expression(expression, assignment) + simpval = evaluate_expression(simplified, assignment) + if (trueval != simpval) break + truevals[[i]] = trueval + } + stats$was_tautology[[length(stats$was_tautology) + 1]] = all(truevals) + stats$was_contradiction[[length(stats$was_contradiction) + 1]] = all(!truevals) + expect_equal(trueval, simpval, + info = sprintf("Expression: %s\nAssignment:\n%s\nSimplified to: %s", + deparse1(expression), + paste(capture.output(print(assignment)), collapse = "\n"), + deparse1(simplified) + )) + } + } + dti <- as.data.table(stats) + +saveRDS(dti, sprintf("expression_experiments_%05i.rds", ss)) + +dti[, .( + ew = mean(expweight), sw = mean(simpweight), + etriv = mean(expweight == 0), + striv = mean(simpweight == 0), + could_simplify = mean(expweight > simpweight), + was_tautology = mean(was_tautology), + was_contradiction = mean(was_contradiction), + tautologies_not_recognized = mean(was_tautology & simpweight > 0), + contradictions_not_recognized = mean(was_contradiction & simpweight > 0) + ), by = "depth"] From a0ff583457a2e03bd351988362165e6b68ce5f92 Mon Sep 17 00:00:00 2001 From: mb706 Date: Tue, 17 Sep 2024 05:52:28 +0200 Subject: [PATCH 41/87] bugfixes --- DESCRIPTION | 1 + R/CnfFormula_simplify2.R | 31 ++++++++++++++++--------------- tests/testthat/test_CnfFormula.R | 2 ++ 3 files changed, 19 insertions(+), 15 deletions(-) diff --git a/DESCRIPTION b/DESCRIPTION index a856345cc..79e005d63 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -102,6 +102,7 @@ Collate: 'CnfClause.R' 'CnfFormula.R' 'CnfFormula_simplify.R' + 'CnfFormula_simplify2.R' 'CnfSymbol.R' 'CnfUniverse.R' 'Graph.R' diff --git a/R/CnfFormula_simplify2.R b/R/CnfFormula_simplify2.R index 0d4419b8a..e4052b70a 100644 --- a/R/CnfFormula_simplify2.R +++ b/R/CnfFormula_simplify2.R @@ -150,6 +150,19 @@ simplify_cnf = function(entries, universe) { # is_not_subset_of was built, because unit-propagation could be cascading from a unit elimination. if (meta_idx > meta_idx_outer) return(FALSE) + if (!is_unit_propagation) { + # we are not propagating units, so we need to update the subset relations in the other direction. + # we do this first, in case on_update_subset_relations gets too eager later + idx_to_check = which(available %in% symbol_registry[[symbol]] & available <= meta_idx_outer) + for (other_meta_idx in idx_to_check) { + # was the other a subset of us before? that could have changed now. + if (!is_not_subset_of[[other_meta_idx]][meta_idx, symbol] && !all(entries[[available[[other_meta_idx]]]][[symbol]] %in% entries[[clause_idx]][[symbol]])) { + is_not_subset_of[[other_meta_idx]][meta_idx, symbol] <<- TRUE + # no need to call on_updated_subset_relations, since we are increasing rowsums, not decreasing them + } + } + } + is_not_subset_of_col = match(symbol, colnames(is_not_subset_of[[meta_idx]])) # * We could now be a subset of things that we were not a subset of before, so we only need to check the TRUE entries and may be setting them to FALSE. # --> hence `is_not_subset_of[meta_idx][is_not_subset_of[meta_idx]` @@ -176,23 +189,9 @@ simplify_cnf = function(entries, universe) { if (identical(ousr, TRUE)) return(TRUE) # forward contradiction signal. We don't care if other_meta_idx was eliminated. if (eliminated[[clause_idx]]) return(NULL) # need to check more directly if things escalated somehow and clause_idx was eliminated indirectly } - if (!is_unit_propagation) { - # we are not propagating units, so we need to update the subset relations in the other direction as well - idx_to_check = which(available %in% symbol_registry[[symbol]] & available <= meta_idx_outer) - for (other_meta_idx in idx_to_check) { - # was the other a subset of us before? that could have changed now. - if (!is_not_subset_of[[other_meta_idx]][meta_idx, symbol] && !all(entries[[available[[other_meta_idx]]]][[symbol]] %in% entries[[clause_idx]][[symbol]])) { - is_not_subset_of[[other_meta_idx]][meta_idx, symbol] <<- TRUE - # no need to call on_updated_subset_relations, since we are increasing rowsums, not decreasing them - } - } - } FALSE # no contradiction } - - - # eliminate `symbol` from `clause_idx` # returns 'NULL' for turned into a unit or eliminated, 'TRUE' for contradiction, 'FALSE' for nothing happened eliminate_symbol_from_clause = function(clause_idx, symbol) { @@ -230,7 +229,9 @@ simplify_cnf = function(entries, universe) { is_not_subset_of[[others_ref_this_symbol]][meta_idx, symbol] <<- TRUE } } - for (meta_idx_other in rows_changed) { + # we could have some leftover TRUEs from eliminated or unit-ed clauses + rows_changed_ids = available[rows_changed] + for (meta_idx_other in rows_changed[!eliminated[rows_changed_ids] & !is_unit[rows_changed_ids] & rows_changed <= meta_idx_outer]) { # We have to do this *after* we set the corresponding values to TRUE for others_ref_this_symbol, # since calling this could realistically change the symbol registry (e.g. if it leads to a symbol # being eliminated from other clauses). diff --git a/tests/testthat/test_CnfFormula.R b/tests/testthat/test_CnfFormula.R index 43bbc5b91..3a51b288b 100644 --- a/tests/testthat/test_CnfFormula.R +++ b/tests/testthat/test_CnfFormula.R @@ -627,6 +627,7 @@ test_that("Brute-force test", { stats = list(depth = integer(0), expweight = numeric(0), simpweight = numeric(0), was_tautology = logical(0), was_contradiction = logical(0)) set.seed(3 + ss) + for (depth_to_check in 2:11) { for (repetition in seq_len(200)) { if (depth_to_check == 10) { @@ -662,6 +663,7 @@ test_that("Brute-force test", { )) } } + dti <- as.data.table(stats) # }) From ef121ab4dbe54f70a0b8d92559a3beb0d61973a0 Mon Sep 17 00:00:00 2001 From: mb706 Date: Tue, 17 Sep 2024 05:54:52 +0200 Subject: [PATCH 42/87] better output --- attic/expression_experiments.R | 1 + 1 file changed, 1 insertion(+) diff --git a/attic/expression_experiments.R b/attic/expression_experiments.R index 72031b0b9..18feac796 100644 --- a/attic/expression_experiments.R +++ b/attic/expression_experiments.R @@ -6,6 +6,7 @@ checkmate::assert_integer(ss <- as.integer(args[1]), lower = 1, len = 1, any.mis library("mlr3pipelines") library("testthat") library("data.table") +options(width = 200) u = CnfUniverse() W = CnfSymbol(u, "W", c("p", "q", "r")) From 20e5b005039bee548a56bc89096d09da9a944650 Mon Sep 17 00:00:00 2001 From: mb706 Date: Wed, 18 Sep 2024 11:28:56 +0200 Subject: [PATCH 43/87] bugfix --- R/CnfFormula_simplify2.R | 50 +++++++++++++++++++++++++++------- attic/expression_experiments.R | 3 +- 2 files changed, 42 insertions(+), 11 deletions(-) diff --git a/R/CnfFormula_simplify2.R b/R/CnfFormula_simplify2.R index e4052b70a..8a67ac640 100644 --- a/R/CnfFormula_simplify2.R +++ b/R/CnfFormula_simplify2.R @@ -397,45 +397,65 @@ simplify_cnf = function(entries, universe) { if (ousr) return(return_entries(FALSE)) ousr = on_updated_subset_relations(meta_idx_outer, meta_idx_inner) + if (identical(ousr, TRUE)) return(return_entries(FALSE)) if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) break # honestly not sure if this could happen here if (is.null(ousr)) next - if (ousr) return(return_entries(FALSE)) } } # Now for the big one: Asymmetric Hidden Literal Addition - # we only loop over the entries that have not been eliminated yet. + # First, we do non-units, then we do units separately. + # We go big to small, since eliminating one clause could prevent us from eliminating other clauses, and all things being equal, we prefer eliminating long ones. + + # We only loop over the entries that have not been eliminated yet. # We update `remaining_nonunit_entries` inside the loop whenever a clause is eliminated. remaining_entries = which(!eliminated)[order(lengths(entries[!eliminated]), decreasing = TRUE)] remaining_nonunit_entries = remaining_entries[seq_len(length(remaining_entries) - length(unit_domains))] remaining_unit_entries = if (length(unit_domains)) remaining_entries[seq.int(length(remaining_entries) - length(unit_domains) + 1L, length(remaining_entries))] + + # iterating from large to small entries for (clause_idx in remaining_nonunit_entries) { clause = entries[[clause_idx]] + + # index inside `is_not_subset_of` meta_idx = available_inverse[[clause_idx]] remaining_other_entries = remaining_nonunit_entries[remaining_nonunit_entries != clause_idx] + # we keep track of which clauses were used for HLA, since every other clause can only do that once. + was_used = logical(length(remaining_other_entries)) + + # for each of the other clauses, how many of their symbols are not a subset of the current clause? not_subset_count = integer(length(remaining_other_entries)) - was_used = logical(length(remaining_other_entries)) # we keep track of which clauses were used for HLA, since every other clause can only do that once. for (roe_idx in seq_along(remaining_other_entries)) { + # if we had set up is_not_subset_of as a 3-dim array, then the following could just have been a colSums over is_not_subset_of[, meta_idx, ] + # However, that array would take a lot of memory: N_clauses^2 x N_all_symbols; The current setup has N_clauses^2 x max(N_symbols_per_clause) other_clause_idx = remaining_other_entries[[roe_idx]] meta_idx_other = available_inverse[[other_clause_idx]] not_subset_count[[roe_idx]] = sum(is_not_subset_of[[meta_idx_other]][meta_idx, ]) } repeat { - hla_clause_idx = match(TRUE, not_subset_count == 1 & !was_used) - if (is.na(hla_clause_idx)) break + # we do HLA by looking for a clause that is a subset of the current clause w/r/t all except one symbol. + # We also only consider every clause at most once, since it won't have anything else to add a second time. + # No need to check for == 0 here: if it was the case before, then we eliminated the clause already. If it becomes the case during the loop, we check + # for it further down. + hla_clause_idx = match(TRUE, not_subset_count == 1L & !was_used) + if (is.na(hla_clause_idx)) break # no more clauses to consider: all are either used or have no_subset_count > 1 clause_idx_other = remaining_other_entries[[hla_clause_idx]] meta_idx_other = available_inverse[[clause_idx_other]] symbol = colnames(is_not_subset_of[[meta_idx_other]])[is_not_subset_of[[meta_idx_other]][meta_idx, ]] range_old = clause[[symbol]] + # new range of the symbol inside the clause: Union of old range and complement of that symbol's range in the other clause. range_new = c(range_old, char_setdiff(universe[[symbol]], c(range_old, entries[[clause_idx_other]][[symbol]]))) if (length(range_new) == length(universe[[symbol]])) { # hidden tautology elimination + + # We still need the symbol registry (see below), so this can not be replaced by just `eliminated[[clause_idx]] = TRUE` eliminate_clause_update_sr(clause_idx) remaining_nonunit_entries = remaining_other_entries break } + # Now loop over clauses that also use the symbol, checking if they have one less `not_subset_count` because of that for (updating_clause_meta_idx in available_inverse[symbol_registry[[symbol]]]) { # we don't want to skip 'was_used' here, since we might still do hidden subsumption elimination with them. if (is_not_subset_of[[updating_clause_meta_idx]][meta_idx, symbol] && @@ -443,7 +463,7 @@ simplify_cnf = function(entries, universe) { is_not_subset_of[[updating_clause_meta_idx]][meta_idx, symbol] = FALSE roe_idx = match(available[[updating_clause_meta_idx]], remaining_other_entries) # I wished I didn't have to do this not_subset_count[[roe_idx]] = not_subset_count[[roe_idx]] - 1L - if (not_subset_count[[roe_idx]] == 0) { + if (not_subset_count[[roe_idx]] == 0L) { # hidden subsumption elimination eliminate_clause_update_sr(clause_idx) remaining_nonunit_entries = remaining_other_entries @@ -457,7 +477,11 @@ simplify_cnf = function(entries, universe) { } } - delayedAssign("roe_inverse", match(seq_along(entries), remaining_nonunit_entries)) + # We now do the same thing as above, only for units. + # Units are different, because they don't have the `is_not_subset_of` matrices. These are trivially constructed from + # The symbol registry: "is_not_subset_of" for unit relating to symbol `s` is TRUE for all symbols in a clause that are not `s`. + # We deliberately make use of `remaining_nonunit_entries` here, which has been updated in the loop above as nonunit-clauses were eliminated + delayedAssign("roe_inverse", match(seq_along(entries), remaining_nonunit_entries)) # only do this match()-call if it is actually needed for (clause_idx in remaining_unit_entries) { clause = entries[[clause_idx]] unitsymbol = names(clause) @@ -467,10 +491,13 @@ simplify_cnf = function(entries, universe) { # otherwise (if it does not contain the unit symbol), all N symbols are not subsets. not_subset_count = lengths(entries[remaining_nonunit_entries]) - (remaining_nonunit_entries %in% symbol_registry[[unitsymbol]]) + # corresponding to `is_not_subset_of` matrix; only construct this for entries where it is needed. is_not_subset_of_unit = vector("list", length(remaining_nonunit_entries)) + + # The following loop is mostly identical to the loop above, only for units. repeat { - hla_clause_idx = match(TRUE, not_subset_count == 1 & !was_used) - if (is.na(hla_clause_idx)) break + hla_clause_idx = match(TRUE, not_subset_count == 1L & !was_used) + if (is.na(hla_clause_idx)) break # no more clauses to consider: all are either used or have no_subset_count > 1 clause_idx_other = remaining_nonunit_entries[[hla_clause_idx]] clause_other = entries[[clause_idx_other]] if (is.null(is_not_subset_of_unit[[hla_clause_idx]])) { @@ -482,13 +509,16 @@ simplify_cnf = function(entries, universe) { range_new = c(range_old, char_setdiff(universe[[symbol]], c(range_old, clause_other[[symbol]]))) if (length(range_new) == length(universe[[symbol]])) { # hidden tautology elimination - # no more need to update unit registry etc. + # no more need to update the unit registry eliminated[[clause_idx]] = TRUE break } + # Now loop over clauses that also use the symbol, checking if they have one less `not_subset_count` because of that for (updating_clause_idx in symbol_registry[[symbol]]) { updating_hla_clause_idx = roe_inverse[[updating_clause_idx]] if (is.null(is_not_subset_of_unit[[updating_hla_clause_idx]])) { + # Dynamically construct this entry if it is not set yet. + # We could delay this further, but that would make things even more complicated updating_clause = entries[[updating_clause_idx]] is_not_subset_of_unit[[updating_hla_clause_idx]] = structure(names(updating_clause) != unitsymbol, names = names(updating_clause)) } diff --git a/attic/expression_experiments.R b/attic/expression_experiments.R index 18feac796..ffa82501d 100644 --- a/attic/expression_experiments.R +++ b/attic/expression_experiments.R @@ -6,7 +6,7 @@ checkmate::assert_integer(ss <- as.integer(args[1]), lower = 1, len = 1, any.mis library("mlr3pipelines") library("testthat") library("data.table") -options(width = 200) +options(width = 10000) u = CnfUniverse() W = CnfSymbol(u, "W", c("p", "q", "r")) @@ -70,6 +70,7 @@ expression_weight = function(expression) { } else { expression = random_cnf_expression(depth_to_check) } + cat(sprintf("%s\n", deparse1(expression))) simplified = formula_to_expression(eval(expression)) stats$depth[[length(stats$depth) + 1]] = depth_to_check stats$expweight[[length(stats$expweight) + 1]] = expression_weight(expression) From d87692b8bb43adb6025d2d53d171581af60d41b5 Mon Sep 17 00:00:00 2001 From: mb706 Date: Wed, 18 Sep 2024 11:29:18 +0200 Subject: [PATCH 44/87] regression tests --- tests/testthat/test_CnfFormula_simplify.R | 89 +++ tests/testthat/testdata/cnfcases.txt | 669 ++++++++++++++++++++++ 2 files changed, 758 insertions(+) create mode 100644 tests/testthat/test_CnfFormula_simplify.R create mode 100644 tests/testthat/testdata/cnfcases.txt diff --git a/tests/testthat/test_CnfFormula_simplify.R b/tests/testthat/test_CnfFormula_simplify.R new file mode 100644 index 000000000..22e14db0d --- /dev/null +++ b/tests/testthat/test_CnfFormula_simplify.R @@ -0,0 +1,89 @@ + + + + +test_that("CnfFormula Regression Tests", { + + testcases = readLines(test_path("testdata", "cnfcases.txt")) + + u = CnfUniverse() + W = CnfSymbol(u, "W", c("p", "q", "r")) + X = CnfSymbol(u, "X", c("s", "t", "u")) + Y = CnfSymbol(u, "Y", c("v", "w", "x")) + Z = CnfSymbol(u, "Z", c("y", "z", "a")) + + formula_to_expression = function(formula) { + if (is.logical(formula)) return(c(formula)) + clause_exprs = lapply(as.CnfFormula(formula), function(clause) { + atom_exprs = lapply(clause, function(atom) { + substitute(symbol %among% values, list(symbol = as.name(atom$symbol), values = atom$values)) + }) + Reduce(function(x, y) substitute(x | y, list(x = x, y = y)), atom_exprs) + }) + Reduce(function(x, y) substitute(x & y, list(x = x, y = y)), clause_exprs) + } + + evaluate_expression = function(expression, assignment) { + substituted = do.call(substitute, list(expression, c(list("%among%" = quote(`%in%`)), assignment))) + eval(substituted, envir = baseenv()) + } + + expression_weight = function(expression) { + if (is.logical(expression)) return(0) + sum(all.names(expression) %in% c("|", "&")) + 1 + } + + stats = list(depth = integer(0), expweight = numeric(0), simpweight = numeric(0), was_tautology = logical(0), was_contradiction = logical(0)) + + for (line in testcases) { + expression = parse(text = line)[[1]] + simplified = formula_to_expression(eval(expression)) + stats$depth[[length(stats$depth) + 1]] = depth_to_check + stats$expweight[[length(stats$expweight) + 1]] = expression_weight(expression) + stats$simpweight[[length(stats$simpweight) + 1]] = expression_weight(simplified) + vars = intersect(names(u), all.names(expression)) + assignments = expand.grid(lapply(vars, function(var) u[[var]]), stringsAsFactors = FALSE) + colnames(assignments) = vars + + truevals = rep(NA, nrow(assignments)) + for (i in seq_len(nrow(assignments))) { + assignment = assignments[i, , drop = FALSE] + trueval = evaluate_expression(expression, assignment) + simpval = evaluate_expression(simplified, assignment) + if (trueval != simpval) break + truevals[[i]] = trueval + } + stats$was_tautology[[length(stats$was_tautology) + 1]] = all(truevals) + stats$was_contradiction[[length(stats$was_contradiction) + 1]] = all(!truevals) + expect_equal(trueval, simpval, + info = sprintf("Expression: %s\nAssignment:\n%s\nSimplified to: %s", + deparse1(expression), + paste(capture.output(print(assignment)), collapse = "\n"), + deparse1(simplified) + )) + cat(".") + } + + dti <- as.data.table(stats) + # }) + + # dti <- rbindlist(dti_col, idcol = "seedoffset") + + dti[, .( + ew = mean(expweight), sw = mean(simpweight), + etriv = mean(expweight == 0), + striv = mean(simpweight == 0), + could_simplify = mean(expweight > simpweight), + was_tautology = mean(was_tautology), + was_contradiction = mean(was_contradiction), + tautologies_not_recognized = mean(was_tautology & simpweight > 0), + contradictions_not_recognized = mean(was_contradiction & simpweight > 0) + ), by = "depth"] + + + + + +}) + + diff --git a/tests/testthat/testdata/cnfcases.txt b/tests/testthat/testdata/cnfcases.txt new file mode 100644 index 000000000..1820e5e2c --- /dev/null +++ b/tests/testthat/testdata/cnfcases.txt @@ -0,0 +1,669 @@ +(((Y %among% c("w", "x") | X %among% "u") & (Z %among% "y" & W %among% c("p", "q")) | (X %among% c("u", "t") | W %among% "q") & (Z %among% c("y", "a") & W %among% "p")) & (X %among% c("u", "s") | X %among% c("s", "u") | (Y %among% c("x", "v") | Z %among% "a") | (X %among% c("t", "u") & W %among% "r" | (Z %among% "y" | W %among% "r"))) & ((Y %among% c("v", "x") | W %among% "q" | X %among% "t" & W %among% c("q", "p")) & (Y %among% "w" | Z %among% c("a", "y") | (W %among% "r" | W %among% "p")) | (X %among% "s" | Z %among% c("y", "a") | (W %among% c("q", "r") | W %among% c("q", "p")) | (Z %among% "z" | Y %among% c("w", "x")) & (X %among% c("u", "s") & X %among% "t"))) | (Y %among% c("w", "x") & Z %among% "y" & (W %among% "r" & Z %among% "a") | W %among% c("r", "p") & Y %among% "v" & (Y %among% c("v", "x") & W %among% c("q", "p"))) & (Y %among% c("v", "x") & W %among% "r" | (Z %among% c("y", "a") | W %among% c("r", "q")) | (X %among% c("s", "u") | Z %among% "y" | (X %among% "t" | X %among% "s"))) & ((X %among% c("u", "s") | Y %among% "w") & (Z %among% c("z", "y") | Y %among% c("w", "x")) & (Y %among% c("w", "v") & X %among% c("u", "s") & (W %among% "r" | X %among% c("s", "u"))) | ((X %among% "s" | Z %among% c("a", "y")) & (Y %among% c("x", "w") | Z %among% c("a", "z")) | X %among% "t" & W %among% c("r", "p") & (W %among% "p" & X %among% c("u", "t")))) | (W %among% c("p", "r") & Y %among% "w" & (X %among% "s" & X %among% "t") | W %among% "p" & Z %among% c("z", "y") & (W %among% c("p", "q" ) & Y %among% c("w", "v")) | (X %among% "t" | W %among% "p" | Y %among% "v" & Z %among% "a") & ((W %among% c("q", "p") | Y %among% "v") & (Y %among% c("x", "v") & Z %among% "a"))) & (W %among% "r" & X %among% "u" | (W %among% "q" | X %among% "s") | W %among% c("p", "q") & W %among% "p" & (W %among% "q" & W %among% "q") | (X %among% c("u", "t") & Z %among% "y" | Z %among% c("z", "y") & Y %among% "w" | W %among% c("r", "p") & W %among% c("r", "q") & (X %among% c("u", "t") & W %among% "p"))) & ((Z %among% c("z", "y") | W %among% c("q", "p") | (W %among% c("p", "r") | Y %among% "v") | (Z %among% "z" & W %among% c("q", "r") | Y %among% c("w", "x") & W %among% "p") | ((Z %among% c("y", "z") | W %among% "p") & (W %among% "p" | X %among% "t") | (Z %among% "y" | Z %among% "z" | Y %among% "x" & Y %among% "w"))) & ((Z %among% c("y", "a") | X %among% "t" | (W %among% c("p", "r") | X %among% c("t", "u"))) & (X %among% "t" & W %among% "p" & (W %among% c("q", "r") | Y %among% "w")) & (Z %among% "a" & W %among% "p" & (X %among% c("s", "t") | X %among% c("s", "u")) & (W %among% "p" & W %among% c("p", "r") | (W %among% c("p", "r") | W %among% c("p", "r"))))))) & (((Z %among% c("z", "y") & W %among% "q" | (Z %among% c("z", "y") | Y %among% "v")) & (Z %among% "a" | W %among% c("q", "p") | Z %among% c("y", "a") & Y %among% c("w", "x")) & (Y %among% "x" & Y %among% c("v", "x") & (W %among% "p" | Z %among% "z") | Z %among% "z" & Z %among% c("y", "z") & (Y %among% "w" & W %among% c("p", "r"))) | (Y %among% "v" | X %among% c("u", "s")) & (Z %among% "y" & Y %among% "v") & (Y %among% c("v", "x") & X %among% c("u", "s") | (X %among% "t" | Y %among% "w")) & ((Z %among% c("a", "z") | W %among% "q") & (Z %among% "y" | Z %among% "z") | Z %among% "a" & Z %among% "a" & (W %among% "q" | X %among% c("s", "t")))) & ((Y %among% "v" | X %among% "u" | Z %among% "a" & Z %among% c("z", "a")) & (W %among% c("p", "r") | Z %among% c("z", "y") | (X %among% c("t", "u") | Y %among% c("x", "v"))) & (Z %among% "a" | Y %among% "w" | X %among% c("t", "u") & W %among% c("p", "q") | Z %among% c("a", "y") & Y %among% "w" & (Z %among% "z" | Y %among% "w")) & ((Z %among% c("y", "z") & W %among% "q" | (X %among% c("u", "t") | X %among% c("s", "u"))) & ((Y %among% "v" | Z %among% c("z", "y")) & (W %among% c("q", "r") & Y %among% c("x", "v"))) & ((Y %among% "x" | Z %among% "y") & (W %among% c("r", "q") | W %among% "p") & (W %among% c("q", "r") & Y %among% "w" | (Z %among% "z" | X %among% "t"))))) | (Y %among% "w" | W %among% c("p", "r") | (Z %among% c("a", "y") | X %among% c("s", "u")) | (X %among% "s" | W %among% c("p", "r")) & (Y %among% c("v", "w") | Y %among% "v") | (W %among% "r" & X %among% "s" | (W %among% c("r", "q") | W %among% "q")) & (Y %among% c("v", "x") & Z %among% "a" | (W %among% "q" | Y %among% "w")) | (W %among% "p" & Y %among% c("v", "x") & (Y %among% "x" | W %among% "p") | (X %among% c("u", "s") | Y %among% "x") & (X %among% "s" & Z %among% "a") | (Z %among% c("z", "a") | X %among% c("t", "s")) & (Y %among% "v" | W %among% c("r", "q")) & (X %among% c("u", "t") & Z %among% "z" & (W %among% c("q", "p") & W %among% "p")))) & (((Z %among% "a" & X %among% c("s", "t") | (X %among% "t" | Z %among% "z")) & (Y %among% "x" & X %among% "t" & (Z %among% c("y", "a") | Y %among% c("w", "x"))) | (Z %among% "y" | Z %among% "z") & (W %among% "p" & X %among% "u") & ((Z %among% "a" | Z %among% "y") & (X %among% c("s", "t") | Y %among% c("x", "v")))) & ((X %among% c("u", "s") & Z %among% "y" | Z %among% "y" & Y %among% "x" | (Z %among% c("y", "z") & Z %among% c("y", "z") | (W %among% "r" | W %among% c("q", "p")))) & ((X %among% c("u", "s") & Z %among% c("z", "a") | (Z %among% "z" | Z %among% c("z", "a"))) & (Z %among% c("y", "z") | Z %among% "z" | (Y %among% c("w", "v") | X %among% c("s", "u"))))))) | ((Y %among% c("w", "x") | W %among% c("q", "r")) & (Z %among% c("a", "y") | Y %among% "x") & (Z %among% "a" | Z %among% "z" | (W %among% c("r", "q") | Y %among% "x")) & ((W %among% "r" | W %among% "p") & (X %among% "u" | Z %among% c("a", "z")) & (Y %among% "w" & Y %among% c("w", "x") | W %among% "r" & X %among% c("s", "u"))) | ((X %among% c("t", "s") | Y %among% c("x", "v")) & (W %among% "p" & X %among% "t") | (W %among% "q" | Y %among% "x" | (W %among% "r" | W %among% c("q", "r"))) | (Y %among% "v" | Z %among% "a" | Z %among% c("y", "z") & X %among% c("u", "s")) & (Z %among% "a" & Z %among% c("y", "z") & (Y %among% c("v", "w") & W %among% "p")))) & ((X %among% c("t", "s") & W %among% c("p", "r") & (W %among% "q" | Z %among% c("z", "y")) & (Y %among% "w" & W %among% c("q", "r") | Y %among% "x" & W %among% "p") | (Z %among% c("y", "z") & X %among% c("s", "u") | W %among% "p" & Y %among% c("x", "v")) & (Z %among% c("a", "z") & X %among% "t" & (Y %among% c("x", "v") | Y %among% "v"))) & ((Z %among% c("y", "z") | W %among% c("p", "q") | Z %among% "z" & W %among% "r") & ((Z %among% c("z", "a") | W %among% "q") & (Z %among% "a" | Z %among% "y")) & ((X %among% c("t", "s") | Y %among% c("x", "v") | (W %among% c("r", "p") | W %among% c("p", "q"))) & (W %among% c("p", "q") & X %among% "t" & (X %among% c("t", "s") | Y %among% "w"))))) & ((W %among% c("q", "p") & X %among% c("u", "t") | X %among% c("u", "s") & X %among% "t") & (X %among% "t" | Z %among% "a" | Y %among% "v" & Y %among% c("w", "x")) & (Z %among% "y" & Z %among% c("z", "a") & (X %among% "t" | W %among% "q") & (W %among% c("p", "q") | X %among% "s" | (Z %among% "y" | Y %among% c("x", "w")))) | (X %among% "u" & W %among% c("q", "r") | W %among% c("p", "q") & W %among% c("p", "r") | Y %among% c("x", "v") & Y %among% "v" & (W %among% "r" & Z %among% "a") | (Z %among% c("a", "z") | X %among% c("u", "t") | Z %among% "z" & X %among% "t") & (W %among% c("r", "p") & X %among% "u" | X %among% c("t", "s") & X %among% c("s", "t"))) | ((W %among% c("p", "q") | W %among% c("q", "p")) & (W %among% c("p", "r") | W %among% c("r", "p")) & (X %among% "t" & W %among% "p" | (Z %among% "a" | Z %among% "a")) | (W %among% "r" & Y %among% "x" & (Y %among% "v" & Z %among% "z") | (W %among% c("r", "p") | Z %among% "a" | Y %among% "v" & X %among% "s"))) & ((Z %among% "y" | X %among% c("s", "t")) & (Z %among% "a" & Y %among% "x") & (X %among% c("s", "t") & Z %among% c("y", "z") | Y %among% "v" & Z %among% c("y", "z")) | (Z %among% c("a", "y") | X %among% "t" | (W %among% "q" | Z %among% c("y", "z"))) & (Y %among% c("v", "x") & Y %among% c("x", "v") | (Z %among% "z" | Y %among% "v")))) & ((Z %among% c("z", "y") & Z %among% c("z", "y" ) & (W %among% "r" & Y %among% c("x", "w")) | (X %among% c("s", "t") | W %among% "q") & (W %among% "r" & W %among% c("p", "q"))) & ((Y %among% "v" | Y %among% "w") & (Z %among% "z" | Y %among% "x") & ((W %among% "p" | Z %among% "a") & (Z %among% c("z", "a") & W %among% c("r", "p")))) & ((Y %among% c("w", "v") | Y %among% c("x", "v") | (Y %among% c("x", "w") | W %among% "q") | X %among% c("t", "u") & Z %among% "z" & (W %among% c("r", "q") & X %among% "s")) & ((Y %among% c("v", "w") & Z %among% c("z", "y") | X %among% "s" & W %among% c("q", "p")) & ((W %among% "q" | W %among% c("p", "r")) & (Y %among% c("w", "x") | X %among% "t")))) & ((Z %among% "a" | W %among% c("r", "q")) & (W %among% c("p", "r") | Y %among% c("v", "x")) & (W %among% c("r", "p") & Z %among% "y" | (Z %among% "a" | Z %among% c("y", "z"))) & ((Y %among% "v" & X %among% "s" | Z %among% c("z", "y") & Y %among% "w") & (W %among% c("p", "q") & X %among% c("s", "u") | (X %among% c("u", "t") | W %among% "q"))) | (W %among% "r" | X %among% "t" | X %among% "u" & W %among% c("r", "p") | (X %among% c("s", "t") & X %among% "t" | (X %among% c("s", "t") | X %among% "s"))) & ((W %among% "q" | Z %among% c("a", "y")) & (X %among% "s" & Y %among% "w") | (Z %among% c("y", "a") & W %among% "p" | W %among% "p" & Y %among% "w"))) & ((X %among% "u" & Z %among% "z" | Y %among% c("w", "x") & Y %among% c("x", "w") | (X %among% c("s", "u") | W %among% "r" | (W %among% "q" | Y %among% "w"))) & (Z %among% c("z", "y") & Y %among% "w" & (W %among% "q" & Y %among% c("w", "x")) | (X %among% c("t", "u") | Y %among% c("x", "v")) & (Y %among% "w" & X %among% "s")) | (Y %among% "x" | Y %among% c("v", "x") | (Y %among% c("v", "w") | W %among% c("r", "q")) | (W %among% "p" | Y %among% c("v", "x")) & (W %among% "r" & W %among% "p")) & ((Y %among% c("v", "w") & W %among% "q" | Z %among% c("z", "a") & X %among% c("s", "u")) & (X %among% "u" & W %among% "q" & (W %among% "p" & Z %among% "a"))) | ((Z %among% "y" | W %among% "p" | (Z %among% c("y", "z") | Z %among% c("z", "y"))) & (Y %among% c("v", "w") | Z %among% c("z", "y") | (Z %among% c("y", "a") | X %among% c("s", "t"))) | (Z %among% "z" | X %among% "t" | (W %among% "q" | Y %among% "w") | Y %among% c("w", "x") & Y %among% c("x", "v") & (Y %among% c("x", "v") & X %among% c("s", "t")))) & ((W %among% "p" | Z %among% c("y", "z")) & (Z %among% c("z", "y") & Y %among% c("x", "v")) & (Z %among% c("a", "y") & Z %among% "a" & (W %among% c("p", "r") & Y %among% c("v", "x"))) & ((Y %among% "w" | X %among% "s") & (W %among% c("r", "p") & Z %among% c("a", "z")) & (Z %among% c("a", "z") | X %among% c("s", "t") | Y %among% "w" & W %among% "q"))))) +(W %among% c("p", "r") | X %among% c("s", "t") | (W %among% c("p", "q") | Y %among% c("w", "x")) | (W %among% "r" | Y %among% c("v", "x")) & (W %among% c("r", "p") & Y %among% c("x", "w")) | (X %among% "s" & Y %among% "v" | Y %among% "x" & X %among% "u") & (Z %among% c("a", "z") & Z %among% c("z", "y") | (Z %among% c("y", "a") | X %among% "u")) | ((W %among% "p" | Z %among% "a" | (Z %among% c("y", "a") | Z %among% c("a", "y"))) & ((Z %among% "a" | Z %among% c("y", "z")) & (X %among% "s" | Z %among% c("z", "y"))) | ((X %among% "s" | Z %among% "a") & (Y %among% c("x", "w") & W %among% c("r", "q")) | (Y %among% "w" | W %among% "r" | (Y %among% "v" | W %among% c("p", "r")))))) & ((Z %among% "z" | X %among% "t" | (Z %among% "z" | W %among% "r") | X %among% "u" & X %among% "u" & (W %among% "q" & W %among% c("q", "p"))) & ((Y %among% c("x", "v") & W %among% c("p", "q") | (X %among% "t" | Y %among% c("v", "w"))) & (Z %among% "y" & Y %among% c("w", "x") | Z %among% c("a", "z") & X %among% "t")) & ((W %among% c("p", "q") | X %among% c("t", "u")) & (X %among% c("t", "s") | W %among% "r") & (X %among% c("s", "u") & W %among% c("q", "r") & (Z %among% "a" | Y %among% "v")) | W %among% "p" & W %among% c("q", "r") & (X %among% "s" | X %among% c("s", "u")) & (Z %among% "z" | Y %among% "v" | (Y %among% c("x", "w") | W %among% "r")))) | Y %among% c("v", "x") & X %among% "s" & (X %among% "u" & Y %among% c("x", "w")) & ((X %among% "u" | X %among% "t") & (W %among% c("p", "r") | Z %among% "z")) & (X %among% "u" & W %among% c("r", "p") & (Y %among% c("w", "v") | W %among% c("r", "q")) & (Z %among% c("z", "y") | Z %among% "a" | W %among% "p" & Y %among% "v")) & ((X %among% "u" | W %among% c("q", "p")) & (X %among% c("u", "t") | Z %among% "y") & (Z %among% c("a", "z") & W %among% "r" | X %among% "t" & Z %among% c("y", "a")) & (Y %among% c("v", "x") & Z %among% "a" & (W %among% c("p", "q") & W %among% "q") | (Y %among% "w" & Y %among% "w" | (Y %among% "w" | Y %among% c("v", "x"))))) & ((Z %among% "z" | Z %among% c("a", "y") | Y %among% c("x", "w") & W %among% c("q", "p") | (Y %among% "v" | X %among% "s") & (X %among% c("u", "t") | X %among% "u")) & ((Z %among% c("y", "z") | X %among% "t" | (W %among% c("q", "r") | W %among% "q")) & (Z %among% c("z", "y") & W %among% "p" | Y %among% c("w", "x") & Y %among% c("w", "v"))) & ((Z %among% "a" & W %among% c("p", "q") & (X %among% "u" | W %among% c("p", "r")) | (Z %among% c("y", "a") | Z %among% c("a", "z") | (Z %among% "z" | W %among% c("q", "p")))) & (Y %among% "x" & Y %among% "v" & (W %among% c("q", "p") | Y %among% "w") | Z %among% "y" & X %among% c("u", "t") & (X %among% c("t", "s") | W %among% "r")))) | ((X %among% "s" & X %among% "t" & (W %among% c("q", "r") & X %among% "s") | (Y %among% c("v", "w") & X %among% "u" | Z %among% c("a", "y") & W %among% c("r", "q"))) & (X %among% "u" | Z %among% "z" | Y %among% "v" & X %among% c("s", "u") | (Z %among% c("a", "z") & W %among% c("q", "p") | X %among% c("t", "s") & Y %among% c("v", "x" ))) | (W %among% "r" | X %among% c("s", "t") | Z %among% "a" & Z %among% c("z", "y") | (W %among% c("p", "q") | W %among% c("q", "p") | (X %among% c("t", "u") | Z %among% "a"))) & ((X %among% "u" | Z %among% c("a", "z")) & (Z %among% c("a", "z") & Y %among% c("x", "w")) & (Y %among% "x" | W %among% "r" | Y %among% "v" & Y %among% "w")) | (((Z %among% "y" | Z %among% "z") & (X %among% c("u", "t") & Z %among% "z") | Y %among% c("x", "v") & X %among% "s" & (X %among% "s" & Y %among% c("w", "x"))) & (Z %among% "a" | W %among% c("r", "p") | W %among% "q" & Z %among% "a" | (Z %among% "z" | Z %among% "y" | (Z %among% "z" | Y %among% "w"))) | (Y %among% c("v", "w") | W %among% c("r", "p")) & (Y %among% c("w", "x") & Y %among% c("x", "w")) & (X %among% c("s", "t") | Z %among% "z" | (Z %among% c("z", "y") | Y %among% "x")) & ((Y %among% c("v", "w") | Z %among% c("y", "z")) & (Y %among% "w" & W %among% "r") | (Z %among% "a" & W %among% c("p", "r") | (Y %among% c("v", 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c("s", "t") & W %among% c("q", "p"))) & ((Z %among% c("a", "y") & Z %among% "y" | (Z %among% "y" | W %among% "r")) & ((Y %among% "w" | Y %among% c("v", "x")) & (X %among% "s" | W %among% "p")) & (Z %among% c("y", "a") & W %among% "r" | (Y %among% c("x", "v") | W %among% "p") | (Z %among% "a" & W %among% "q" | (W %among% "q" | Y %among% c("v", "w"))))))) & ((W %among% c("p", "r") & W %among% c("p", "r") | Z %among% c("a", "y") & Y %among% c("v", "x") | (X %among% c("t", "u") | Y %among% "v") & (X %among% "s" & W %among% "p")) & (W %among% c("q", "p") & X %among% "u" & (X %among% c("u", "t") & Z %among% "z") | (Z %among% "a" | Z %among% "y") & (Y %among% c("v", "w") | Y %among% c("w", "v"))) & ((Z %among% c("a", "y") | X %among% "t" | (X %among% "t" | X %among% "t") | (X %among% c("t", "u") | Z %among% "y" | Y %among% c("w", "x") & Z %among% c("a", "z"))) & ((W %among% "q" | Y %among% c("w", "x")) & (X %among% c("s", "u") & W %among% c("r", "p")) | Y %among% "x" & Z %among% c("a", "z") & (Y %among% "x" | Y %among% "x"))) & (((W %among% "r" | Y %among% "w") & (Z %among% "a" | Y %among% "x") & ((W %among% "r" | Z %among% c("a", "y")) & (Z %among% c("z", "a") & X %among% c("t", "u"))) | (X %among% "u" | W %among% "p" | Y %among% "v" & W %among% c("p", "q")) & (W %among% "r" & Z %among% c("y", "z") & (X %among% "u" & X %among% "s"))) & ((X %among% c("u", "s") | W %among% "q" | (Z %among% "y" | X %among% "t")) & ((Y %among% c("v", "w") | Y %among% "w") & (Y %among% c("w", "x") | Z %among% "a")) | (X %among% "t" & Z %among% "y" | X %among% c("s", "u") & Y %among% c("v", "x") | (X %among% c("t", "u") & X %among% "s" | (Y %among% "v" | W %among% c("q", "r")))))) & (((Z %among% "y" | Y %among% c("x", "w")) & (Y %among% c("w", "v") & W %among% c("p", "r")) | (X %among% "t" | Z %among% "y" | (Y %among% "v" | X %among% c("s", "u"))) | ((Y %among% c("x", "v") | Y %among% "v") & (X %among% "t" & Y %among% "w") | (Y %among% c("v", "x") & X %among% "t" | Y %among% c("v", "x") & W %among% c("p", "r")))) & (Y %among% "v" & Z %among% "a" & (Y %among% c("x", "w") | X %among% "u") & (X %among% c("s", "t") & W %among% "p" | W %among% c("r", "p") & Z %among% "z") & (Y %among% "w" & Z %among% "z" & (X %among% c("t", "s") | Z %among% c("a", "z")) & (Z %among% "z" & Z %among% c("y", "z") & (W %among% c("r", "p" ) | W %among% c("r", "q"))))) | X %among% c("u", "s") & W %among% c("q", "p") & (Z %among% c("a", "z") & Y %among% "v") & (Z %among% c("z", "y") & Z %among% "y" & (Y %among% "v" | X %among% c("s", "t"))) & (X %among% "u" & X %among% c("u", "s") & (Y %among% "x" & Y %among% c("w", "v")) & (Y %among% c("x", "w") & W %among% "p" & (W %among% c("p", "r") | X %among% c("s", "u")))) & (((Z %among% c("z", "y") | W %among% c("q", "p")) & (X %among% c("u", "t") & W %among% "p") | X %among% c("s", "u") & W %among% c("r", "p") & (X %among% "u" | W %among% c("q", "p"))) & ((W %among% "r" | X %among% "t") & (Y %among% "w" | X %among% c("u", "s")) | Y %among% "w" & W %among% c("r", "p") & (X %among% "s" | W %among% "p"))))) +(((Y %among% c("v", "w") & Y %among% "w" | Y %among% "v" & Y %among% c("w", "v")) & (X %among% "u" & Z %among% c("y", "z") & (Z %among% c("a", "y") | Z %among% "z")) | (X %among% c("s", "u") & W %among% "q" & (Y %among% c("w", "v") & Z %among% c("y", "z")) | (Y %among% "v" | X %among% "t" | (Y %among% c("v", "x") | Y %among% c("x", "v")))) | (X %among% c("s", "u") | Y %among% "v" | W %among% "r" & W %among% "r" | (Y %among% c("w", "x") | Z %among% c("y", "z") | W %among% "r" & Y %among% c("w", "v" )) | (Y %among% "w" & Y %among% c("x", "w") & (W %among% c("r", "q") & X %among% "u") | (Y %among% "w" | Y %among% c("x", "w")) & (W %among% "q" | Y %among% "v")))) & ((W %among% "q" & X %among% "s" & (X %among% "s" & Y %among% c("w", "x")) | X %among% "u" & W %among% "r" & (W %among% c("p", "r") & Y %among% "v")) & ((W %among% "q" | X %among% "s") & (W %among% "p" & Y %among% "w") | (X %among% c("t", "u") & X %among% "s" | Y %among% "x" & W 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%among% "v") & (X %among% "s" & X %among% c("s", "u"))))) & ((W %among% c("p", "r") & W %among% "r" & (Y %among% "w" & Y %among% "x") & ((Y %among% c("v", "w") | W %among% "p") & (Z %among% "y" | Y %among% c("v", "x"))) | (Z %among% "a" & Y %among% c("w", "x") | (Z %among% "z" | Y %among% "w")) & ((Y %among% "w" | Y %among% "w") & (X %among% c("s", "t") & Z %among% c("y", "z")))) & (W %among% "q" | Y %among% c("v", "w") | Y %among% c("w", "x") & X %among% "t" | Y %among% c("v", "w") & Z %among% c("y", "z") & (X %among% c("u", "t") & X %among% c("u", "t")) | (X %among% c("s", "u") | Z %among% "a") & (Y %among% c("w", "x") | Z %among% "y") & (Y %among% c("v", "w") | Y %among% c("w", "v") | (X %among% c("t", "u") | X %among% "u")))) | (Z %among% "a" | Y %among% c("w", "v")) & (W %among% "q" | Y %among% c("x", "v")) & (W %among% c("q", "r") & X %among% "s" | W %among% c("r", "p") & Z %among% "y") & (X %among% c("t", "u") & Z %among% "a" & (Y %among% "w" | Z %among% "y") | W %among% c("p", "r") & X %among% "s" & (Y %among% c("w", "v") & Z %among% c("a", "y"))) & ((X %among% "t" & X %among% c("s", "t") | (Y %among% c("w", "v") | Z %among% c("z", "y")) | X %among% c("t", "u") & Z %among% c("y", "z") & (Y %among% c("w", "x") & Z %among% "z")) & ((Z %among% c("y", "z") | W %among% "p" | (X %among% "t" | Z %among% "y")) & (W %among% "r" | Y %among% "x" | Z %among% c("y", "a") & Z %among% "z"))) & ((Y %among% "w" & X %among% c("t", "s") & (Y %among% "w" & W %among% c("r", "q")) | (W %among% c("p", "q") | Y %among% c("w", "v")) & (W %among% c("r", "p") | W %among% "p") | (W %among% c("p", "q") | W %among% c("p", "r") | Y %among% "x" & Z %among% c("y", "a") | (W %among% c("p", "q") & Y %among% "w" | (Z %among% c("y", "z") | Z %among% c("y", "a"))))) & ((Z %among% c("a", "z") | Y %among% c("v", "w") | (Y %among% "x" | W %among% "p")) & (Y %among% "v" & Y %among% "x" | Y %among% c("v", "x") & Z %among% c("a", "y")) | (X %among% c("s", "t") & W %among% "p" & (X %among% c("s", "t") & Y %among% "v") | (Z %among% c("a", "y") | Y %among% "v") & (X %among% "u" | Z %among% c("z", "a"))))) & (X %among% "t" & Y %among% c("x", "w") & (W %among% c("p", "r") & W %among% "q") | (Z %among% c("a", "y") | Y %among% c("v", "w")) & (W %among% c("r", "p") | X %among% "t") | (Z %among% "a" & Y %among% "x" & (X %among% "u" | Z %among% c("z", "a")) | (Y %among% c("w", "v") | X %among% "t") & (X %among% c("t", "u") | X %among% c("s", "u"))) | ((X %among% "t" | Y %among% c("x", "w") | (W %among% "r" | Y %among% c("x", "v"))) & (Y %among% "w" & Y %among% c("v", "w") & (Z %among% c("z", "y") & Z %among% "z")) | (W %among% "p" | Y %among% c("w", "x")) & (Z %among% "a" & Y %among% "v") & (Y %among% "w" & Z %among% c("a", "z") | (Z %among% c("z", "a") | X %among% "u"))) | ((X %among% c("t", "s") | Y %among% "x") & (Y %among% c("w", "x") & Y %among% c("w", "x")) & (Y %among% "v" | Z %among% c("z", "a") | (Y %among% "v" | X %among% "u")) & ((W %among% c("r", "p") | Z %among% c("a", "z")) & 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%among% c("s", "u") | X %among% c("t", "u")) & (W %among% c("r", "p") | Z %among% c("y", "a") | W %among% c("q", "p") & X %among% c("t", "u")) & (W %among% c("p", "r") & X %among% c("t", "u") & (X %among% "t" | X %among% "u") | (Z %among% c("a", "y") & X %among% c("s", "t") | Y %among% "w" & W %among% "p")) & (Y %among% "w" & Y %among% c("w", "x") & (Z %among% c("y", "a") & W %among% c("r", "p")) | X %among% "t" & W %among% "p" & (Y %among% c("w", "v") & W %among% "p") | W %among% c("q", "p") & X %among% c("s", "u") & (Y %among% c("w", "x") | X %among% c("s", "u")) & (Z %among% "y" & Y %among% "x" | (Z %among% c("a", "z") | W %among% c("r", "q"))))) & ((Y %among% c("w", "v") & W %among% c("r", "q") & (Y %among% "w" & W %among% c("r", "q")) | (Z %among% c("z", "a") | Z %among% "y" | (Z %among% c("y", "z") | W %among% "q"))) & (W %among% "q" & W %among% "q" | (Z %among% c("z", "a") | Y %among% "x") | (W %among% c("r", "p") | W %among% c("r", "q") | X %among% "t" & Y %among% c("x", "v"))) 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"z")) & (Z %among% "a" & Y %among% c("v", "x")) | (X %among% "s" | Y %among% "w") & (Y %among% "w" | Z %among% "z")) & (W %among% c("r", "p") & Y %among% "w" | Y %among% c("x", "w") & W %among% "q" | (Y %among% c("x", "w") | Y %among% c("v", "w")) & (Y %among% "w" & Y %among% c("x", "v")))) & ((Z %among% "z" | Y %among% c("w", "x") | (X %among% "u" | X %among% c("t", "u"))) & (Z %among% c("a", "z") | W %among% "r" | (X %among% c("s", "t") | Y %among% c("x", "w"))) & ((W %among% "r" | Z %among% "a") & (Y %among% "v" | Z %among% c("z", "y")) | (Z %among% "y" | Y %among% "v") & (Y %among% "v" & W %among% "p")) | ((X %among% "u" | W %among% c("r", "p")) & (W %among% "q" | Y %among% "w") | (W %among% c("r", "q") & Y %among% "w" | (Z %among% c("a", "y") | Z %among% "a"))) & ((Z %among% c("y", "z") | Z %among% "z") & (Z %among% "a" | Y %among% "v") & (Y %among% "x" & X %among% "s" & (Y %among% "x" | W %among% c("q", "p"))))) | ((Y %among% c("w", "x") | X %among% c("t", "s")) & (W %among% "p" 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c("t", "u") | (X %among% "s" | Y %among% c("x", "w")))) | ((W %among% c("p", "q") & Z %among% c("y", "a") | Z %among% "a" & X %among% c("t", "s")) & (Y %among% "v" & Y %among% "x" | Y %among% c("v", "w") & Z %among% "z") | (Y %among% "w" | W %among% c("r", "q") | (Y %among% c("v", "x") | Y %among% c("w", "v")) | (Z %among% "a" & Z %among% c("y", "z") | (Z %among% c("y", "z") | W %among% "r")))) & ((W %among% "r" & Z %among% c("z", "a") | X %among% "u" & W %among% "p") & (W %among% c("p", "q") | W %among% c("q", "r") | Z %among% c("y", "a") & W %among% c("r", "q")) | (W %among% c("q", "r") | W %among% c("p", "r") | Y %among% "v" & Z %among% c("a", "y") | (W %among% "r" | W %among% "r" | (Y %among% "v" | Y %among% "w")))))) & (Y %among% "x" & W %among% "q" | W %among% c("q", "r" ) & Y %among% c("w", "x") | (Z %among% "a" | Y %among% "w") & (Y %among% "v" | Z %among% "a") | Z %among% "y" & X %among% "t" & (W %among% "q" | X %among% "u") & ((X %among% c("s", "t") | X %among% "t") & (Y %among% "w" & X %among% "s")) | (W %among% c("q", "r") | X %among% c("t", "s") | W %among% "r" & Z %among% c("a", "y") | (Y %among% c("x", "v") | Z %among% c("y", "z")) & (X %among% "t" & X %among% c("t", "u"))) & ((Y %among% c("v", "w") | Y %among% c("v", "x")) & (Z %among% "y" | Z %among% "y") | (Z %among% "a" & W %among% c("r", "p") | W %among% c("p", "q") & X %among% "s")) | ((W %among% c("r", "p") & X %among% "t" & (Y %among% "w" | X %among% "t") | (X %among% c("t", "s") | Z %among% "y") & (W %among% c("r", "p") & Z %among% c("z", "a"))) & (Y %among% c("x", "v") | Z %among% "a" | (W %among% "p" | Z %among% "y") | (Z %among% "y" & Y %among% c("x", "w") | (X %among% c("s", "u") | W %among% "p"))) | (Y %among% c("v", "x") | W %among% c("r", "q")) & (Y %among% "w" | Z %among% c("y", "z" )) & (X %among% "s" & X %among% c("s", "t") & (Y %among% "x" | X %among% c("s", "u"))) & (W %among% "q" & W %among% "r" & (Z %among% c("z", "y") & Y %among% c("x", "v")) & (X %among% c("s", "t") & W %among% "q" | (Z %among% "z" | Z %among% c("y", "z"))))) | (X %among% "u" & X %among% c("s", "t") & (W %among% "r" | Y %among% "v") & ((Y %among% "v" | X %among% c("u", "t")) & (X %among% c("u", "t") | W %among% c("p", "q"))) | (W %among% c("r", "p") & Y %among% "x" | Y %among% c("x", "w") & X %among% c("u", "t")) & (Z %among% c("z", "y") & W %among% c("r", "p") & (Z %among% "a" | X %among% "t")) | ((X %among% "t" & X %among% c("s", "u") | Y %among% "v" & X %among% c("s", "u")) & (X %among% "s" & X %among% c("s", "u") & (W %among% c("p", "q") & Z %among% "a")) | (W %among% c("p", "r") & Z %among% c("z", "y") | X %among% "t" & W %among% "r") & (W %among% c("r", "p") & W %among% c("p", "r") & (Z %among% "z" | Z %among% "z")))) & ((Y %among% c("w", "v") & W %among% "p" | Z %among% "z" & Z %among% c("z", "y")) & (W %among% c("r", "p") | X %among% "t" | (Z %among% "a" | Y %among% "w")) & ((Y %among% c("v", "x") | Y %among% "w" | (Z %among% c("z", "y") | Z %among% "z")) & (X %among% c("s", "t") & X %among% c("t", "u") | X %among% c("u", "s") & W %among% c("r", "q"))) | (Y %among% "w" & Z %among% "a" | (W %among% c("q", "r") | W %among% c("q", "r"))) & (Y %among% c("x", "w") | W %among% "p" | (Z %among% "y" | X %among% c("u", "s"))) & (Y %among% c("w", "x") & W %among% "q" & (Z %among% c("y", "a") & W %among% "r") | Z %among% c("y", "z") & X %among% c("t", "s") & (Z %among% "z" | W %among% "q"))) | ((Y %among% c("x", "w") & X %among% c("u", "t") | W %among% "r" & Z %among% c("z", "a") | W %among% c("q", "p") & X %among% c("t", "u") & (W %among% c("r", "q") | X %among% "u")) & ((W %among% c("r", "q") | X %among% c("u", "s") | (Y %among% "w" | X %among% "s")) & (X %among% c("u", "t") & X %among% c("t", "u") | Z %among% "z" & Z %among% c("a", "y"))) | ((Z %among% "y" & X %among% c("s", "t" ) | (W %among% "q" | X %among% c("t", "u"))) & (W %among% "r" & W %among% c("q", "p") & (Z %among% c("y", "z") | Y %among% "v")) | (Z %among% "y" & Y %among% "x" & (Z %among% "y" | Z %among% c("y", "z")) | Z %among% c("y", "z") & Z %among% "a" & (Z %among% "y" | W %among% "p"))) | ((Y %among% c("v", "x") | W %among% "p") & (W %among% "r" & X %among% "s") & ((Y %among% c("w", "x") | Y %among% "w") & (Z %among% "z" | Z %among% "a")) | (W %among% c("r", "q") | X %among% c("u", "s") | W %among% "r" & X %among% c("u", "s") | (Y %among% c("w", "x") | Z %among% "y") & (W %among% "p" & W %among% "r"))) & ((Z %among% c("a", "y") | Y %among% "x" | Z %among% c("z", "y") & Y %among% c("v", "w")) & (W %among% c("q", "p") | Y %among% c("x", "w") | (Y %among% c("w", "v") | Z %among% "a")) & ((W %among% "r" | Y %among% "v") & (Y %among% "v" & Z %among% c("y", "a")) | W %among% "p" & Z %among% c("z", "a") & (Z %among% c("z", "a") | Y %among% c("v", "x"))))) & ((Y %among% "x" | X %among% c("s", "u") | (X %among% c("t", "u") | W %among% c("r", "q"))) & (Y %among% c("x", "w") | W %among% "q" | Z %among% "z" & Z %among% "y") | (X %among% c("s", "t") & Y %among% c("w", "x") & (Y %among% c("x", "w") | Z %among% "z") | (Y %among% c("x", "w") | Y %among% "x") & (Z %among% c("a", "z") & Y %among% "v")) | (W %among% "q" & W %among% "r" | (X %among% c("s", "u") | X %among% "s")) & (Z %among% "y" & Y %among% c("v", "x") & (W %among% "p" | W %among% c("p", "q"))) & (X %among% "s" & W %among% "p" | X %among% "s" & X %among% c("t", "u") | (Y %among% c("x", "v") | Y %among% c("w", "x")) & (X %among% c("t", "s") & Y %among% c("w", "x"))) | ((Y %among% "v" & W %among% c("q", "p") | W %among% c("r", "p") & W %among% "q") & (W %among% c("p", "q") & Z %among% "z" & (X %among% c("u", "s") & W %among% c("q", "r"))) | (Z %among% "y" & Y %among% "x" & (X %among% "t" | Z %among% "z") | W %among% "p" & W %among% c("r", "p") & (Z %among% c("z", "a") & X %among% "u"))) & ((W %among% c("p", "r") | W %among% c("p", "r") | Z %among% c("z", "y") & W %among% "q" | Y %among% c("v", "w") & W %among% "r" & (X %among% "s" & Y %among% c("w", "v"))) & ((W %among% "p" & X %among% "s" | (W %among% c("q", "r") | W %among% "r")) & (Z %among% "a" & X %among% "u" | Z %among% c("y", "a") & Y %among% "v"))))) From d3f7827e1fde9f3f09cafa195e90a22db829d9dc Mon Sep 17 00:00:00 2001 From: mb706 Date: Wed, 18 Sep 2024 14:45:25 +0200 Subject: [PATCH 45/87] another bugfix --- R/CnfFormula_simplify2.R | 31 ++++++---- attic/experiments.R | 72 +++++++++++++++++++++++ tests/testthat/test_CnfFormula_simplify.R | 21 +++---- 3 files changed, 102 insertions(+), 22 deletions(-) diff --git a/R/CnfFormula_simplify2.R b/R/CnfFormula_simplify2.R index 8a67ac640..4a56f3402 100644 --- a/R/CnfFormula_simplify2.R +++ b/R/CnfFormula_simplify2.R @@ -152,8 +152,8 @@ simplify_cnf = function(entries, universe) { if (!is_unit_propagation) { # we are not propagating units, so we need to update the subset relations in the other direction. - # we do this first, in case on_update_subset_relations gets too eager later - idx_to_check = which(available %in% symbol_registry[[symbol]] & available <= meta_idx_outer) + # we do this first, in case on_updated_subset_relations gets too eager later + idx_to_check = which(available[seq_len(meta_idx_outer)] %in% symbol_registry[[symbol]]) for (other_meta_idx in idx_to_check) { # was the other a subset of us before? that could have changed now. if (!is_not_subset_of[[other_meta_idx]][meta_idx, symbol] && !all(entries[[available[[other_meta_idx]]]][[symbol]] %in% entries[[clause_idx]][[symbol]])) { @@ -174,7 +174,7 @@ simplify_cnf = function(entries, universe) { # --> hence `available %in% symbol_registry[[symbol]]` # * We only need to check up to the point where we have built is_not_subset_of # --> hence `available <= meta_idx_outer` - rows_to_check = which(is_not_subset_of[[meta_idx]][, is_not_subset_of_col] & available %in% symbol_registry[[symbol]] & available <= meta_idx_outer) + rows_to_check = which((is_not_subset_of[[meta_idx]][, is_not_subset_of_col] & available %in% symbol_registry[[symbol]])[seq_len(meta_idx_outer)]) for (other_meta_idx in rows_to_check) { # when we get here, that means that the symbol exists both in clause_idx and in other_ref_this symbol, *and* we have seen both clauses # in the is_not_subset_of building process. @@ -370,6 +370,8 @@ simplify_cnf = function(entries, universe) { # symbols that are not in common trivially get the matrix entry TRUE # (they are not subsets of their counterpart in the other clause, since the other ones are empty) + updated_inso_inner = FALSE + updated_inso_outer = FALSE for (symbol_idx_inner in sci_names_in_common) { symbol_idx_outer = sci_sc_map[[symbol_idx_inner]] @@ -381,29 +383,34 @@ simplify_cnf = function(entries, universe) { inner_subset_of_outer = all(range_inner %in% range_outer) outer_subset_of_inner = (inner_subset_of_outer && length(range_outer) == length(range_inner)) || all(range_outer %in% range_inner) if (inner_subset_of_outer) { + updated_inso_inner = TRUE # Avoid assigning TRUE to matrix that is initialized with TRUE. # We index by column name here, since it is possible that clauses were shortened by # unit propagation or self subsumption elimination somewhere on the way here is_not_subset_of[[meta_idx_inner]][meta_idx_outer, symbol] = FALSE } if (outer_subset_of_inner) { + updated_inso_outer = TRUE is_not_subset_of[[meta_idx_outer]][meta_idx_inner, symbol] = FALSE } } # prefer to eliminate the outer loopo clause first, since we have already # done more work for the inner loop clause (which comes earlier in 'entries') - ousr = on_updated_subset_relations(meta_idx_inner, meta_idx_outer) - if (is.null(ousr)) break - if (ousr) return(return_entries(FALSE)) - - ousr = on_updated_subset_relations(meta_idx_outer, meta_idx_inner) - if (identical(ousr, TRUE)) return(return_entries(FALSE)) - if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) break # honestly not sure if this could happen here - if (is.null(ousr)) next + if (updated_inso_inner) { + ousr = on_updated_subset_relations(meta_idx_inner, meta_idx_outer) + if (is.null(ousr)) break + if (ousr) return(return_entries(FALSE)) + } + if (updated_inso_outer) { + ousr = on_updated_subset_relations(meta_idx_outer, meta_idx_inner) + if (identical(ousr, TRUE)) return(return_entries(FALSE)) + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) break # probably this can happen if things cascade onwards when updating clause_inner + if (is.null(ousr)) next + } } } - # Now for the big one: Asymmetric Hidden Literal Addition + # Now for the big one: Asymmetric Hidden Literal Addition (Marijn et al.) # First, we do non-units, then we do units separately. # We go big to small, since eliminating one clause could prevent us from eliminating other clauses, and all things being equal, we prefer eliminating long ones. diff --git a/attic/experiments.R b/attic/experiments.R index e94bfad85..9791cfb04 100644 --- a/attic/experiments.R +++ b/attic/experiments.R @@ -913,3 +913,75 @@ gr <- po("replicate", reps = ntree) %>>% "one" %<>>% "two" %<>>% "three" #> 'one' >> 'two' #> 'onetwo' >> 'three' + +# W X Y Z +#29 q s v z + +quote( + ((Z %among% "y" & Z %among% c("y", "z")) & (Y %among% "w" & X %among% c("t", "u") | Y %among% c("v", "w") & X %among% "t")) | + (Y %among% c("w", "v") & (Z %among% "z" | Y %among% "w") & (X %among% "s" & Y %among% "w" | X %among% c("u", "s") & W %among% "p")) +) -> expr_full ; evaluate_expression(expr_full, assignment) != evaluate_expression(formula_to_expression(eval(expr_full)), assignment) + +evaluate_expression(expr_full, assignment) + +clause1 <- ((Z %among% "y" & Z %among% c("y", "z")) & (Y %among% "w" & X %among% c("t", "u") | Y %among% c("v", "w") & X %among% "t")) +clause2 <- (Y %among% c("w", "v") & (Z %among% "z" | Y %among% "w") & (X %among% "s" & Y %among% "w" | X %among% c("u", "s") & W %among% "p")) + + +formula_to_expression(clause1) |> evaluate_expression(assignment) +formula_to_expression(clause2) |> evaluate_expression(assignment) + + +clause1 +clause2 + +clause1 | clause2 + +formula_to_expression(clause1 | clause2) |> evaluate_expression(assignment) + +# > clause1 +# CnfFormula: +# (Z ∈ {y}) !! +# & (Y ∈ {w, v}) +# & (X ∈ {t, u}) !! +# & (X ∈ {t} | Y ∈ {w}) !! +# > clause2 +# CnfFormula: +# (Y ∈ {w, v}) +# & (X ∈ {s, u}) +# & (Z ∈ {z} | Y ∈ {w}) +# & (W ∈ {p} | X ∈ {s}) +# & (W ∈ {p} | Y ∈ {w}) !! +# > clause1 | clause2 +# CnfFormula: +# (Y ∈ {w, v}) +# & (X ∈ {s, u} | Z ∈ {y}) +# & (W ∈ {p} | X ∈ {s} | Z ∈ {y}) +# & (Z ∈ {z} | Y ∈ {w} | X ∈ {t}) + + +# clause 10: W ∈ {p} | X ∈ {s} | Z ∈ {y} +# clause 16: W ∈ {p} | X ∈ {t} | Y ∈ {w} +# for some reason, clasue10$X is registered as subset of clause 16 + +eval(expr_full) + +formula_to_expression(eval(expr_full)) |> evaluate_expression(assignment) + +simplified + +quote( + (Z %among% c("a", "z") | X %among% c("u", "t")) & + (W %among% c("r", "p") | X %among% "s" | Z %among% "y") & + (X %among% c("s", "u") | Z %among% "y" | Y %among% "v") & + (Z %among% c("z", "y") | Y %among% "v" | X %among% "s") & + (Z %among% "z" | X %among% c("u", "t") | W %among% c("r", "q")) & + (Y %among% c("w", "v") | X %among% "u" | Z %among% "a") & + (W %among% "p" | X %among% "s" | Z %among% "y" | Y %among% "v") & + (Y %among% c("v", "w") | Z %among% "z" | W %among% "r" | X %among% "s") & + (Z %among% c("a", "z") | X %among% "t" | Y %among% c("x", "w") | W %among% "p") +) |> evaluate_expression(assignment) + + + + diff --git a/tests/testthat/test_CnfFormula_simplify.R b/tests/testthat/test_CnfFormula_simplify.R index 22e14db0d..ed4d7548f 100644 --- a/tests/testthat/test_CnfFormula_simplify.R +++ b/tests/testthat/test_CnfFormula_simplify.R @@ -45,22 +45,23 @@ test_that("CnfFormula Regression Tests", { assignments = expand.grid(lapply(vars, function(var) u[[var]]), stringsAsFactors = FALSE) colnames(assignments) = vars - truevals = rep(NA, nrow(assignments)) - for (i in seq_len(nrow(assignments))) { - assignment = assignments[i, , drop = FALSE] - trueval = evaluate_expression(expression, assignment) - simpval = evaluate_expression(simplified, assignment) - if (trueval != simpval) break - truevals[[i]] = trueval - } + truevals = evaluate_expression(expression, assignments) + simpvals = evaluate_expression(simplified, assignments) + stats$was_tautology[[length(stats$was_tautology) + 1]] = all(truevals) stats$was_contradiction[[length(stats$was_contradiction) + 1]] = all(!truevals) - expect_equal(trueval, simpval, + + if (!all(truevals == simpvals)) { + trueval = truevals[[which(!truevals == simpvals)[1]]] + simpval = simpvals[[which(!truevals == simpvals)[1]]] + assignment = assignments[which(!truevals == simpvals)[1], , drop = FALSE] + expect_equal(trueval, simpval, info = sprintf("Expression: %s\nAssignment:\n%s\nSimplified to: %s", deparse1(expression), paste(capture.output(print(assignment)), collapse = "\n"), deparse1(simplified) - )) + )) + } cat(".") } From c2da00252a4496a9c2beb94011ad04b062a79b1b Mon Sep 17 00:00:00 2001 From: mb706 Date: Wed, 18 Sep 2024 15:28:37 +0200 Subject: [PATCH 46/87] further bugfixes --- R/CnfFormula_simplify2.R | 11 +++++++++++ 1 file changed, 11 insertions(+) diff --git a/R/CnfFormula_simplify2.R b/R/CnfFormula_simplify2.R index 4a56f3402..520c38474 100644 --- a/R/CnfFormula_simplify2.R +++ b/R/CnfFormula_simplify2.R @@ -176,6 +176,11 @@ simplify_cnf = function(entries, universe) { # --> hence `available <= meta_idx_outer` rows_to_check = which((is_not_subset_of[[meta_idx]][, is_not_subset_of_col] & available %in% symbol_registry[[symbol]])[seq_len(meta_idx_outer)]) for (other_meta_idx in rows_to_check) { + clause_idx_other = available[[other_meta_idx]] + # while we only get here for rows that are in the symbol_registry and therefore not eliminated / units, we need to check again since on_update_subset_relations() + # can change this during the loop. + if (eliminated[[clause_idx_other]] || is_unit[[clause_idx_other]]) next + # when we get here, that means that the symbol exists both in clause_idx and in other_ref_this symbol, *and* we have seen both clauses # in the is_not_subset_of building process. # If this were not the case, then we would not need to change anything. @@ -235,6 +240,9 @@ simplify_cnf = function(entries, universe) { # We have to do this *after* we set the corresponding values to TRUE for others_ref_this_symbol, # since calling this could realistically change the symbol registry (e.g. if it leads to a symbol # being eliminated from other clauses). + clause_idx_other = available[[meta_idx_other]] + # while we *do* restrict meta_idx_other in the for loop already, eliminated and is_unit can still change during the loop, so check here again + if (eliminated[[clause_idx_other]] || is_unit[[clause_idx_other]]) next ousr = on_updated_subset_relations(meta_idx, meta_idx_other) if (identical(ousr, TRUE)) return(TRUE) # on_updated_subset_relations could cascade down to eliminating meta_idx (i.e. clause_idx) @@ -269,6 +277,7 @@ simplify_cnf = function(entries, universe) { # mark a clause as eliminated and update symbol registry # This is relatively safe to call, since it does not modify any other clauses and does not create new units or subset relationships. eliminate_clause_update_sr = function(clause_idx) { + if (is_unit[[clause_idx]]) stop("Bug in the code, this should never happen.") eliminated[[clause_idx]] <<- TRUE for (s in names(entries[[clause_idx]])) { sr = symbol_registry[[s]] @@ -463,6 +472,8 @@ simplify_cnf = function(entries, universe) { break } # Now loop over clauses that also use the symbol, checking if they have one less `not_subset_count` because of that + # Note we do not need to check subsumption w/r/t units any more: All symbols are proper subsets w/r/t units at this point, + # so if adding the complement of one symbol to another made it a superset of a unit, the result was a tautology already. for (updating_clause_meta_idx in available_inverse[symbol_registry[[symbol]]]) { # we don't want to skip 'was_used' here, since we might still do hidden subsumption elimination with them. if (is_not_subset_of[[updating_clause_meta_idx]][meta_idx, symbol] && From 34850268d5f5243f7261e656ae16e9c875aa928a Mon Sep 17 00:00:00 2001 From: mb706 Date: Wed, 18 Sep 2024 15:38:25 +0200 Subject: [PATCH 47/87] more efficient tests --- attic/expression_experiments.R | 29 ++++++---- tests/testthat/test_CnfFormula.R | 29 ++++++---- tests/testthat/test_CnfFormula_simplify.R | 30 +++++----- tests/testthat/testdata/cnfcases.txt | 67 +++++++++++++++++++++++ 4 files changed, 115 insertions(+), 40 deletions(-) diff --git a/attic/expression_experiments.R b/attic/expression_experiments.R index ffa82501d..16e604ee7 100644 --- a/attic/expression_experiments.R +++ b/attic/expression_experiments.R @@ -79,21 +79,26 @@ expression_weight = function(expression) { assignments = expand.grid(lapply(vars, function(var) u[[var]]), stringsAsFactors = FALSE) colnames(assignments) = vars - truevals = rep(NA, nrow(assignments)) - for (i in seq_len(nrow(assignments))) { - assignment = assignments[i, , drop = FALSE] - trueval = evaluate_expression(expression, assignment) - simpval = evaluate_expression(simplified, assignment) - if (trueval != simpval) break - truevals[[i]] = trueval - } + truevals = evaluate_expression(expression, assignments) + simpvals = evaluate_expression(simplified, assignments) + stats$was_tautology[[length(stats$was_tautology) + 1]] = all(truevals) stats$was_contradiction[[length(stats$was_contradiction) + 1]] = all(!truevals) + + if (!all(truevals == simpvals)) { + trueval = truevals[[which(!truevals == simpvals)[1]]] + simpval = simpvals[[which(!truevals == simpvals)[1]]] + assignment = assignments[which(!truevals == simpvals)[1], , drop = FALSE] + } else { + # alibi + trueval = simpval = TRUE + assignment = NULL + } expect_equal(trueval, simpval, - info = sprintf("Expression: %s\nAssignment:\n%s\nSimplified to: %s", - deparse1(expression), - paste(capture.output(print(assignment)), collapse = "\n"), - deparse1(simplified) + info = sprintf("Expression: %s\nAssignment:\n%s\nSimplified to: %s", + deparse1(expression), + paste(capture.output(print(assignment)), collapse = "\n"), + deparse1(simplified) )) } } diff --git a/tests/testthat/test_CnfFormula.R b/tests/testthat/test_CnfFormula.R index 3a51b288b..21cd28b0a 100644 --- a/tests/testthat/test_CnfFormula.R +++ b/tests/testthat/test_CnfFormula.R @@ -645,21 +645,26 @@ test_that("Brute-force test", { assignments = expand.grid(lapply(vars, function(var) u[[var]]), stringsAsFactors = FALSE) colnames(assignments) = vars - truevals = rep(NA, nrow(assignments)) - for (i in seq_len(nrow(assignments))) { - assignment = assignments[i, , drop = FALSE] - trueval = evaluate_expression(expression, assignment) - simpval = evaluate_expression(simplified, assignment) - if (trueval != simpval) break - truevals[[i]] = trueval - } + truevals = evaluate_expression(expression, assignments) + simpvals = evaluate_expression(simplified, assignments) + stats$was_tautology[[length(stats$was_tautology) + 1]] = all(truevals) stats$was_contradiction[[length(stats$was_contradiction) + 1]] = all(!truevals) + + if (!all(truevals == simpvals)) { + trueval = truevals[[which(!truevals == simpvals)[1]]] + simpval = simpvals[[which(!truevals == simpvals)[1]]] + assignment = assignments[which(!truevals == simpvals)[1], , drop = FALSE] + } else { + # alibi + trueval = simpval = TRUE + assignment = NULL + } expect_equal(trueval, simpval, - info = sprintf("Expression: %s\nAssignment:\n%s\nSimplified to: %s", - deparse1(expression), - paste(capture.output(print(assignment)), collapse = "\n"), - deparse1(simplified) + info = sprintf("Expression: %s\nAssignment:\n%s\nSimplified to: %s", + deparse1(expression), + paste(capture.output(print(assignment)), collapse = "\n"), + deparse1(simplified) )) } } diff --git a/tests/testthat/test_CnfFormula_simplify.R b/tests/testthat/test_CnfFormula_simplify.R index ed4d7548f..d3af6c365 100644 --- a/tests/testthat/test_CnfFormula_simplify.R +++ b/tests/testthat/test_CnfFormula_simplify.R @@ -3,7 +3,7 @@ test_that("CnfFormula Regression Tests", { - + skip_on_cran() testcases = readLines(test_path("testdata", "cnfcases.txt")) u = CnfUniverse() @@ -33,12 +33,11 @@ test_that("CnfFormula Regression Tests", { sum(all.names(expression) %in% c("|", "&")) + 1 } - stats = list(depth = integer(0), expweight = numeric(0), simpweight = numeric(0), was_tautology = logical(0), was_contradiction = logical(0)) + stats = list(expweight = numeric(0), simpweight = numeric(0), was_tautology = logical(0), was_contradiction = logical(0)) for (line in testcases) { expression = parse(text = line)[[1]] simplified = formula_to_expression(eval(expression)) - stats$depth[[length(stats$depth) + 1]] = depth_to_check stats$expweight[[length(stats$expweight) + 1]] = expression_weight(expression) stats$simpweight[[length(stats$simpweight) + 1]] = expression_weight(simplified) vars = intersect(names(u), all.names(expression)) @@ -55,20 +54,23 @@ test_that("CnfFormula Regression Tests", { trueval = truevals[[which(!truevals == simpvals)[1]]] simpval = simpvals[[which(!truevals == simpvals)[1]]] assignment = assignments[which(!truevals == simpvals)[1], , drop = FALSE] - expect_equal(trueval, simpval, - info = sprintf("Expression: %s\nAssignment:\n%s\nSimplified to: %s", - deparse1(expression), - paste(capture.output(print(assignment)), collapse = "\n"), - deparse1(simplified) - )) + } else { + # alibi + trueval = simpval = TRUE + assignment = NULL } + expect_equal(trueval, simpval, + info = sprintf("Expression: %s\nAssignment:\n%s\nSimplified to: %s", + deparse1(expression), + paste(capture.output(print(assignment)), collapse = "\n"), + deparse1(simplified) + )) + cat(".") } dti <- as.data.table(stats) - # }) - # dti <- rbindlist(dti_col, idcol = "seedoffset") dti[, .( ew = mean(expweight), sw = mean(simpweight), @@ -79,11 +81,7 @@ test_that("CnfFormula Regression Tests", { was_contradiction = mean(was_contradiction), tautologies_not_recognized = mean(was_tautology & simpweight > 0), contradictions_not_recognized = mean(was_contradiction & simpweight > 0) - ), by = "depth"] - - - - + )] }) diff --git a/tests/testthat/testdata/cnfcases.txt b/tests/testthat/testdata/cnfcases.txt index 1820e5e2c..06fccafac 100644 --- a/tests/testthat/testdata/cnfcases.txt +++ b/tests/testthat/testdata/cnfcases.txt @@ -1,5 +1,6 @@ (((Y %among% c("w", "x") | X %among% "u") & (Z %among% "y" & W %among% c("p", "q")) | (X %among% c("u", "t") | W %among% "q") & (Z %among% c("y", "a") & W %among% "p")) & (X %among% c("u", "s") | X %among% c("s", "u") | (Y %among% c("x", "v") | Z %among% "a") | (X %among% c("t", "u") & W %among% "r" | (Z %among% "y" | W %among% "r"))) & ((Y %among% c("v", "x") | W %among% "q" | X %among% "t" & W %among% c("q", "p")) & (Y %among% "w" | Z %among% c("a", "y") | (W %among% "r" | W %among% "p")) | (X %among% "s" | Z %among% c("y", "a") | (W %among% c("q", "r") | W %among% c("q", "p")) | (Z %among% "z" | Y %among% c("w", "x")) & (X %among% c("u", "s") & X %among% "t"))) | (Y %among% c("w", "x") & Z %among% "y" & (W %among% "r" & Z %among% "a") | W %among% c("r", "p") & Y %among% "v" & (Y %among% c("v", "x") & W %among% c("q", "p"))) & (Y %among% c("v", "x") & W %among% "r" | (Z %among% c("y", "a") | W %among% c("r", "q")) | (X %among% c("s", "u") | Z %among% "y" | (X %among% "t" | X %among% "s"))) & ((X %among% c("u", "s") | Y %among% "w") & (Z %among% c("z", "y") | Y %among% c("w", "x")) & (Y %among% c("w", "v") & X %among% c("u", "s") & (W %among% "r" | X %among% c("s", "u"))) | ((X %among% "s" | Z %among% c("a", "y")) & (Y %among% c("x", "w") | Z %among% c("a", "z")) | X %among% "t" & W %among% c("r", "p") & (W %among% "p" & X %among% c("u", "t")))) | (W %among% c("p", "r") & Y %among% "w" & (X %among% "s" & X %among% "t") | W %among% "p" & Z %among% c("z", "y") & (W %among% c("p", "q" ) & Y %among% c("w", "v")) | (X %among% "t" | W %among% "p" | Y %among% "v" & Z %among% "a") & ((W %among% c("q", "p") | Y %among% "v") & (Y %among% c("x", "v") & Z %among% "a"))) & (W %among% "r" & X %among% "u" | (W %among% "q" | X %among% "s") | W %among% c("p", "q") & W %among% "p" & (W %among% "q" & W %among% "q") | (X %among% c("u", "t") & Z %among% "y" | Z %among% c("z", "y") & Y %among% "w" | W %among% c("r", "p") & W %among% c("r", "q") & (X %among% c("u", "t") & W %among% "p"))) & ((Z %among% c("z", "y") | W %among% c("q", "p") | (W %among% c("p", "r") | Y %among% "v") | (Z %among% "z" & W %among% c("q", "r") | Y %among% c("w", "x") & W %among% "p") | ((Z %among% c("y", "z") | W %among% "p") & (W %among% "p" | X %among% "t") | (Z %among% "y" | Z %among% "z" | Y %among% "x" & Y %among% "w"))) & ((Z %among% c("y", "a") | X %among% "t" | (W %among% c("p", "r") | X %among% c("t", "u"))) & (X %among% "t" & W %among% "p" & (W %among% c("q", "r") | Y %among% "w")) & (Z %among% "a" & W %among% "p" & (X %among% c("s", "t") | X %among% c("s", "u")) & (W %among% "p" & W %among% c("p", "r") | (W %among% c("p", "r") | W %among% c("p", "r"))))))) & (((Z %among% c("z", "y") & W %among% "q" | (Z %among% c("z", "y") | Y %among% "v")) & (Z %among% "a" | W %among% c("q", "p") | Z %among% c("y", "a") & Y %among% c("w", "x")) & (Y %among% "x" & Y %among% c("v", "x") & (W %among% "p" | Z %among% "z") | Z %among% "z" & Z %among% c("y", "z") & (Y %among% "w" & W %among% c("p", "r"))) | (Y %among% "v" | X %among% c("u", "s")) & (Z %among% "y" & Y %among% "v") & (Y %among% c("v", "x") & X %among% c("u", "s") | (X %among% "t" | Y %among% "w")) & ((Z %among% c("a", "z") | W %among% "q") & (Z %among% "y" | Z %among% "z") | Z %among% "a" & Z %among% "a" & (W %among% "q" | X %among% c("s", "t")))) & ((Y %among% "v" | X %among% "u" | Z %among% "a" & Z %among% c("z", "a")) & (W %among% c("p", "r") | Z %among% c("z", "y") | (X %among% c("t", "u") | Y %among% c("x", "v"))) & (Z %among% "a" | Y %among% "w" | X %among% c("t", "u") & W %among% c("p", "q") | Z %among% c("a", "y") & Y %among% "w" & (Z %among% "z" | Y %among% "w")) & ((Z %among% c("y", "z") & W %among% "q" | (X %among% c("u", "t") | X %among% c("s", "u"))) & ((Y %among% "v" | Z %among% c("z", "y")) & (W %among% c("q", "r") & Y %among% c("x", "v"))) & ((Y %among% "x" | Z %among% "y") & (W %among% c("r", "q") | W %among% "p") & (W %among% c("q", "r") & Y %among% "w" | (Z %among% "z" | X %among% "t"))))) | (Y %among% "w" | W %among% c("p", "r") | (Z %among% c("a", "y") | X %among% c("s", "u")) | (X %among% "s" | W %among% c("p", "r")) & (Y %among% c("v", "w") | Y %among% "v") | (W %among% "r" & X %among% "s" | (W %among% c("r", "q") | W %among% "q")) & (Y %among% c("v", "x") & Z %among% "a" | (W %among% "q" | Y %among% "w")) | (W %among% "p" & Y %among% c("v", "x") & (Y %among% "x" | W %among% "p") | (X %among% c("u", "s") | Y %among% "x") & (X %among% "s" & Z %among% "a") | (Z %among% c("z", "a") | X %among% c("t", "s")) & (Y %among% "v" | W %among% c("r", "q")) & (X %among% c("u", "t") & Z %among% "z" & (W %among% c("q", "p") & W %among% "p")))) & (((Z %among% "a" & X %among% c("s", "t") | (X %among% "t" | Z %among% "z")) & (Y %among% "x" & X %among% "t" & (Z %among% c("y", "a") | Y %among% c("w", "x"))) | (Z %among% "y" | Z %among% "z") & (W %among% "p" & X %among% "u") & ((Z %among% "a" | Z %among% "y") & (X %among% c("s", "t") | Y %among% c("x", "v")))) & ((X %among% c("u", "s") & Z %among% "y" | Z %among% "y" & Y %among% "x" | (Z %among% c("y", "z") & Z %among% c("y", "z") | (W %among% "r" | W %among% c("q", "p")))) & ((X %among% c("u", "s") & Z %among% c("z", "a") | (Z %among% "z" | Z %among% c("z", "a"))) & (Z %among% c("y", "z") | Z %among% "z" | (Y %among% c("w", "v") | X %among% c("s", "u"))))))) | ((Y %among% c("w", "x") | W %among% c("q", "r")) & (Z %among% c("a", "y") | Y %among% "x") & (Z %among% "a" | Z %among% "z" | (W %among% c("r", "q") | Y %among% "x")) & ((W %among% "r" | W %among% "p") & (X %among% "u" | Z %among% c("a", "z")) & (Y %among% "w" & Y %among% c("w", "x") | W %among% "r" & X %among% c("s", "u"))) | ((X %among% c("t", "s") | Y %among% c("x", "v")) & (W %among% "p" & X %among% "t") | (W %among% "q" | Y %among% "x" | (W %among% "r" | W %among% c("q", "r"))) | (Y %among% "v" | Z %among% "a" | Z %among% c("y", "z") & X %among% c("u", "s")) & (Z %among% "a" & Z %among% c("y", "z") & (Y %among% c("v", "w") & W %among% "p")))) & ((X %among% c("t", "s") & W %among% c("p", "r") & (W %among% "q" | Z %among% c("z", "y")) & (Y %among% "w" & W %among% c("q", "r") | Y %among% "x" & W %among% "p") | (Z %among% c("y", "z") & X %among% c("s", "u") | W %among% "p" & Y %among% c("x", "v")) & (Z %among% c("a", "z") & X %among% "t" & (Y %among% c("x", "v") | Y %among% "v"))) & ((Z %among% c("y", "z") | W %among% c("p", "q") | Z %among% "z" & W %among% "r") & ((Z %among% c("z", "a") | W %among% "q") & (Z %among% "a" | Z %among% "y")) & ((X %among% c("t", "s") | Y %among% c("x", "v") | (W %among% c("r", "p") | W %among% c("p", "q"))) & (W %among% c("p", "q") & X %among% "t" & (X %among% c("t", "s") | Y %among% "w"))))) & ((W %among% c("q", "p") & X %among% c("u", "t") | X %among% c("u", "s") & X %among% "t") & (X %among% "t" | Z %among% "a" | Y %among% "v" & Y %among% c("w", "x")) & (Z %among% "y" & Z %among% c("z", "a") & (X %among% "t" | W %among% "q") & (W %among% c("p", "q") | X %among% "s" | (Z %among% "y" | Y %among% c("x", "w")))) | (X %among% "u" & W %among% c("q", "r") | W %among% c("p", "q") & W %among% c("p", "r") | Y %among% c("x", "v") & Y %among% "v" & (W %among% "r" & Z %among% "a") | (Z %among% c("a", "z") | X %among% c("u", "t") | Z %among% "z" & X %among% "t") & (W %among% c("r", "p") & X %among% "u" | X %among% c("t", "s") & X %among% c("s", "t"))) | ((W %among% c("p", "q") | W %among% c("q", "p")) & (W %among% c("p", "r") | W %among% c("r", "p")) & (X %among% "t" & W %among% "p" | (Z %among% "a" | Z %among% "a")) | (W %among% "r" & Y %among% "x" & (Y %among% "v" & Z %among% "z") | (W %among% c("r", "p") | Z %among% "a" | Y %among% "v" & X %among% "s"))) & ((Z %among% "y" | X %among% c("s", "t")) & (Z %among% "a" & Y %among% "x") & (X %among% c("s", "t") & Z %among% c("y", "z") | Y %among% "v" & Z %among% c("y", "z")) | (Z %among% c("a", "y") | X %among% "t" | (W %among% "q" | Z %among% c("y", "z"))) & (Y %among% c("v", "x") & Y %among% c("x", "v") | (Z %among% "z" | Y %among% "v")))) & ((Z %among% c("z", "y") & Z %among% c("z", "y" ) & (W %among% "r" & Y %among% c("x", "w")) | (X %among% c("s", "t") | W %among% "q") & (W %among% "r" & W %among% c("p", "q"))) & ((Y %among% "v" | Y %among% "w") & (Z %among% "z" | Y %among% "x") & ((W %among% "p" | Z %among% "a") & (Z %among% c("z", "a") & W %among% c("r", "p")))) & ((Y %among% c("w", "v") | Y %among% c("x", "v") | (Y %among% c("x", "w") | W %among% "q") | X %among% c("t", "u") & Z %among% "z" & (W %among% c("r", "q") & X %among% "s")) & ((Y %among% c("v", "w") & Z %among% c("z", "y") | X %among% "s" & W %among% c("q", "p")) & ((W %among% "q" | W %among% c("p", "r")) & (Y %among% c("w", "x") | X %among% "t")))) & ((Z %among% "a" | W %among% c("r", "q")) & (W %among% c("p", "r") | Y %among% c("v", "x")) & (W %among% c("r", "p") & Z %among% "y" | (Z %among% "a" | Z %among% c("y", "z"))) & ((Y %among% "v" & X %among% "s" | Z %among% c("z", "y") & Y %among% "w") & (W %among% c("p", "q") & X %among% c("s", "u") | (X %among% c("u", "t") | W %among% "q"))) | (W %among% "r" | X %among% "t" | X %among% "u" & W %among% c("r", "p") | (X %among% c("s", "t") & X %among% "t" | (X %among% c("s", "t") | X %among% "s"))) & ((W %among% "q" | Z %among% c("a", "y")) & (X %among% "s" & Y %among% "w") | (Z %among% c("y", "a") & W %among% "p" | W %among% "p" & Y %among% "w"))) & ((X %among% "u" & Z %among% "z" | Y %among% c("w", "x") & Y %among% c("x", "w") | (X %among% c("s", "u") | W %among% "r" | (W %among% "q" | Y %among% "w"))) & (Z %among% c("z", "y") & Y %among% "w" & (W %among% "q" & Y %among% c("w", "x")) | (X %among% c("t", "u") | Y %among% c("x", "v")) & (Y %among% "w" & X %among% "s")) | (Y %among% "x" | Y %among% c("v", "x") | (Y %among% c("v", "w") | W %among% c("r", "q")) | (W %among% "p" | Y %among% c("v", "x")) & (W %among% "r" & W %among% "p")) & ((Y %among% c("v", "w") & W %among% "q" | Z %among% c("z", "a") & X %among% c("s", "u")) & (X %among% "u" & W %among% "q" & (W %among% "p" & Z %among% "a"))) | ((Z %among% "y" | W %among% "p" | (Z %among% c("y", "z") | Z %among% c("z", "y"))) & (Y %among% c("v", "w") | Z %among% c("z", "y") | (Z %among% c("y", "a") | X %among% c("s", "t"))) | (Z %among% "z" | X %among% "t" | (W %among% "q" | Y %among% "w") | Y %among% c("w", "x") & Y %among% c("x", "v") & (Y %among% c("x", "v") & X %among% c("s", "t")))) & ((W %among% "p" | Z %among% c("y", "z")) & (Z %among% c("z", "y") & Y %among% c("x", "v")) & (Z %among% c("a", "y") & Z %among% "a" & (W %among% c("p", "r") & Y %among% c("v", "x"))) & ((Y %among% "w" | X %among% "s") & (W %among% c("r", "p") & Z %among% c("a", "z")) & (Z %among% c("a", "z") | X %among% c("s", "t") | Y %among% "w" & W %among% "q"))))) (W %among% c("p", "r") | X %among% c("s", "t") | (W %among% c("p", "q") | Y %among% c("w", "x")) | (W %among% "r" | Y %among% c("v", "x")) & (W %among% c("r", "p") & Y %among% c("x", "w")) | (X %among% "s" & Y %among% "v" | Y %among% "x" & X %among% "u") & (Z %among% c("a", "z") & Z %among% c("z", "y") | (Z %among% c("y", "a") | X %among% "u")) | ((W %among% "p" | Z %among% "a" | (Z %among% c("y", "a") | Z %among% c("a", "y"))) & ((Z %among% "a" | Z %among% c("y", "z")) & (X %among% "s" | Z %among% c("z", "y"))) | ((X %among% "s" | Z %among% "a") & (Y %among% c("x", "w") & W %among% c("r", "q")) | (Y %among% "w" | W %among% "r" | (Y %among% "v" | W %among% c("p", "r")))))) & ((Z %among% "z" | X %among% "t" | (Z %among% "z" | W %among% "r") | X %among% "u" & X %among% "u" & (W %among% "q" & W %among% c("q", "p"))) & ((Y %among% c("x", "v") & W %among% c("p", "q") | (X %among% "t" | Y %among% c("v", "w"))) & (Z %among% "y" & Y %among% c("w", "x") | Z %among% c("a", "z") & X %among% "t")) & ((W %among% c("p", "q") | X %among% c("t", "u")) & (X %among% c("t", "s") | W %among% "r") & (X %among% c("s", "u") & W %among% c("q", "r") & (Z %among% "a" | Y %among% "v")) | W %among% "p" & W %among% c("q", "r") & (X %among% "s" | X %among% c("s", "u")) & (Z %among% "z" | Y %among% "v" | (Y %among% c("x", "w") | W %among% "r")))) | Y %among% c("v", "x") & X %among% "s" & (X %among% "u" & Y %among% c("x", "w")) & ((X %among% "u" | X %among% "t") & (W %among% c("p", "r") | Z %among% "z")) & (X %among% "u" & W %among% c("r", "p") & (Y %among% c("w", "v") | W %among% c("r", "q")) & (Z %among% c("z", "y") | Z %among% "a" | W %among% "p" & Y %among% "v")) & ((X %among% "u" | W %among% c("q", "p")) & (X %among% c("u", "t") | Z %among% "y") & (Z %among% c("a", "z") & W %among% "r" | X %among% "t" & Z %among% c("y", "a")) & (Y %among% c("v", "x") & Z %among% "a" & (W %among% c("p", "q") & W %among% 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& Y %among% c("x", "v") | (Z %among% "y" | W %among% c("q", "p")) | Y %among% "w" & Y %among% "w" & (Y %among% "w" | Z %among% c("y", "z")))))) X %among% c("u", "s") & X %among% c("u", "s") & (W %among% "r" | W %among% "q") & (W %among% c("q", "r") & Z %among% "a" & (Z %among% c("z", "a") & X %among% c("t", "s"))) | (W %among% "p" | X %among% "t" | (Z %among% c("a", "z") | W %among% c("p", "q"))) & (W %among% c("r", "p") & Y %among% "v" & (Y %among% "x" | X %among% c("u", "t"))) | (Y %among% "x" | Z %among% c("y", "a") | Y %among% "v" & Z %among% "y") & (X %among% "s" & X %among% "u" & (Y %among% "x" & X %among% "t")) & ((X %among% c("s", "t") | Z %among% c("z", "y") | W %among% c("q", "r") & W %among% c("q", "p")) & (Y %among% c("w", "x") & W %among% c("r", "p") | Z %among% "y" & W %among% "q")) | ((Z %among% "z" | Y %among% c("w", "v")) & (Z %among% "y" & Z %among% c("y", "z")) & (Y %among% "w" & X %among% c("t", "u") | Y %among% c("v", "w") & X %among% "t") | Y %among% c("w", "v") & 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(Y %among% c("x", "v") | X %among% "t") & (Z %among% c("y", "z") & Z %among% c("z", "a") | (W %among% c("p", "q") | X %among% c("s", "t"))))) & ((Y %among% "x" & X %among% c("t", "u") & (W %among% "r" | Z %among% "a") | (X %among% "t" & Y %among% c("x", "v") | Z %among% "a" & Y %among% c("v", "w"))) & ((Z %among% "a" & Y %among% "x" | Y %among% c("v", "w") & Z %among% c("a", "z")) & (X %among% "t" | W %among% "r" | (Z %among% "y" | W %among% "r"))) & ((W %among% c("q", "p") | X %among% c("u", "s") | X %among% c("t", "s") & X %among% c("u", "s") | Z %among% c("y", "z") & Z %among% "a" & (Y %among% c("w", "x") | Z %among% c("y", "a"))) & (W %among% c("p", "q") & Z %among% c("z", "y") & (Z %among% "a" | Y %among% c("w", "v")) | Y %among% "w" & Y %among% "w" & (W %among% c("r", "p") | Y %among% "x")))) & ((X %among% c("s", "t") & Y %among% c("w", "v") | W %among% "p" & X %among% c("u", "s")) & (W %among% "r" & X %among% "t" & (Y %among% "w" | W %among% c("p", "r"))) & (X %among% c("u", "t") & Z %among% "y" | (X %among% "u" | W %among% c("p", "r")) | (X %among% "u" & Y %among% c("x", "v") | Z %among% "y" & Y %among% "w")) & ((Z %among% c("a", "y") & Y %among% c("x", "v") | Y %among% c("v", "w") & X %among% "t" | (Z %among% "z" | W %among% "q") & (W %among% "r" | X %among% c("s", "u"))) & (W %among% c("p", "q") & X %among% c("t", "u") | (Y %among% c("w", "v") | X %among% "u") | (W %among% c("p", "q") & Z %among% c("a", "y") | X %among% "s" & W %among% "p"))) & ((Z %among% "y" & Y %among% c("x", "v") & (Z %among% "y" | X %among% "s") & ((X %among% c("s", "t") | Z %among% c("y", "z")) & (W %among% "q" | X %among% "s")) | (W %among% "p" & X %among% "s" | (Z %among% c("a", "z") | W %among% "p") | (W %among% c("r", "q") | X %among% c("u", "t")) & (Z %among% "y" | Z %among% c("z", "a")))) & (Z %among% "z" & Y %among% "w" | W %among% "q" & W %among% c("r", "p") | (W %among% "r" | Y %among% c("w", "x") | (Z %among% c("y", "a") | Z %among% "y")) | (Z %among% "z" & W %among% "q" | (X %among% "u" | X %among% c("s", "u")) | (W %among% c("q", "p") | W %among% "r") & (Y %among% "w" & X %among% "u"))))) & (((Y %among% c("v", "x") & W %among% c("q", "p") | (X %among% "t" | Z %among% c("y", "a")) | X %among% "u" & Z %among% c("a", "z") & (X %among% c("s", "u") | Y %among% c("v", "w")) | Z %among% c("z", "a") & W %among% c("q", "p") & (Z %among% "z" & X %among% c("t", "u")) & (Z %among% "a" | Y %among% "w" | (Y %among% c("x", "w") | W %among% c("q", "r" )))) & ((Z %among% c("z", "y") | Y %among% "v") & (Z %among% "z" | Y %among% c("v", "x")) & (Y %among% "w" | Z %among% c("a", "y") | X %among% c("s", "t") & Y %among% c("x", "v")) | ((W %among% c("p", "r") | W %among% c("r", "p")) & (W %among% "p" & W %among% c("r", "q")) | (X %among% c("s", "u") & W %among% "r" | W %among% "q" & Z %among% "a"))) | Z %among% c("a", "y") & Z %among% c("z", "y") & (W %among% "r" & Y %among% c("x", "v")) & ((Y %among% c("w", "x") | W %among% "r") & (W %among% "q" & W %among% c("q", "p"))) & (X %among% c("s", "t") & Z %among% c("z", "a") & (X %among% c("u", "s") & X %among% "s") | (W %among% c("p", "q") | X %among% "t") & (Z %among% "y" & Z %among% "z")) & ((X %among% "t" | W %among% c("r", "q")) & (X %among% c("s", "t") & X %among% c("t", "s")) | (Y %among% "x" | Y %among% c("w", "v") | (X %among% "t" | Y %among% "v")) | Z %among% "a" & W %among% c("p", "r") & (Z %among% "z" | Z %among% "y") & ((Y %among% "w" | X %among% c("s", "t")) & (W %among% c("r", "q") | Y %among% c("w", "x"))))) & (((W %among% c("p", "q") | Z %among% "a" | Y %among% "v" & W %among% "q") & (Z %among% "a" & Y %among% c("x", "v") | W %among% c("q", "p") & X %among% "t") & (W %among% "p" & Z %among% "z" & (Y %among% c("v", "w") & Y %among% "w") | (Z %among% c("z", "y") | X %among% "u") & (W %among% c("p", "r") & W %among% "r")) | (W %among% c("r", "q") & Z %among% "a" & (Z %among% "z" & W %among% c("r", "q")) & (Y %among% c("v", "x") | Y %among% "v" | (Y %among% c("x", "v") | X %among% c("s", "u"))) | (W %among% c("r", "p") & Z %among% c("y", "a") | (X %among% "s" | W %among% "q")) & ((X %among% c("u", "s") | Z %among% "a") & (Y %among% c("x", "v") | Z %among% "a")))) & ((X %among% "u" | X %among% c("t", "u")) & (Z %among% c("y", "a") & X %among% c("s", "t")) & ((W %among% c("q", "r") | X %among% c("t", "s")) & (Z %among% c("y", "a") & Y %among% c("x", "w"))) & (W %among% c("p", "q") | W %among% "q" | (Y %among% c("v", "x") | Z %among% "z") | W %among% "p" & X %among% "t" & (Z %among% "y" | X %among% "u")) & ((W %among% "q" & Z %among% "y" | Y %among% "w" & X %among% c("u", "s") | W %among% "r" & Y %among% "v" & (W %among% c("q", "p") & Z %among% c("y", "z"))) & ((X %among% "u" | Z %among% "y" | Y %among% "v" & Y %among% c("v", "w")) & (W %among% c("r", "p") & X %among% "s" & (X %among% c("u", "t") | X %among% c("t", "s")))))))) W %among% c("q", "p") & W %among% c("r", "p") & (Y %among% c("x", "w") | Y %among% "w") & ((X %among% "s" | Z %among% "a") & (X %among% c("s", "t") | X %among% c("t", "u"))) & ((Y %among% "v" | Z %among% "a" | (Y %among% c("w", "v") | W %among% "q")) & (X %among% c("s", "u") & Y %among% c("w", "v") | (X %among% c("s", "t") | Y %among% c("w", "v")))) & ((Z %among% c("y", "a") | W %among% "q") & (Y %among% c("w", "v") & Z %among% c("a", "y")) & (X %among% "u" | W %among% c("r", "q") | (X %among% "t" | Y %among% c("v", "w"))) & ((Z %among% "a" | Z %among% "z") & (W %among% "p" | Z %among% c("z", "a")) & (Y %among% "v" & X %among% c("t", "s") | (W %among% c("p", "r") | W %among% c("p", "r"))))) & (((W %among% c("r", "q") | Z %among% c("a", "z")) & (Z %among% "y" | Z %among% "y") | Z %among% "y" & Z %among% "a" & (W %among% "p" & Y %among% c("v", "x"))) & ((Z %among% c("y", "a") | Y %among% c("x", "v")) & (Z %among% c("y", "a") | W %among% c("q", "p")) & (Y %among% c("x", "v") | Z %among% "z" | (X %among% "t" | Y %among% "w"))) & ((Y %among% "w" & W %among% c("p", "r") & (W %among% c("r", "p") & Y %among% "v") | (X %among% "s" | W %among% "p" | (W %among% c("r", "p") | Y %among% "w"))) & (Y %among% c("v", "w") & W %among% "p" | (X %among% c("s", "u") | X %among% "u") | (Y %among% c("x", "v") & Y %among% "x" | (X %among% c("t", "s") | Z %among% "a"))))) & ((Z %among% c("a", "z") & W %among% c("p", "q") | W %among% "r" & Z %among% c("a", "y")) & (Y %among% "w" & Y %among% "w" & (Z %among% c("a", "z") | Z %among% c("z", "y"))) | (W %among% "q" | W %among% "r" | Z %among% "a" & Z %among% c("y", "z")) & (Z %among% "y" | X %among% c("u", "t") | (X %among% c("t", "u") | Y %among% "w")) | (X %among% "s" | Z %among% "y" | Y %among% "x" & X %among% "t" | Z %among% c("z", "y") & W %among% c("r", "q") & (Y %among% "v" & X %among% c("t", "s"))) & ((W %among% c("r", "q") | Y %among% "w" | (Z %among% c("y", "z") | W %among% c("p", "r"))) & (W %among% c("r", "q") & Y %among% c("w", "x") & (X %among% c("u", "t") | Z %among% "a"))) | (Y %among% c("x", "v") | Y %among% "w" | (Y %among% c("v", "x") | Z %among% "a") | (X %among% c("t", "u") | W %among% c("r", "p")) & (Y %among% c("v", "w") & Z %among% c("a", "z"))) & (X %among% c("u", "s") & Z %among% c("a", "z") & (W %among% c("q", "p") | W %among% c("p", "q")) | Z %among% "a" & W %among% c("p", "q") & (Y %among% c("v", "w") | Z %among% "z")) & ((Z %among% "a" & Y %among% "v" | Z %among% c("y", "z") & X %among% "t" | (Y %among% c("x", "w") & X %among% "s" | Y %among% c("v", "x") & W %among% "r")) & (W %among% c("p", "q") | X %among% c("u", "t") | (W %among% c("q", "p") | Z %among% c("z", "y")) | (W %among% "p" | X %among% c("u", "s") | X %among% c("t", "s") & Y %among% c("x", "v"))))) | ((X %among% "s" & W %among% c("p", "q") & (Z %among% c("y", "a") | X %among% c("u", "s")) | (X %among% c("t", "u") | X %among% "s") & (Z %among% c("z", "a") & X %among% c("s", "u"))) & ((X %among% "u" | W %among% "p") & (W %among% c("r", "q") & W %among% "q") | X %among% "s" & Y %among% c("v", "w") & (X %among% c("t", "s") & Y %among% "v")) & ((X %among% "s" | Z %among% "z" | (X %among% "s" | Y %among% c("v", "w"))) & (Z %among% c("a", "y") & Z %among% "a" & (Y %among% c("x", "w") & X %among% c("t", "u"))) & (X %among% c("s", "t") & Y %among% "x" | (W %among% c("p", "r") | Y %among% c("w", "v")) | (Y %among% "x" | Z %among% "a" | X %among% "u" & Y %among% c("v", "w")))) | (X %among% c("t", "u") & Y %among% c("x", "v") & (Z %among% "y" & X %among% "t") & (Z %among% "y" | Y %among% c("w", "x") | X %among% c("u", "t") & W %among% c("r", "p")) | Z %among% c("z", "y") & Y %among% c("w", "x") & (Y %among% c("w", "x") | Z %among% "y") & (W %among% "p" & Z %among% c("y", "z") & (Z %among% c("z", "a") | Y %among% "w"))) & ((X %among% "s" & X %among% c("t", "s") | (Y %among% c("w", "v") | Y %among% "x")) & (W %among% "r" & W %among% c("p", "r") | Y %among% c("w", "v") & X %among% "u") & ((X %among% "s" | X %among% "u") & (X %among% "s" | Y %among% c("v", "x")) | Y %among% c("w", "v") & Z %among% "a" & (W %among% "r" & W %among% "r")))) & ((W %among% c("q", "r") & Z %among% c("y", "z") & (X %among% c("s", "u") & W %among% c("p", "q")) & (W %among% c("q", "p") | W %among% c("q", "r") | Y %among% c("v", "w") & W %among% "q") & ((X %among% "t" | Y %among% "w" | Z %among% c("y", "z") & Y %among% "w") & (Y %among% "w" & Z %among% c("a", "z") | (X %among% c("u", "s") | Z %among% "a"))) | (Z %among% c("z", "y") | W %among% "p") & (X %among% "s" | Z %among% c("a", "z")) & (Z %among% c("y", "z") | X %among% "t" | W %among% "p" & Y %among% "x") & ((Y %among% c("w", "x") | X %among% "u" | (W %among% c("q", "p") | X %among% "t")) & (Y %among% c("x", "v") & X %among% "u" & (X %among% "s" & Z %among% "z")))) & ((Y %among% "v" | Y %among% "w" | (Z %among% c("z", "y") | W %among% "p")) & ((X %among% "t" | Z %among% c("a", "z")) & (X %among% "s" | Z %among% c("a", "y"))) | (Y %among% "v" & Z %among% "a" | (X %among% c("u", "s") | Z %among% c("y", "z"))) & (Y %among% c("w", "x") & X %among% c("s", "u") & (X %among% "s" & X %among% "t")) | (X %among% c("s", "u") & Y %among% "x" | (Y %among% "v" | X %among% c("s", "t"))) & ((Y %among% c("v", "x") | W %among% c("p", "r")) & (W %among% "r" | X %among% c("s", "u"))) & (W %among% "r" & X %among% c("t", "u") & (Y %among% "x" & W %among% "q") & ((W %among% c("q", "r") | Y %among% "v") & (Y %among% c("v", "x") | Z %among% "a"))))) @@ -647,8 +648,10 @@ Y %among% "w" & Y %among% c("x", "v") & (Y %among% "v" & Y %among% "v") & (Z %am (((X %among% c("t", "u") | W %among% "p") & (W %among% c("r", "q") & Y %among% "x") | (Z %among% "a" | W %among% "r" | W %among% "r" & W %among% c("p", "q"))) & ((Z %among% c("a", "z") & X %among% c("u", "s") | X %among% c("s", "u") & X %among% "u") & ((Z %among% c("z", "y") | Z %among% "z") & (X %among% "u" | Z %among% "z"))) | (Y %among% "v" | Y %among% "x") & (Z %among% c("z", "a") | Y %among% c("w", "v")) & (X %among% c("u", "t") & X %among% c("s", "u") | Z %among% "a" & W %among% "r") & ((W %among% "q" | W %among% "q") & (Z %among% c("z", "a") & X %among% c("t", "u")) & (W %among% "p" & Y %among% c("w", "v") | (X %among% c("t", "s") | Z %among% c("y", "a"))))) & ((W %among% "r" & X %among% "t" & (W %among% "r" & W %among% "q") | (X %among% c("u", "t") & X %among% c("t", "s") | (X %among% c("s", "u") | Z %among% c("z", "a")))) & ((W %among% c("r", "p") | Y %among% "v" | Y %among% c("x", "w") & Z %among% c("y", "z")) & ((X %among% "u" | Y %among% c("x", "v")) & (W %among% c("p", "r") | Y %among% c("w", "x")))) | ((Z %among% c("y", "z") | W %among% "p") & (X %among% "s" | Z %among% c("y", "z")) | (Z %among% "y" & Z %among% "y" | X %among% "u" & W %among% c("p", "q"))) & ((W %among% "r" | X %among% "t") & (W %among% "q" & Y %among% c("w", "v")) & (X %among% c("t", "s") & W %among% "r" | X %among% "t" & W %among% "p"))) ((Z %among% "y" & X %among% "s" | X %among% c("t", "s") & X %among% c("u", "s") | X %among% "t" & Z %among% c("y", "a") & (W %among% "q" | X %among% c("u", "t"))) & (W %among% "q" & Y %among% c("v", "x") & (X %among% "s" | W %among% c("p", "q")) & (Z 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& (W %among% "p" | W %among% "q")) & (Y %among% "x" | Y %among% "v" | W %among% c("p", "q") & W %among% "q" | (Z %among% c("z", "a") & Y %among% c("w", "x") | (X %among% "s" | W %among% c("p", "q"))))) & ((Y %among% c("x", "v") & X %among% "u" & (X %among% c("u", "s") | X %among% c("t", "s")) | (Z %among% c("y", "z") | Z %among% "a" | (Z %among% c("z", "a") | X %among% c("t", "u"))) | ((Z %among% c("y", "z") | X %among% "s") & (Y %among% "v" & X %among% "t") | (Y %among% c("w", "v") | X %among% c("u", "s") | (Y %among% "w" | X %among% c("t", "s"))))) & ((Y %among% "x" | W %among% "p") & (X %among% "t" | Z %among% c("y", "z")) | (Z %among% "z" | Y %among% "w" | W %among% "p" & Y %among% c("x", "w")) | Z %among% c("y", "a") & Y %among% "x" & (Y %among% c("v", "w") & Y %among% c("w", "x")) & ((Y %among% c("x", "v") | W %among% "q") & (Z %among% "z" & Z %among% "y")))))) +(Z %among% "a" | Y %among% "v") & (Y %among% "v" | X %among% c("s", "t")) & ((W %among% "q" | Z %among% c("y", "a")) & 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"u"))) & (((X %among% c("t", "s") | W %among% c("r", "p")) & (X %among% "u" | W %among% "p") | (W %among% "p" | Z %among% "a" | Y %among% c("w", "x") & X %among% "t")) & ((Z %among% "z" | X %among% "s") & (Y %among% "v" & X %among% "s") & ((X %among% c("t", "s") | W %among% "q") & (X %among% c("u", "s") & Z %among% c("y", "z")))) & (Z %among% c("a", "z") & Y %among% "v" & (W %among% "p" | W %among% c("r", "q")) & ((Z %among% "z" | W %among% c("p", "q")) & (W %among% c("p", "r") | W %among% "p")) & (W %among% c("q", "r") & X %among% "u" & (Y %among% "x" | W %among% "r") & (W %among% c("q", "p") | W %among% c("q", "p") | W %among% "p" & W %among% c("r", "p"))))) | ((Z %among% "a" | Y %among% c("x", "v")) & (Y %among% "w" & Y %among% c("v", "w")) | (W %among% c("q", "r") | Z %among% c("a", "z") | W %among% "q" & Y %among% "w") | (Y %among% "w" & W %among% "p" | (W %among% c("q", "r") | Z %among% c("z", "y"))) & ((W %among% c("q", "p") | X %among% "u") & (W %among% "p" & W %among% c("q", 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"u"))))) & (((Y %among% "x" | W %among% "p" | (Y %among% c("w", "x") | Y %among% c("w", "v"))) & (Z %among% c("a", "y") & X %among% c("u", "s") | Z %among% "a" & W %among% "q") & (Y %among% c("x", "v") & Z %among% c("z", "y") & (X %among% "t" & W %among% c("r", "q")) & (X %among% c("s", "t") & Y %among% c("x", "v") & (Z %among% c("z", "a") & W %among% c("r", "q")))) | Y %among% c("v", "w") & Y %among% "x" & (W %among% "q" & Y %among% "w") & (W %among% "q" | W %among% c("q", "r") | X %among% "s" & Z %among% "a") & (Y %among% c("x", "v") | Y %among% "v" | W %among% "r" & W %among% c("q", "p") | (Z %among% c("z", "y") | Y %among% "w" | (X %among% "t" | Y %among% "x")))) & (X %among% c("s", "u") & W %among% c("q", "p") & (X %among% c("u", "t") | Y %among% c("w", "v")) & (Z %among% c("y", "a") | X %among% "s" | (Z %among% "a" | W %among% "r")) & ((W %among% c("q", "r") | Z %among% "a") & (X %among% "t" & Z %among% c("y", "a")) & (X %among% c("s", "t") & Y %among% "w" | Y %among% "x" & X %among% "s")) | (Z %among% "y" & X %among% c("t", "s") & (W %among% "q" & X %among% "s") | (Y %among% "x" & W %among% c("q", "r") | Z %among% c("y", "z") & Y %among% c("v", "w"))) & ((X %among% "u" | Z %among% c("y", "z") | (Z %among% "z" | Y %among% c("w", "v"))) & (Z %among% c("y", "a") & W %among% "q" | (Y %among% c("w", "v") | X %among% "t")))) | ((Y %among% "w" | X %among% "s" | (Z %among% "a" | X %among% c("t", "u"))) & ((Z %among% "z" | W %among% "p") & (Y %among% c("w", "x") | Y %among% "x")) & (Z %among% c("y", "a") & Y %among% c("v", "w") & (X %among% "u" | X %among% c("s", "u")) & (Y %among% "x" & W %among% c("q", "p") & (X %among% c("t", "s") & Y %among% c("x", "w")))) & (W %among% c("q", "p") & W %among% c("q", "p") & (Y %among% c("w", "x") | Y %among% "w") | W %among% c("p", "r") & Y %among% "x" & (W %among% c("q", "r") | X %among% c("u", "t")) | X %among% c("u", "s") & Z %among% c("y", "a") & (X %among% c("u", "t") & Y %among% "v") & (W %among% "r" & W %among% "r" | Z %among% c("z", "a") & Z %among% c("z", "y"))) | (W %among% "r" | Z %among% "z" | Y %among% c("x", "v") & Y %among% c("v", "x")) & (Y %among% "x" & X %among% c("s", "t") | X %among% c("u", "s") & X %among% c("t", "s")) & (X %among% "u" | Y %among% "w" | (X %among% c("t", "s") | X %among% c("s", "u")) | W %among% c("r", "p") & W %among% "p" & (X %among% "u" | W %among% "q")) & (Y %among% "x" & X %among% c("t", "u") & (Z %among% "a" & X %among% c("u", "t")) & (X %among% c("t", "s") & W %among% "q" & (Y %among% "w" & X %among% c("s", "u"))) & (Y %among% "v" | X %among% "s" | X %among% "u" & W %among% c("q", "r") | (Y %among% c("x", "w") & Y %among% "v" | (W %among% "r" | Y %among% c("v", "x"))))))) & (((X %among% "u" & Y %among% "x" | (Y %among% "x" | X %among% c("t", "u")) | (Z %among% c("z", "a") & Y %among% c("x", "w") | X %among% c("t", "s") & Y %among% "w")) & ((X %among% "t" | Z %among% c("z", "y")) & (W %among% "r" & Z %among% c("z", "a")) & ((Z %among% "y" | W %among% c("q", "p")) & (X %among% c("t", "u") & X %among% c("s", "t")))) | (X %among% "t" & Y %among% c("v", "w") & (X %among% c("u", "t") & Y %among% "v") & (Y %among% "v" & X %among% "t" | (X %among% "s" | Y %among% c("v", "w"))) | (X %among% "s" | Z %among% "y") & (Z %among% c("a", "z") & Z %among% c("y", "a")) & ((W %among% "r" | X %among% c("u", "s")) & (Y %among% c("x", "w") | W %among% "r")))) & ((W %among% c("p", "q") & X %among% "s" | (W %among% "r" | Z %among% c("a", "y")) | Y %among% "w" & Y %among% "w" & (Z %among% "y" | Y %among% c("x", "w"))) & (W %among% c("q", "r") | Y %among% c("v", "x") | (Y %among% c("x", "w") | W %among% c("q", "p")) | (X %among% c("s", "u") & Z %among% c("z", "a") | Z %among% "y" & Y %among% "w")) & ((Y %among% "w" | Z %among% c("y", "z")) & (Z %among% c("z", "y") | W %among% "p") & (W %among% "r" & Y %among% "v" & (X %among% c("s", "t") & X %among% "t")) | (Z %among% "y" | W %among% c("p", "r")) & (W %among% c("r", "p") | Z %among% c("y", "z")) & (Y %among% c("x", "v") | W %among% "p" | Y %among% c("v", "x") & Y %among% c("x", "v")))) & ((W %among% c("q", "p") | X %among% "u" | (Z %among% "y" | Y %among% "x")) & (Y %among% c("w", "v") | X %among% c("u", "t") | Z %among% "z" & X %among% c("t", "u")) & (Y %among% "x" & Z %among% c("z", "a") & (X %among% c("s", "t") | W %among% "p") | (W %among% c("p", "q") | W %among% c("q", "r")) & (Y %among% "x" | Z %among% c("z", "y"))) & (((Y %among% c("v", "w") | W %among% "r") & (Z %among% "y" | W %among% c("r", "p")) | (W %among% c("q", "p") | W %among% "r" | Z %among% "z" & X %among% "u")) & (W %among% "r" & Y %among% c("v", "w") & (X %among% c("u", "t") | W %among% "r") | W %among% "q" & Y %among% "w" & (W %among% c("p", "q") & Z %among% c("z", "a")))) & (((W %among% c("q", "p") | X %among% "t") & (X %among% c("s", "u") | X %among% c("u", "s")) | X %among% c("u", "s") & Z %among% c("a", "y") & (W %among% "q" | Y %among% "v") | (Y %among% "v" & Z %among% "z" | (Y %among% c("x", "v") | Z %among% c("y", "a"))) & ((W %among% c("r", "q") | X %among% c("t", "s")) & (Z %among% "y" & Y %among% "x"))) & (Z %among% c("z", "y") & X %among% "t" & (X %among% c("s", "u") | Z %among% "y") | Y %among% c("v", "w") & X %among% "s" & (Z %among% c("y", "z") | Y %among% "x") | (Z %among% "z" | X %among% c("u", "t")) & (W %among% "q" & W %among% "q") & (W %among% "q" & Y %among% c("x", "v") & (Z %among% c("a", "z") | Y %among% c("v", "x")))))) & ((X %among% "s" & X %among% "u" | (W %among% "q" | Z %among% c("z", "y")) | (Z %among% c("y", "a") | W %among% c("q", "r") | X %among% c("s", "u") & X %among% "s") | ((Y %among% c("v", "x") | W %among% "r") & (Y %among% c("x", "v") | X %among% "t") | (Y %among% c("v", "x") & W %among% c("p", "r") | W %among% c("r", "q") & X %among% c("u", "t"))) | ((Y %among% c("x", "v") | Z %among% c("z", "a")) & (Z %among% "a" | X %among% "s") | (Z %among% "a" & Z %among% c("z", "y") | W %among% "p" & X %among% c("u", "t"))) & ((Z %among% "a" | W %among% "p" | (Y %among% c("x", "w") | Z %among% c("z", "y"))) & (W %among% "p" & Y %among% c("v", "x") & (X %among% "u" & W %among% c("q", "p"))))) & ((W %among% "q" & W %among% "q" | (X %among% c("s", "u") | Z %among% c("y", "z")) | (W %among% c("q", "r") | Z %among% "y") & (Z %among% c("y", "z") | W %among% c("r", "q"))) & ((W %among% "p" | Y %among% c("x", "w")) & (W %among% "r" | Y %among% c("w", "v")) | (W %among% "r" | Y %among% "w" | X %among% "s" & W %among% "p")) & ((Y %among% c("x", "w") | Z %among% "a" | Z %among% c("y", "a") & X %among% c("t", "s")) & (Z %among% "a" & Z %among% c("a", "y") | Z %among% "a" & Y %among% c("x", "w")) | ((Y %among% "x" | X %among% c("t", "s")) & (Y %among% c("w", "x") | W %among% "r") | (W %among% "r" | Y %among% c("w", "x")) & (X %among% c("t", "u") | Z %among% c("z", "a"))))) | ((W %among% "q" & Z %among% c("y", "a") & (X %among% "s" & Z %among% c("a", "z")) | (X %among% c("t", "s") | Z %among% c("a", "z") | (X %among% "s" | Z %among% c("a", "y")))) & (Z %among% "y" & X %among% c("u", "t") & (W %among% "p" | Y %among% c("w", "x")) | (Y %among% c("x", "w") | X %among% "u") & (W %among% c("q", "r") | X %among% c("t", "u"))) & ((Y %among% "v" & X %among% c("u", "s") | X %among% "t" & X %among% "t") & (Y %among% "w" & Z %among% c("a", "y") & (Z %among% c("y", "z") | W %among% "q")) | (Y %among% "v" | Z %among% c("z", "y")) & (X %among% "s" & W %among% "r") & (Y %among% c("x", "v") & W %among% "p" & (W %among% "p" & W %among% "r"))) | ((W %among% "p" | X %among% c("u", "t")) & (Z %among% "z" | Z %among% "y") & (X %among% "t" & Y %among% "w" & (W %among% "p" | X %among% c("u", "s"))) | (Z %among% "z" & W %among% "r" | Z %among% c("y", "a") & Z %among% "z" | (W %among% "r" | X %among% c("t", "u") | Z %among% "z" & W %among% c("q", "p")))) & ((W %among% "q" | Y %among% c("w", "v")) & (Y %among% "x" & X %among% "t") | (X %among% c("s", "u") | Y %among% "v" | Z %among% c("y", "a") & W %among% "p") | (Y %among% c("v", "w") | X %among% c("s", "t") | (X %among% c("u", "t") | W %among% "p") | (Y %among% "w" & Z %among% c("y", "a") | (Z %among% c("y", "a") | X %among% "u"))))))) (W %among% c("r", "q") | Z %among% c("a", "z")) & (Y %among% c("v", "x") | Z %among% c("y", "z")) & (X %among% c("u", "t") & Y %among% "x" & (Y %among% "x" & W %among% c("p", "q"))) & ((Z %among% c("a", "y") & Y %among% c("x", "v") | X %among% c("t", "s") & X %among% c("u", "s")) & (X %among% "u" & W %among% "r" | Z %among% c("a", "y") & Z %among% "y")) & ((Z %among% "y" | W %among% "p" | (Y %among% "w" | W %among% c("p", "r"))) & ((X %among% "t" | Y %among% c("w", "v")) & (X %among% "s" | Y %among% c("w", "x"))) | (Y %among% "x" & W %among% c("r", "p") | W %among% "r" & W %among% "r") & (Y %among% c("x", "w") & Z %among% "a" & (X %among% "u" | X %among% c("u", "t")))) | (X %among% "u" & Y %among% "w" & (X %among% "t" | X %among% "s") | (Z %among% "a" | Y %among% "w") & (W %among% "q" & Z %among% c("y", "z")) | (Z %among% "y" & W %among% c("p", "r") & (W %among% c("q", "r") & Z %among% "a") | Y %among% "x" & W %among% "r" & (W %among% "q" & Y %among% c("x", "w")))) & ((X %among% "u" | W %among% "p") & (Z %among% "y" & Z %among% "y") & (Y %among% "v" & X %among% "u" & (Z %among% c("y", "z") & W %among% "q")) & ((Z %among% "z" | W %among% c("r", "p") | (W %among% "r" | X %among% "s")) & (Y %among% c("x", "v") & X %among% c("u", "s") | W %among% c("r", "q") & Y %among% c("w", "v")))) | (Y %among% c("x", "w") & Y %among% c("v", "x") & (Z %among% c("a", "z") | Y %among% "w") & ((Z %among% "a" | Z %among% c("a", "z")) & (W %among% c("q", "p") & Z %among% c("y", "a"))) | (W %among% c("q", "p") | X %among% "s") & (X %among% "t" | W %among% "r") & ((X %among% c("u", "s") | Z %among% "z") & (X %among% "s" | Z %among% "a")) | ((Z %among% "a" | Y %among% "w" | (W %among% "q" | X %among% "u")) & (Y %among% c("x", "w") & Y %among% "x" & (W %among% "p" & W %among% "p")) | (Y %among% "v" & X %among% c("t", "s") | W %among% "q" & Y %among% "w" | X %among% "t" & W %among% c("r", "p") & (X %among% "s" & Z %among% c("z", "y"))))) & ((X %among% "u" & W %among% c("p", "r") | (X %among% "s" | Z %among% c("y", "z"))) & ((X %among% "u" | W %among% "q") & (Z %among% c("z", "y") & Y %among% c("v", "w"))) & ((Y %among% "v" | W %among% "p") & (X %among% c("t", "s") & X %among% "t") | (W %among% "r" | W %among% c("r", "q") | X %among% "t" & W %among% "p")) | (Z %among% c("z", "y") & Z %among% c("y", "z") & (Z %among% "z" | W %among% c("r", "p")) | (X %among% c("t", "u") | Y %among% c("v", "w")) & (X %among% c("s", "u") & X %among% "u")) & (Y %among% c("v", "x") & Y %among% "v" & (Y %among% c("w", "v") & Z %among% c("a", "z")) & (Y %among% "v" & Y %among% "w" & (Y %among% "x" | W %among% c("q", "p"))))) @@ -656,14 +659,78 @@ Y %among% "w" & Y %among% c("x", "v") & (Y %among% "v" & Y %among% "v") & (Z %am (W %among% c("p", "q") | Z %among% "y" | Y %among% c("v", "x") & X %among% "s") & ((Z %among% "a" | W %among% c("q", "p")) & (Y %among% c("w", "v") | Z %among% "z")) & ((Y %among% c("w", "v") | Y %among% c("v", "x")) & (X %among% c("s", "t") & Z %among% c("a", "y")) | (W %among% "p" | Z %among% "y" | Z %among% c("z", "y") & X %among% "s")) & (Y %among% "v" | W %among% "p" | Z %among% "z" & Y %among% "x" | (W %among% "q" | X %among% "u" | Z %among% c("a", "z") & Z %among% "z") | ((Y %among% "v" | Y %among% "w") & (X %among% c("s", "t") | X %among% "u") | (W %among% c("r", "p") & W %among% c("r", "q") | (Z %among% c("z", "a") | X %among% c("s", "u"))))) & ((Y %among% c("v", "w") & X %among% c("s", "t") | (W %among% c("p", "r") | Z %among% "a")) & (Z %among% "z" & X %among% c("t", "u") | X %among% "u" & Y %among% "v") & ((X %among% c("u", "t") | X %among% c("u", "t") | (Z %among% "a" | Z %among% c("y", "a"))) & ((X %among% "t" | Z %among% "y") & (W %among% "q" | Y %among% "x"))) & ((Y %among% "w" | Z %among% "z" | X %among% c("u", "s") & X %among% c("s", "u")) & ((Z %among% c("y", "z") | W %among% "p") & (W %among% c("q", "r") & X 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c("z", "y") | Y %among% c("x", "v")) | (X %among% c("t", "s") & W %among% "r" | (X %among% "t" | X %among% "u")) | Y %among% "v" & X %among% "u" & (X %among% c("t", "s") | Y %among% c("w", "x")) & (Y %among% c("x", "v") & Z %among% "z" | Z %among% "y" & W %among% c("q", "r")) | ((W %among% "r" | Y %among% "w" | X %among% "s" & Y %among% c("w", "x")) & (Y %among% "w" | W %among% c("p", "q") | X %among% "t" & X %among% "t") | (Z %among% c("y", "a") & Z %among% c("a", "y") | W %among% "p" & Y %among% c("w", "x")) & ((Y %among% "x" | W %among% "q") & (X %among% c("t", "s") & Y %among% "v")))) & ((Z %among% "y" & Y %among% "w" & (Z %among% c("y", "a") | W %among% c("p", "q")) | (W %among% c("r", "q") | X %among% "t" | Y %among% c("x", "v") & X %among% "s") | (Z %among% c("z", "y") | W %among% "q" | X %among% "u" & W %among% "q" | W %among% "r" & Z %among% "z" & (X %among% "t" & W %among% "q")) | ((Z %among% "z" & W %among% c("p", "q") | (X %among% "s" | W %among% c("p", "r"))) & (Y %among% "v" & X %among% c("t", "u") & (X %among% c("t", "s") | Z %among% c("y", "a"))) | (W %among% "p" | X %among% c("u", "t") | X %among% c("u", "t") & Y %among% c("x", "w") | Y %among% c("w", "x") & W %among% c("q", "p") & (Z %among% c("a", "z") & Z %among% c("z", "a"))))) & (Y %among% "w" | Z %among% "z" | (X %among% "s" | W %among% c("q", "p")) | (Z %among% c("a", "y") | W %among% "q") & (Z %among% c("z", "y") & Y %among% c("v", "w")) | (X %among% "u" & Z %among% "y" & (X %among% "s" | X %among% c("u", "s")) | (Y %among% c("x", "v") | X %among% c("t", "s") | Z %among% c("a", "z") & X %among% c("s", "u"))) | (Z %among% c("a", "y") | W %among% c("p", "q")) & (Y %among% c("v", "x") & Z %among% c("z", "y")) & (Y %among% c("v", "w") & Y %among% "x" & (X %among% "t" & Z %among% "z")) & ((X %among% "u" & W %among% c("r", "p") | (W %among% c("q", "p") | X %among% c("t", "u"))) & (Y %among% "x" & Z %among% "z" | Y %among% c("v", "x") & W %among% "q")))) & ((Y %among% "v" & X %among% "s" | X %among% c("u", "s") & W %among% "q" | Y %among% c("w", "v") & W %among% c("p", "r") & (W %among% "p" | Y %among% "v")) & ((Y %among% c("v", "w") | Z %among% "y") & (Z %among% "y" | X %among% "t") | (W %among% c("q", "r") & Z %among% "y" | X %among% "u" & W %among% "r")) | (X %among% c("s", "t") | Y %among% "w" | W %among% c("p", "q") & Z %among% c("a", "y")) & (Z %among% "a" & Z %among% c("z", "y") | X %among% c("s", "t") & X %among% c("u", "t")) & (X %among% "s" | W %among% c("r", "q") | Z %among% "a" & Z %among% "y" | (Z %among% c("z", "y") | Y %among% "x") & (X %among% c("t", "s") & X %among% "u")) | ((Z %among% "a" & Y %among% c("w", "v") | Y %among% c("w", "x") & W %among% "q" | X %among% "t" & X %among% "s" & (W %among% "p" & Z %among% "z")) & ((X %among% c("s", "u") | Z %among% c("z", "y") | (Y %among% "x" | Y %among% "x")) & (W %among% c("p", "q") | Z %among% "z" | Z %among% "y" & X %among% c("u", "s" ))) | (X %among% c("t", "s") & W %among% c("p", "q") & (W %among% c("p", "q") | Y %among% c("x", "w")) | Y %among% c("v", "x") & X %among% "t" & (X %among% "t" & W %among% c("p", "q")) | (Y %among% "v" & Y %among% "w" | (X %among% "u" | W %among% "p") | Z %among% c("z", "a") & X %among% "s" & (Y %among% "v" | Z %among% c("z", "a"))))) | (((W %among% "p" | X %among% "u" | (W %among% "r" | W %among% c("r", "p"))) & (X %among% c("t", "u") | X %among% c("s", "t") | (X %among% c("s", "u") | Z %among% "a")) | (Y %among% c("w", "v") & W %among% "r" | X %among% "t" & X %among% c("s", "u") | (W %among% c("p", "q") | X %among% "u" | (Z %among% "a" | X %among% c("u", "s"))))) & ((Z %among% "a" | Z %among% "a") & (Z %among% "y" & Y %among% "x") | X %among% "t" & W %among% "q" & (X %among% "u" | Z %among% c("y", "z")) | ((Y %among% c("w", "v") | Z %among% c("z", "a")) & (W %among% "q" & W %among% c("p", "q")) | (Z %among% "y" | Z %among% "z") & (Y %among% c("v", "x") | W %among% c("q", "p")))) | (Z %among% c("y", "z") | X %among% c("s", "u") | Y %among% c("v", "x") & Z %among% "y" | Y %among% "v" & Z %among% c("z", "a") & (Y %among% "w" | Y %among% "v")) & (Z %among% "z" | Y %among% "x" | (W %among% "r" | Y %among% c("w", "x")) | (X %among% "t" | Y %among% c("v", "x") | (W %among% c("p", "q") | Z %among% "y"))) & (Z %among% c("z", "a") & Y %among% "v" | (W %among% c("q", "r") | Y %among% "v") | X %among% "t" & X %among% c("s", "u") & (X %among% "u" & X %among% "s") | X %among% "t" & W %among% "p" & (W %among% c("r", "q") | Z %among% "a") & (W %among% c("r", "p") & Y %among% c("v", "x") | (Y %among% c("v", "x") | X %among% "t"))))) From 36df45ea16b7395afc6ccfc5fecc831013c6f6d8 Mon Sep 17 00:00:00 2001 From: mb706 Date: Wed, 18 Sep 2024 17:42:49 +0200 Subject: [PATCH 48/87] faster tests --- attic/expression_experiments.R | 85 ++++++++------- attic/expression_experiments_2.R | 119 ++++++++++++++++++++ attic/expression_experiments_3.R | 127 ++++++++++++++++++++++ tests/testthat/test_CnfFormula.R | 7 +- tests/testthat/test_CnfFormula_simplify.R | 8 +- 5 files changed, 297 insertions(+), 49 deletions(-) create mode 100644 attic/expression_experiments_2.R create mode 100644 attic/expression_experiments_3.R diff --git a/attic/expression_experiments.R b/attic/expression_experiments.R index 16e604ee7..28138b969 100644 --- a/attic/expression_experiments.R +++ b/attic/expression_experiments.R @@ -59,50 +59,51 @@ expression_weight = function(expression) { sum(all.names(expression) %in% c("|", "&")) + 1 } - stats = list(depth = integer(0), expweight = numeric(0), simpweight = numeric(0), was_tautology = logical(0), was_contradiction = logical(0)) - set.seed(3 + ss) - for (depth_to_check in 2:12) { - for (repetition in seq_len(2000)) { - if (depth_to_check == 11) { - expression = random_cnf_expression(10, TRUE, 4) - } else if (depth_to_check == 12) { - expression = random_cnf_expression(5, TRUE, 2) - } else { - expression = random_cnf_expression(depth_to_check) - } - cat(sprintf("%s\n", deparse1(expression))) - simplified = formula_to_expression(eval(expression)) - stats$depth[[length(stats$depth) + 1]] = depth_to_check - stats$expweight[[length(stats$expweight) + 1]] = expression_weight(expression) - stats$simpweight[[length(stats$simpweight) + 1]] = expression_weight(simplified) - vars = intersect(names(u), all.names(expression)) - assignments = expand.grid(lapply(vars, function(var) u[[var]]), stringsAsFactors = FALSE) - colnames(assignments) = vars - - truevals = evaluate_expression(expression, assignments) - simpvals = evaluate_expression(simplified, assignments) - - stats$was_tautology[[length(stats$was_tautology) + 1]] = all(truevals) - stats$was_contradiction[[length(stats$was_contradiction) + 1]] = all(!truevals) - - if (!all(truevals == simpvals)) { - trueval = truevals[[which(!truevals == simpvals)[1]]] - simpval = simpvals[[which(!truevals == simpvals)[1]]] - assignment = assignments[which(!truevals == simpvals)[1], , drop = FALSE] - } else { - # alibi - trueval = simpval = TRUE - assignment = NULL - } - expect_equal(trueval, simpval, - info = sprintf("Expression: %s\nAssignment:\n%s\nSimplified to: %s", - deparse1(expression), - paste(capture.output(print(assignment)), collapse = "\n"), - deparse1(simplified) - )) +varnames = names(u) +assignments = expand.grid(lapply(varnames, function(var) u[[var]]), stringsAsFactors = FALSE) +colnames(assignments) = varnames + +stats = list(depth = integer(0), expweight = numeric(0), simpweight = numeric(0), was_tautology = logical(0), was_contradiction = logical(0)) +set.seed(3 + ss) +for (depth_to_check in 2:12) { + for (repetition in seq_len(2000)) { + if (depth_to_check == 11) { + expression = random_cnf_expression(10, TRUE, 4) + } else if (depth_to_check == 12) { + expression = random_cnf_expression(5, TRUE, 2) + } else { + expression = random_cnf_expression(depth_to_check) + } + cat(sprintf("%s\n", deparse1(expression))) + simplified = formula_to_expression(eval(expression)) + stats$depth[[length(stats$depth) + 1]] = depth_to_check + stats$expweight[[length(stats$expweight) + 1]] = expression_weight(expression) + stats$simpweight[[length(stats$simpweight) + 1]] = expression_weight(simplified) + + truevals = evaluate_expression(expression, assignments) + simpvals = evaluate_expression(simplified, assignments) + + stats$was_tautology[[length(stats$was_tautology) + 1]] = all(truevals) + stats$was_contradiction[[length(stats$was_contradiction) + 1]] = all(!truevals) + + if (!all(truevals == simpvals)) { + trueval = truevals[[which(!truevals == simpvals)[1]]] + simpval = simpvals[[which(!truevals == simpvals)[1]]] + assignment = assignments[which(!truevals == simpvals)[1], , drop = FALSE] + } else { + # alibi + trueval = simpval = TRUE + assignment = NULL } + expect_equal(trueval, simpval, + info = sprintf("Expression: %s\nAssignment:\n%s\nSimplified to: %s", + deparse1(expression), + paste(capture.output(print(assignment)), collapse = "\n"), + deparse1(simplified) + )) } - dti <- as.data.table(stats) +} +dti <- as.data.table(stats) saveRDS(dti, sprintf("expression_experiments_%05i.rds", ss)) diff --git a/attic/expression_experiments_2.R b/attic/expression_experiments_2.R new file mode 100644 index 000000000..4a51709eb --- /dev/null +++ b/attic/expression_experiments_2.R @@ -0,0 +1,119 @@ +# Get 'ss' from command line arguments +args <- commandArgs(trailingOnly = TRUE) +checkmate::assert_integer(ss <- as.integer(args[1]), lower = 1, len = 1, any.missing = FALSE) + +library("mlr3pipelines") +library("testthat") +library("data.table") +options(width = 10000) + +u = CnfUniverse() +V = CnfSymbol(u, "V", c("m", "n", "o")) +W = CnfSymbol(u, "W", c("p", "q", "r")) +X = CnfSymbol(u, "X", c("s", "t", "u")) +Y = CnfSymbol(u, "Y", c("v", "w", "x")) +Z = CnfSymbol(u, "Z", c("y", "z", "a")) + +random_atom_expression = function() { + symbol = sample(alist(V, W, X, Y, Z), 1)[[1]] + values = sample(u[[deparse(symbol)]], sample(2, 1)) + substitute(symbol %among% values, list(symbol = symbol, values = values)) +} + +random_cnf_expression = function(depth, do_cnf = FALSE, ddepth = 0) { + if (depth <= 1) { + # base case: return a random symbol expression call + return(random_atom_expression()) + } + # recursively build a random tree of expressions + if (do_cnf) { + op = if (depth <= ddepth) quote(`|`) else quote(`&`) + } else { + op = sample(alist(`&`, `|`), 1)[[1]] # randomly choose between AND and OR + } + left_expr = random_cnf_expression(depth - 1, do_cnf, ddepth) + right_expr = random_cnf_expression(depth - 1, do_cnf, ddepth) + + # create a call object for the expression: (left_expr op right_expr) + substitute(op(left_expr, right_expr), list(op = op, left_expr = left_expr, right_expr = right_expr)) +} + +formula_to_expression = function(formula) { + if (is.logical(formula)) return(c(formula)) + clause_exprs = lapply(as.CnfFormula(formula), function(clause) { + atom_exprs = lapply(clause, function(atom) { + substitute(symbol %among% values, list(symbol = as.name(atom$symbol), values = atom$values)) + }) + Reduce(function(x, y) substitute(x | y, list(x = x, y = y)), atom_exprs) + }) + Reduce(function(x, y) substitute(x & y, list(x = x, y = y)), clause_exprs) +} + +evaluate_expression = function(expression, assignment) { + substituted = do.call(substitute, list(expression, c(list("%among%" = quote(`%in%`)), assignment))) + eval(substituted, envir = baseenv()) +} + +expression_weight = function(expression) { + if (is.logical(expression)) return(0) + sum(all.names(expression) %in% c("|", "&")) + 1 +} + +varnames = names(u) +assignments = expand.grid(lapply(varnames, function(var) u[[var]]), stringsAsFactors = FALSE) +colnames(assignments) = varnames + +stats = list(depth = integer(0), expweight = numeric(0), simpweight = numeric(0), was_tautology = logical(0), was_contradiction = logical(0)) +set.seed(3 + ss) +for (depth_to_check in 2:13) { + for (repetition in seq_len(2000)) { + if (depth_to_check == 12) { + expression = random_cnf_expression(10, TRUE, 4) + } else if (depth_to_check == 13) { + expression = random_cnf_expression(5, TRUE, 2) + } else { + expression = random_cnf_expression(depth_to_check) + } + cat(sprintf("%s\n", deparse1(expression))) + simplified = formula_to_expression(eval(expression)) + stats$depth[[length(stats$depth) + 1]] = depth_to_check + stats$expweight[[length(stats$expweight) + 1]] = expression_weight(expression) + stats$simpweight[[length(stats$simpweight) + 1]] = expression_weight(simplified) + + truevals = evaluate_expression(expression, assignments) + simpvals = evaluate_expression(simplified, assignments) + + stats$was_tautology[[length(stats$was_tautology) + 1]] = all(truevals) + stats$was_contradiction[[length(stats$was_contradiction) + 1]] = all(!truevals) + + if (!all(truevals == simpvals)) { + trueval = truevals[[which(!truevals == simpvals)[1]]] + simpval = simpvals[[which(!truevals == simpvals)[1]]] + assignment = assignments[which(!truevals == simpvals)[1], , drop = FALSE] + } else { + # alibi + trueval = simpval = TRUE + assignment = NULL + } + expect_equal(trueval, simpval, + info = sprintf("Expression: %s\nAssignment:\n%s\nSimplified to: %s", + deparse1(expression), + paste(capture.output(print(assignment)), collapse = "\n"), + deparse1(simplified) + )) + } +} +dti <- as.data.table(stats) + +saveRDS(dti, sprintf("expression_experiments_2_%05i.rds", ss)) + +dti[, .( + ew = mean(expweight), sw = mean(simpweight), + etriv = mean(expweight == 0), + striv = mean(simpweight == 0), + could_simplify = mean(expweight > simpweight), + was_tautology = mean(was_tautology), + was_contradiction = mean(was_contradiction), + tautologies_not_recognized = mean(was_tautology & simpweight > 0), + contradictions_not_recognized = mean(was_contradiction & simpweight > 0) + ), by = "depth"] diff --git a/attic/expression_experiments_3.R b/attic/expression_experiments_3.R new file mode 100644 index 000000000..87da76abf --- /dev/null +++ b/attic/expression_experiments_3.R @@ -0,0 +1,127 @@ + +# Get 'ss' from command line arguments +args <- commandArgs(trailingOnly = TRUE) +checkmate::assert_integer(ss <- as.integer(args[1]), lower = 1, len = 1, any.missing = FALSE) + +library("mlr3pipelines") +library("testthat") +library("data.table") +options(width = 10000) + +u = CnfUniverse() +W = CnfSymbol(u, "W", c("p", "q", "r")) +X = CnfSymbol(u, "X", c("s", "t", "u")) +Y = CnfSymbol(u, "Y", c("v", "w", "x")) +Z = CnfSymbol(u, "Z", c("y", "z", "a")) + +random_atom_expression = function() { + symbol = sample(alist(W, X, Y, Z), 1)[[1]] + values = sample(u[[deparse(symbol)]], sample(2, 1)) + substitute(symbol %among% values, list(symbol = symbol, values = values)) +} + +random_cnf_expression = function(depth, do_cnf = FALSE, ddepth = 0) { + if (depth <= 1) { + # base case: return a random symbol expression call + return(random_atom_expression()) + } + # recursively build a random tree of expressions + if (do_cnf) { + op = if (depth <= ddepth) quote(`|`) else quote(`&`) + } else { + op = sample(alist(`&`, `|`), 1)[[1]] # randomly choose between AND and OR + } + left_expr = random_cnf_expression(depth - 1, do_cnf, ddepth) + right_expr = random_cnf_expression(depth - 1, do_cnf, ddepth) + + # create a call object for the expression: (left_expr op right_expr) + substitute(op(left_expr, right_expr), list(op = op, left_expr = left_expr, right_expr = right_expr)) +} + +formula_to_expression = function(formula) { + if (is.logical(formula)) return(c(formula)) + clause_exprs = lapply(as.CnfFormula(formula), function(clause) { + atom_exprs = lapply(clause, function(atom) { + substitute(symbol %among% values, list(symbol = as.name(atom$symbol), values = atom$values)) + }) + Reduce(function(x, y) substitute(x | y, list(x = x, y = y)), atom_exprs) + }) + Reduce(function(x, y) substitute(x & y, list(x = x, y = y)), clause_exprs) +} + +evaluate_expression = function(expression, assignment) { + substituted = do.call(substitute, list(expression, c(list("%among%" = quote(`%in%`)), assignment))) + eval(substituted, envir = baseenv()) +} + +expression_weight = function(expression) { + if (is.logical(expression)) return(0) + sum(all.names(expression) %in% c("|", "&")) + 1 +} + +varnames = names(u) +assignments = expand.grid(lapply(varnames, function(var) u[[var]]), stringsAsFactors = FALSE) +colnames(assignments) = varnames + +stats = list(depth = integer(0), expweight = numeric(0), simpweight = numeric(0), was_tautology = logical(0), was_contradiction = logical(0)) +set.seed(3 + ss) +for (depth_to_check in 2:12) { + for (repetition in seq_len(2000)) { + subexps = replicate(10, { + if (depth_to_check == 11) { + expression = random_cnf_expression(10, TRUE, 4) + } else if (depth_to_check == 12) { + expression = random_cnf_expression(5, TRUE, 2) + } else { + expression = random_cnf_expression(depth_to_check) + } + cat(sprintf("%s\n", deparse1(expression))) + eval(expression) + }, simplify = FALSE) + subexps = Filter(function(x) !is.logical(x), subexps) + if (!length(subexps)) next + expression = Reduce(function(x, y) substitute(x & y, list(x = x, y = y)), lapply(subexps, formula_to_expression)) + cat(sprintf("%s\n\n", deparse1(expression))) + + simplified = formula_to_expression(CnfFormula(subexps)) + stats$depth[[length(stats$depth) + 1]] = depth_to_check + stats$expweight[[length(stats$expweight) + 1]] = expression_weight(expression) + stats$simpweight[[length(stats$simpweight) + 1]] = expression_weight(simplified) + + truevals = evaluate_expression(expression, assignments) + simpvals = evaluate_expression(simplified, assignments) + + stats$was_tautology[[length(stats$was_tautology) + 1]] = all(truevals) + stats$was_contradiction[[length(stats$was_contradiction) + 1]] = all(!truevals) + + if (!all(truevals == simpvals)) { + trueval = truevals[[which(!truevals == simpvals)[1]]] + simpval = simpvals[[which(!truevals == simpvals)[1]]] + assignment = assignments[which(!truevals == simpvals)[1], , drop = FALSE] + } else { + # alibi + trueval = simpval = TRUE + assignment = NULL + } + expect_equal(trueval, simpval, + info = sprintf("Expression: %s\nAssignment:\n%s\nSimplified to: %s", + deparse1(expression), + paste(capture.output(print(assignment)), collapse = "\n"), + deparse1(simplified) + )) + } +} +dti <- as.data.table(stats) + +saveRDS(dti, sprintf("expression_experiments_3_%05i.rds", ss)) + +dti[, .( + ew = mean(expweight), sw = mean(simpweight), + etriv = mean(expweight == 0), + striv = mean(simpweight == 0), + could_simplify = mean(expweight > simpweight), + was_tautology = mean(was_tautology), + was_contradiction = mean(was_contradiction), + tautologies_not_recognized = mean(was_tautology & simpweight > 0), + contradictions_not_recognized = mean(was_contradiction & simpweight > 0) + ), by = "depth"] diff --git a/tests/testthat/test_CnfFormula.R b/tests/testthat/test_CnfFormula.R index 21cd28b0a..d605f03a1 100644 --- a/tests/testthat/test_CnfFormula.R +++ b/tests/testthat/test_CnfFormula.R @@ -625,6 +625,10 @@ test_that("Brute-force test", { ss = 0 # dti_col <- parallel::mclapply(mc.cores = 16, 1:16, function(ss) { + varnames = names(u) + assignments = expand.grid(lapply(varnames, function(var) u[[var]]), stringsAsFactors = FALSE) + colnames(assignments) = varnames + stats = list(depth = integer(0), expweight = numeric(0), simpweight = numeric(0), was_tautology = logical(0), was_contradiction = logical(0)) set.seed(3 + ss) @@ -641,9 +645,6 @@ test_that("Brute-force test", { stats$depth[[length(stats$depth) + 1]] = depth_to_check stats$expweight[[length(stats$expweight) + 1]] = expression_weight(expression) stats$simpweight[[length(stats$simpweight) + 1]] = expression_weight(simplified) - vars = intersect(names(u), all.names(expression)) - assignments = expand.grid(lapply(vars, function(var) u[[var]]), stringsAsFactors = FALSE) - colnames(assignments) = vars truevals = evaluate_expression(expression, assignments) simpvals = evaluate_expression(simplified, assignments) diff --git a/tests/testthat/test_CnfFormula_simplify.R b/tests/testthat/test_CnfFormula_simplify.R index d3af6c365..1db9b5dec 100644 --- a/tests/testthat/test_CnfFormula_simplify.R +++ b/tests/testthat/test_CnfFormula_simplify.R @@ -33,6 +33,10 @@ test_that("CnfFormula Regression Tests", { sum(all.names(expression) %in% c("|", "&")) + 1 } + varnames = names(u) + assignments = expand.grid(lapply(varnames, function(var) u[[var]]), stringsAsFactors = FALSE) + colnames(assignments) = varnames + stats = list(expweight = numeric(0), simpweight = numeric(0), was_tautology = logical(0), was_contradiction = logical(0)) for (line in testcases) { @@ -40,9 +44,6 @@ test_that("CnfFormula Regression Tests", { simplified = formula_to_expression(eval(expression)) stats$expweight[[length(stats$expweight) + 1]] = expression_weight(expression) stats$simpweight[[length(stats$simpweight) + 1]] = expression_weight(simplified) - vars = intersect(names(u), all.names(expression)) - assignments = expand.grid(lapply(vars, function(var) u[[var]]), stringsAsFactors = FALSE) - colnames(assignments) = vars truevals = evaluate_expression(expression, assignments) simpvals = evaluate_expression(simplified, assignments) @@ -66,7 +67,6 @@ test_that("CnfFormula Regression Tests", { deparse1(simplified) )) - cat(".") } dti <- as.data.table(stats) From db09b09f3102262c90c9beaa9e27ee01fcdfd92c Mon Sep 17 00:00:00 2001 From: mb706 Date: Wed, 18 Sep 2024 20:53:55 +0200 Subject: [PATCH 49/87] documentation --- R/CnfFormula.R | 24 +++++++++++++++++++++--- attic/expression_experiments_3.R | 2 +- man/CnfFormula.Rd | 24 +++++++++++++++++++++--- 3 files changed, 43 insertions(+), 7 deletions(-) diff --git a/R/CnfFormula.R b/R/CnfFormula.R index 434ec2e09..145b76f14 100644 --- a/R/CnfFormula.R +++ b/R/CnfFormula.R @@ -32,8 +32,8 @@ #' Note that the simplified form of a formula containing a tautology is the empty list. #' #' Upon construction, the `CnfFormula` is simplified by using various heuristics. -#' This includes unit propagation, subsumption elimination, and self/hidden subsumption elimination -#' (see examples). +#' This includes unit propagation, subsumption elimination, self/hidden subsumption elimination, +#' hidden tautology elimination, and resolution subsumption elimination (see examples). #' Note that the order of clauses in a formula is not preserved. #' #' Using `CnfFormula()` on lists that contain other `CnfFormula` objects will create @@ -95,7 +95,7 @@ #' (X %among% c("a", "b") | Y %among% "d") & #' (X %among% "a" | Y %among% "e") #' -#' ## hidden subsumption elimination +#' ## resolution subsumption elimination #' # The first two statements can only be satisfied if Y is either "d" or "e", #' # since when X is "a" then Y must be "e", and when X is "b" then Y must be "d". #' # The third statement is therefore implied by the first two, and can be @@ -104,6 +104,24 @@ #' (X %among% "b" | Y %among% "e") & #' (Y %among% c("d", "e")) #' +#' ## hidden tautology elimination / hidden subsumption elimination +#' # When considering the first two clauses only, adding another atom +#' # `Z %among% "i"` to the first clause would not change the formula, since +#' # whenever Z is "i", the second clause would need to be satisfied in a way +#' # that would also satisfy the first clause, making this atom redundant +#' # ("hidden literal addition"). Considering the pairs of clause 1 and 3, and +#' # clauses 1 and 4, one could likewise add `Z %among% "g"` and +#' #' `Z %among% "h"`, respectively. This would reveal the first clausee to be +#' # a "hidden" tautology: it is equivalent to a clause containing the +#' # atom `Z %among% c("g", "h", "i")` == TRUE. +#' # Alternatively, one could perform "hidden" resolution subsumption using +#' # clause 4 after having added the atom `Z %among% c("g", "i")` to the first +#' # clause by using clauses 2 and 3. +#' (X %among% c("a", "b") | Y %among% c("d", "e")) & +#' (X %among% "a" | Z %among% c("g", "h")) & +#' (X %among% "b" | Z %among% c("h", "i")) & +#' (Y %among% c("d", "e") | Z %among% c("g", "i")) +#' #' ## Simple contradictions are recognized: #' (X %among% "a") & (X %among% "b") #' # Tautologies are preserved diff --git a/attic/expression_experiments_3.R b/attic/expression_experiments_3.R index 87da76abf..0e9d56789 100644 --- a/attic/expression_experiments_3.R +++ b/attic/expression_experiments_3.R @@ -67,7 +67,7 @@ stats = list(depth = integer(0), expweight = numeric(0), simpweight = numeric(0) set.seed(3 + ss) for (depth_to_check in 2:12) { for (repetition in seq_len(2000)) { - subexps = replicate(10, { + subexps = replicate(4, { if (depth_to_check == 11) { expression = random_cnf_expression(10, TRUE, 4) } else if (depth_to_check == 12) { diff --git a/man/CnfFormula.Rd b/man/CnfFormula.Rd index 8d7e006f9..845516e10 100644 --- a/man/CnfFormula.Rd +++ b/man/CnfFormula.Rd @@ -34,8 +34,8 @@ To get individual clauses from a formula, \code{[[} should not be used; instead, Note that the simplified form of a formula containing a tautology is the empty list. Upon construction, the \code{CnfFormula} is simplified by using various heuristics. -This includes unit propagation, subsumption elimination, and self/hidden subsumption elimination -(see examples). +This includes unit propagation, subsumption elimination, self/hidden subsumption elimination, +hidden tautology elimination, and resolution subsumption elimination (see examples). Note that the order of clauses in a formula is not preserved. Using \code{CnfFormula()} on lists that contain other \code{CnfFormula} objects will create @@ -91,7 +91,7 @@ as.list(frm) (X \%among\% c("a", "b") | Y \%among\% "d") & (X \%among\% "a" | Y \%among\% "e") -## hidden subsumption elimination +## resolution subsumption elimination # The first two statements can only be satisfied if Y is either "d" or "e", # since when X is "a" then Y must be "e", and when X is "b" then Y must be "d". # The third statement is therefore implied by the first two, and can be @@ -100,6 +100,24 @@ as.list(frm) (X \%among\% "b" | Y \%among\% "e") & (Y \%among\% c("d", "e")) +## hidden tautology elimination / hidden subsumption elimination +# When considering the first two clauses only, adding another atom +# `Z \%among\% "i"` to the first clause would not change the formula, since +# whenever Z is "i", the second clause would need to be satisfied in a way +# that would also satisfy the first clause, making this atom redundant +# ("hidden literal addition"). Considering the pairs of clause 1 and 3, and +# clauses 1 and 4, one could likewise add `Z \%among\% "g"` and +#' `Z \%among\% "h"`, respectively. This would reveal the first clausee to be +# a "hidden" tautology: it is equivalent to a clause containing the +# atom `Z \%among\% c("g", "h", "i")` == TRUE. +# Alternatively, one could perform "hidden" resolution subsumption using +# clause 4 after having added the atom `Z \%among\% c("g", "i")` to the first +# clause by using clauses 2 and 3. +(X \%among\% c("a", "b") | Y \%among\% c("d", "e")) & + (X \%among\% "a" | Z \%among\% c("g", "h")) & + (X \%among\% "b" | Z \%among\% c("h", "i")) & + (Y \%among\% c("d", "e") | Z \%among\% c("g", "i")) + ## Simple contradictions are recognized: (X \%among\% "a") & (X \%among\% "b") # Tautologies are preserved From 191aa241518a53f3e5fc0385418b12f7f5cc5211 Mon Sep 17 00:00:00 2001 From: mb706 Date: Wed, 18 Sep 2024 23:07:17 +0200 Subject: [PATCH 50/87] more aggressive experiments --- attic/expression_experiments_3.R | 24 ++++++++++++------------ 1 file changed, 12 insertions(+), 12 deletions(-) diff --git a/attic/expression_experiments_3.R b/attic/expression_experiments_3.R index 0e9d56789..36acbede2 100644 --- a/attic/expression_experiments_3.R +++ b/attic/expression_experiments_3.R @@ -65,21 +65,21 @@ colnames(assignments) = varnames stats = list(depth = integer(0), expweight = numeric(0), simpweight = numeric(0), was_tautology = logical(0), was_contradiction = logical(0)) set.seed(3 + ss) -for (depth_to_check in 2:12) { +for (depth_to_check in 2:11) { for (repetition in seq_len(2000)) { - subexps = replicate(4, { - if (depth_to_check == 11) { - expression = random_cnf_expression(10, TRUE, 4) - } else if (depth_to_check == 12) { - expression = random_cnf_expression(5, TRUE, 2) - } else { - expression = random_cnf_expression(depth_to_check) + subexps = replicate(if (depth_to_check == 11) 10 else 4, { + repeat { + if (depth_to_check == 11) { + expression = random_cnf_expression(10, TRUE, 4) + } else { + expression = random_cnf_expression(depth_to_check) + } + cat(sprintf("%s\n", deparse1(expression))) + result = eval(expression) + if (!is.logical(result)) break } - cat(sprintf("%s\n", deparse1(expression))) - eval(expression) + result }, simplify = FALSE) - subexps = Filter(function(x) !is.logical(x), subexps) - if (!length(subexps)) next expression = Reduce(function(x, y) substitute(x & y, list(x = x, y = y)), lapply(subexps, formula_to_expression)) cat(sprintf("%s\n\n", deparse1(expression))) From fa400884b849c81e1dd685cae5ac60d7f712a08b Mon Sep 17 00:00:00 2001 From: mb706 Date: Wed, 18 Sep 2024 23:48:00 +0200 Subject: [PATCH 51/87] compress testdata --- tests/testthat/test_CnfFormula_simplify.R | 4 +- tests/testthat/testdata/cnf.xz | Bin 0 -> 318188 bytes tests/testthat/testdata/cnfcases.txt | 736 ---------------------- 3 files changed, 3 insertions(+), 737 deletions(-) create mode 100644 tests/testthat/testdata/cnf.xz delete mode 100644 tests/testthat/testdata/cnfcases.txt diff --git a/tests/testthat/test_CnfFormula_simplify.R b/tests/testthat/test_CnfFormula_simplify.R index 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"p")) & (X %among% c("u", "s") | X %among% c("s", "u") | (Y %among% c("x", "v") | Z %among% "a") | (X %among% c("t", "u") & W %among% "r" | (Z %among% "y" | W %among% "r"))) & ((Y %among% c("v", "x") | W %among% "q" | X %among% "t" & W %among% c("q", "p")) & (Y %among% "w" | Z %among% c("a", "y") | (W %among% "r" | W %among% "p")) | (X %among% "s" | Z %among% c("y", "a") | (W %among% c("q", "r") | W %among% c("q", "p")) | (Z %among% "z" | Y %among% c("w", "x")) & (X %among% c("u", "s") & X %among% "t"))) | (Y %among% c("w", "x") & Z %among% "y" & (W %among% "r" & Z %among% "a") | W %among% c("r", "p") & Y %among% "v" & (Y %among% c("v", "x") & W %among% c("q", "p"))) & (Y %among% c("v", "x") & W %among% "r" | (Z %among% c("y", "a") | W %among% c("r", "q")) | (X %among% c("s", "u") | Z %among% "y" | (X %among% "t" | X %among% "s"))) & ((X %among% c("u", "s") | Y %among% "w") & (Z %among% c("z", "y") | Y %among% c("w", "x")) & (Y %among% c("w", "v") & X %among% c("u", "s") & (W %among% "r" | X %among% c("s", "u"))) | ((X %among% "s" | Z %among% c("a", "y")) & (Y %among% c("x", "w") | Z %among% c("a", "z")) | X %among% "t" & W %among% c("r", "p") & (W %among% "p" & X %among% c("u", "t")))) | (W %among% c("p", "r") & Y %among% "w" & (X %among% "s" & X %among% "t") | W %among% "p" & Z %among% c("z", "y") & (W %among% c("p", "q" ) & Y %among% c("w", "v")) | (X %among% "t" | W %among% "p" | Y %among% "v" & Z %among% "a") & ((W %among% c("q", "p") | Y %among% "v") & (Y %among% c("x", "v") & Z %among% "a"))) & (W %among% "r" & X %among% "u" | (W %among% "q" | X %among% "s") | W %among% c("p", "q") & W %among% "p" & (W %among% "q" & W %among% "q") | (X %among% c("u", "t") & Z %among% "y" | Z %among% c("z", "y") & Y %among% "w" | W %among% c("r", "p") & W %among% c("r", "q") & (X %among% c("u", "t") & W %among% "p"))) & ((Z %among% c("z", "y") | W %among% c("q", "p") | (W %among% c("p", "r") | Y %among% "v") | (Z %among% "z" & W %among% c("q", "r") | Y %among% c("w", "x") & W %among% "p") | ((Z %among% c("y", "z") | W %among% "p") & (W %among% "p" | X %among% "t") | (Z %among% "y" | Z %among% "z" | Y %among% "x" & Y %among% "w"))) & ((Z %among% c("y", "a") | X %among% "t" | (W %among% c("p", "r") | X %among% c("t", "u"))) & (X %among% "t" & W %among% "p" & (W %among% c("q", "r") | Y %among% "w")) & (Z %among% "a" & W %among% "p" & (X %among% c("s", "t") | X %among% c("s", "u")) & (W %among% "p" & W %among% c("p", "r") | (W %among% c("p", "r") | W %among% c("p", "r"))))))) & (((Z %among% c("z", "y") & W %among% "q" | (Z %among% c("z", "y") | Y %among% "v")) & (Z %among% "a" | W %among% c("q", "p") | Z %among% c("y", "a") & Y %among% c("w", "x")) & (Y %among% "x" & Y %among% c("v", "x") & (W %among% "p" | Z %among% "z") | Z %among% "z" & Z %among% c("y", "z") & (Y %among% "w" & W %among% c("p", "r"))) | (Y %among% "v" | X %among% c("u", "s")) & (Z %among% "y" & Y %among% "v") & (Y %among% c("v", "x") & X %among% c("u", "s") | (X %among% "t" | Y %among% "w")) & ((Z %among% c("a", "z") | W %among% "q") & (Z %among% "y" | Z %among% "z") | Z %among% "a" & Z %among% "a" & (W %among% "q" | X %among% c("s", "t")))) & ((Y %among% "v" | X %among% "u" | Z %among% "a" & Z %among% c("z", "a")) & (W %among% c("p", "r") | Z %among% c("z", "y") | (X %among% c("t", "u") | Y %among% c("x", "v"))) & (Z %among% "a" | Y %among% "w" | X %among% c("t", "u") & W %among% c("p", "q") | Z %among% c("a", "y") & Y %among% "w" & (Z %among% "z" | Y %among% "w")) & ((Z %among% c("y", "z") & W %among% "q" | (X %among% c("u", "t") | X %among% c("s", "u"))) & ((Y %among% "v" | Z %among% c("z", "y")) & (W %among% c("q", "r") & Y %among% c("x", "v"))) & ((Y %among% "x" | Z %among% "y") & (W %among% c("r", "q") | W %among% "p") & (W %among% c("q", "r") & Y %among% "w" | (Z %among% "z" | X %among% "t"))))) | (Y %among% "w" | W %among% c("p", "r") | (Z %among% c("a", "y") | X %among% c("s", "u")) | (X %among% "s" | W %among% c("p", "r")) & (Y %among% c("v", "w") | Y %among% "v") | (W %among% "r" & X %among% "s" | (W %among% c("r", "q") | W %among% "q")) & (Y %among% c("v", "x") & Z %among% "a" | (W %among% "q" | Y %among% "w")) | (W %among% "p" & Y %among% c("v", "x") & (Y %among% "x" | W %among% "p") | (X %among% c("u", "s") | Y %among% "x") & (X %among% "s" & Z %among% "a") | (Z %among% c("z", "a") | X %among% c("t", "s")) & (Y %among% "v" | W %among% c("r", "q")) & (X %among% c("u", "t") & Z %among% "z" & (W %among% c("q", "p") & W %among% "p")))) & (((Z %among% "a" & X %among% c("s", "t") | (X %among% "t" | Z %among% "z")) & (Y %among% "x" & X %among% "t" & (Z %among% c("y", "a") | Y %among% c("w", "x"))) | (Z %among% "y" | Z %among% "z") & (W %among% "p" & X %among% "u") & ((Z %among% "a" | Z %among% "y") & (X %among% c("s", "t") | Y %among% c("x", "v")))) & ((X %among% c("u", "s") & Z %among% "y" | Z %among% "y" & Y %among% "x" | (Z %among% c("y", "z") & Z %among% c("y", "z") | (W %among% "r" | W %among% c("q", "p")))) & ((X %among% c("u", "s") & Z %among% c("z", "a") | (Z %among% "z" | Z %among% c("z", "a"))) & (Z %among% c("y", "z") | Z %among% "z" | (Y %among% c("w", "v") | X %among% c("s", "u"))))))) | ((Y %among% c("w", "x") | W %among% c("q", "r")) & (Z %among% c("a", "y") | Y %among% "x") & (Z %among% "a" | Z %among% "z" | (W %among% c("r", "q") | Y %among% "x")) & ((W %among% "r" | W %among% "p") & (X %among% "u" | Z %among% c("a", "z")) & (Y %among% "w" & Y %among% c("w", "x") | W %among% "r" & X %among% c("s", "u"))) | ((X %among% c("t", "s") | Y %among% c("x", "v")) & (W %among% "p" & X %among% "t") | (W %among% "q" | Y %among% "x" | (W %among% "r" | W %among% c("q", "r"))) | (Y %among% "v" | Z %among% "a" | Z %among% c("y", "z") & X %among% c("u", "s")) & (Z %among% "a" & Z %among% c("y", "z") & (Y %among% c("v", "w") & W %among% "p")))) & ((X %among% c("t", "s") & W %among% c("p", "r") & (W %among% "q" | Z %among% c("z", "y")) & (Y %among% "w" & W %among% c("q", "r") | Y %among% "x" & W %among% "p") | (Z %among% 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(Z %among% c("a", "z") | X %among% c("u", "t") | Z %among% "z" & X %among% "t") & (W %among% c("r", "p") & X %among% "u" | X %among% c("t", "s") & X %among% c("s", "t"))) | ((W %among% c("p", "q") | W %among% c("q", "p")) & (W %among% c("p", "r") | W %among% c("r", "p")) & (X %among% "t" & W %among% "p" | (Z %among% "a" | Z %among% "a")) | (W %among% "r" & Y %among% "x" & (Y %among% "v" & Z %among% "z") | (W %among% c("r", "p") | Z %among% "a" | Y %among% "v" & X %among% "s"))) & ((Z %among% "y" | X %among% c("s", "t")) & (Z %among% "a" & Y %among% "x") & (X %among% c("s", "t") & Z %among% c("y", "z") | Y %among% "v" & Z %among% c("y", "z")) | (Z %among% c("a", "y") | X %among% "t" | (W %among% "q" | Z %among% c("y", "z"))) & (Y %among% c("v", "x") & Y %among% c("x", "v") | (Z %among% "z" | Y %among% "v")))) & ((Z %among% c("z", "y") & Z %among% c("z", "y" ) & (W %among% "r" & Y %among% c("x", "w")) | (X %among% c("s", "t") | W %among% "q") & (W %among% "r" & W %among% c("p", "q"))) & 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"t"))) | (Z %among% "z" | X %among% "t" | (W %among% "q" | Y %among% "w") | Y %among% c("w", "x") & Y %among% c("x", "v") & (Y %among% c("x", "v") & X %among% c("s", "t")))) & ((W %among% "p" | Z %among% c("y", "z")) & (Z %among% c("z", "y") & Y %among% c("x", "v")) & (Z %among% c("a", "y") & Z %among% "a" & (W %among% c("p", "r") & Y %among% c("v", "x"))) & ((Y %among% "w" | X %among% "s") & (W %among% c("r", "p") & Z %among% c("a", "z")) & (Z %among% c("a", "z") | X %among% c("s", "t") | Y %among% "w" & W %among% "q"))))) -(W %among% c("p", "r") | X %among% c("s", "t") | (W %among% c("p", "q") | Y %among% c("w", "x")) | (W %among% "r" | Y %among% c("v", "x")) & (W %among% c("r", "p") & Y %among% c("x", "w")) | (X %among% "s" & Y %among% "v" | Y %among% "x" & X %among% "u") & (Z %among% c("a", "z") & Z %among% c("z", "y") | (Z %among% c("y", "a") | X %among% "u")) | ((W %among% "p" | Z %among% "a" | (Z %among% c("y", "a") | Z %among% c("a", "y"))) & ((Z %among% "a" | Z %among% c("y", "z")) & (X %among% "s" | Z %among% c("z", "y"))) | ((X %among% "s" | Z %among% "a") & (Y %among% c("x", "w") & W %among% c("r", "q")) | (Y %among% "w" | W %among% "r" | (Y %among% "v" | W %among% c("p", "r")))))) & ((Z %among% "z" | X %among% "t" | (Z %among% "z" | W %among% "r") | X %among% "u" & X %among% "u" & (W %among% "q" & W %among% c("q", "p"))) & ((Y %among% c("x", "v") & W %among% c("p", "q") | (X %among% "t" | Y %among% c("v", "w"))) & (Z %among% "y" & Y %among% c("w", "x") | Z %among% c("a", "z") & X %among% "t")) & ((W %among% c("p", "q") | X %among% c("t", "u")) & (X %among% c("t", "s") | W %among% "r") & (X %among% c("s", "u") & W %among% c("q", "r") & (Z %among% "a" | Y %among% "v")) | W %among% "p" & W %among% c("q", "r") & (X %among% "s" | X %among% c("s", "u")) & (Z %among% "z" | Y %among% "v" | (Y %among% c("x", "w") | W %among% "r")))) | Y %among% c("v", "x") & X %among% "s" & (X %among% "u" & Y %among% c("x", "w")) & ((X %among% "u" | X %among% "t") & (W %among% c("p", "r") | Z %among% "z")) & (X %among% "u" & W %among% c("r", "p") & (Y %among% c("w", "v") | W %among% c("r", "q")) & (Z %among% c("z", "y") | Z %among% "a" | W %among% "p" & Y %among% "v")) & ((X %among% "u" | W %among% c("q", "p")) & (X %among% c("u", "t") | Z %among% "y") & (Z %among% c("a", "z") & W %among% "r" | X %among% "t" & Z %among% c("y", "a")) & (Y %among% c("v", "x") & Z %among% "a" & (W %among% c("p", "q") & W %among% "q") | (Y %among% "w" & Y %among% "w" | (Y %among% "w" | Y %among% c("v", "x"))))) & ((Z %among% "z" | Z %among% c("a", "y") | Y %among% c("x", "w") & W %among% c("q", "p") | (Y %among% "v" | X %among% "s") & (X %among% c("u", "t") | X %among% "u")) & ((Z %among% c("y", "z") | X %among% "t" | (W %among% c("q", "r") | W %among% "q")) & (Z %among% c("z", "y") & W %among% "p" | Y %among% c("w", "x") & Y %among% c("w", "v"))) & ((Z %among% "a" & W %among% c("p", "q") & (X %among% "u" | W %among% c("p", "r")) | (Z %among% c("y", "a") | Z %among% c("a", "z") | (Z %among% "z" | W %among% c("q", "p")))) & (Y %among% "x" & Y %among% "v" & (W %among% c("q", "p") | Y %among% "w") | Z %among% "y" & X %among% c("u", "t") & (X %among% c("t", "s") | W %among% "r")))) | ((X %among% "s" & X %among% "t" & (W %among% c("q", "r") & X %among% "s") | (Y %among% c("v", "w") & X %among% "u" | Z %among% c("a", "y") & W %among% c("r", "q"))) & (X %among% "u" | Z %among% "z" | Y %among% "v" & X %among% c("s", "u") | (Z %among% c("a", "z") & W %among% c("q", "p") | X %among% c("t", "s") & Y %among% c("v", "x" ))) | (W %among% "r" | X %among% c("s", "t") | Z %among% "a" & Z %among% c("z", "y") | (W %among% c("p", "q") | W %among% c("q", "p") | (X %among% c("t", "u") | Z %among% "a"))) & ((X %among% "u" | Z %among% c("a", "z")) & (Z %among% c("a", "z") & Y %among% c("x", "w")) & (Y %among% "x" | W %among% "r" | Y %among% "v" & Y %among% "w")) | (((Z %among% "y" | Z %among% "z") & (X %among% c("u", "t") & Z %among% "z") | Y %among% c("x", "v") & X %among% "s" & (X 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c("v", "x") & Z %among% c("a", "y" )) | Y %among% "w" & W %among% c("q", "p") & (Y %among% "x" | X %among% c("s", "t")) & ((Y %among% c("x", "v") | W %among% "q") & (W %among% c("p", "q") | W %among% c("p", "r")))) | ((Y %among% "w" | X %among% "t") & (Z %among% "y" & Y %among% c("w", "x")) | (X %among% "t" & Z %among% "a" | Z %among% c("a", "z") & X %among% "t") | (W %among% c("r", "q") | W %among% c("p", "q")) & (X %among% "u" & W %among% c("p", "r")) & ((Y %among% "v" | W %among% c("p", "r")) & (Z %among% c("a", "y") & Y %among% "v")) | Z %among% "y" & X %among% c("t", "s") & (Z %among% c("a", "y") | Y %among% c("x", "w")) & ((X %among% "u" | X %among% c("u", "t")) & (Y %among% c("w", "v") & Z %among% c("a", "z"))) & ((Z %among% "z" & X %among% c("u", "t") | W %among% c("q", "p") & Y %among% "x") & (W %among% "q" & Z %among% "a" | (W %among% "r" | W %among% "p"))))) -((Z %among% "a" | X %among% "t") & (X %among% c("s", "t") | X %among% c("s", "u")) | (W %among% "p" | X %among% "t") & (W %among% c("q", "p") & Z %among% "y") | Z %among% "a" & Z %among% c("a", "y") & (Z %among% "y" & Y %among% c("v", "w")) & (Z %among% c("y", "a") & Y %among% c("x", "v") & (Z %among% c("a", "z") & Y %among% c("w", "v"))) | ((Y %among% "w" | X %among% c("s", "u")) & (W %among% "r" & Y %among% "x") | (X %among% c("s", "u") | X %among% c("s", "t")) & (X %among% c("s", "t") & Y %among% "w") | (Z %among% c("y", "a") | W %among% c("p", "q")) & (Y %among% c("x", "w") | X %among% c("u", "s")) & ((X %among% c("s", "u") | Y %among% c("v", "x")) & (W %among% "r" | Y %among% "x"))) | (W %among% "q" & W %among% "q" & (Z %among% "a" | W %among% "r") | (X %among% "s" & Y %among% c("x", "w") | Y %among% c("w", "v") & X %among% "t")) & ((Z %among% c("z", "y") & Y %among% "x" | (W %among% "q" | W %among% "r")) & (Z %among% c("z", "a") & Z %among% "z" | X %among% "u" & X %among% "t")) & ((Z %among% c("y", "z") | X %among% c("s", "t")) & (Z %among% c("z", "a") & Y %among% c("x", "w")) | (W %among% "q" 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& ((W %among% "r" | Z %among% "y" | X %among% c("u", "s") & X %among% "u") & ((X %among% c("t", "u") | Z %among% "a") & (Y %among% c("x", "w") | X %among% c("t", "s"))) & ((Y %among% "v" | X %among% "t") & (Z %among% "a" | Y %among% "x") | (W %among% "r" | W %among% c("p", "r")) & (W %among% c("p", "q") | X %among% "u")) & ((W %among% "p" | X %among% "t") & (Y %among% c("v", "w") & Y %among% "w") | (Z %among% "z" | Z %among% c("a", "z") | (Y %among% "x" | W %among% "p")) | (Y %among% c("v", "x") | W %among% "p" | W %among% c("q", "p") & X %among% c("u", "s")) & (Y %among% c("x", "w") & Z %among% "z" & (W %among% "q" & W %among% c("q", "r"))))) | ((Z %among% "y" | Y %among% "x" | (W %among% c("r", "q") | W %among% "r")) & (Z %among% c("y", "z") & Z %among% "a" | X %among% "s" & Z %among% "y") & (Y %among% c("w", "v") & W %among% "q" & (Z %among% c("z", "y") | X %among% "t") | Y %among% c("w", "v") & Y %among% "x" & (Y %among% c("v", "w") & Y %among% "v")) | (Y %among% c("x", "w") | Z 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"a")))) & (Z %among% "a" & X %among% c("s", "t") & (Z %among% c("a", "z") & Z %among% c("z", "a")) & (X %among% "u" & W %among% "q" & (Y %among% "x" & Z %among% c("a", "z"))) & ((W %among% c("p", "r") | W %among% c("r", "p")) & (Y %among% c("w", "x") & X %among% c("s", "u")) | (X %among% "u" | X %among% "s") & (Y %among% "v" | X %among% "t")) & ((W %among% "q" | X %among% "s" | Y %among% c("v", "x") & X %among% c("t", "u")) & (W %among% c("p", "q") & Y %among% c("w", "v") & (X %among% c("t", "u") | X %among% "t")) & (W %among% c("r", "p") & X %among% "s" | (Z %among% "y" | X %among% "s") | (W %among% c("p", "r") & Z %among% "a" | (Y %among% "x" | X %among% "t"))))) | (X %among% "s" & Z %among% "a" & (Y %among% "w" & W %among% c("r", "p")) | (Z %among% "a" | Y %among% c("x", "v") | Z %among% "y" & W %among% c("r", "p"))) & ((Y %among% c("v", "x") & W %among% "p" | Z %among% c("y", "z") & W %among% c("p", "r")) & (X %among% "u" | Y %among% c("x", "w") | (X %among% "t" | Y %among% "x"))) 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"w") & Y %among% c("v", "w") | W %among% c("q", "r") & Y %among% "x")) & (((X %among% "s" | Y %among% "v") & (Y %among% "x" | Z %among% "z") | (W %among% "p" | Z %among% c("a", "z") | Z %among% "a" & Y %among% "v")) & (Z %among% c("y", "a") & Y %among% "w" & (Z %among% "a" & Y %among% "v") | (Z %among% c("z", "a") | Y %among% "v") & (Z %among% "z" | W %among% c("r", "q"))))) & (X %among% "u" & Z %among% c("z", "y") & (X %among% "t" & X %among% "t") | (W %among% c("r", "p") | W %among% "p" | (Y %among% "w" | W %among% "q")) | Z %among% c("z", "y") & X %among% "s" & (Z %among% "y" & Y %among% "v") & (Y %among% c("v", "x") | Z %among% c("z", "y") | (Y %among% c("v", "x") | Z %among% "y")) | (Z %among% "y" & W %among% "r" | Y %among% "x" & W %among% c("p", "r")) & (Y %among% "x" & Y %among% "w" & (W %among% "r" & Z %among% c("z", "a"))) & ((W %among% c("r", "q") | W %among% c("q", "r")) & (Y %among% "w" & Z %among% "z") | (Y %among% "v" | W %among% c("q", "r") | (Y %among% "x" | W %among% 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%among% "q") & (Z %among% "z" | W %among% c("r", "q")))) & ((W %among% "p" | X %among% "t" | (W %among% c("p", "q") | X %among% "u")) & (X %among% c("s", "u") | Z %among% c("a", "z") | (W %among% c("p", "q") | Z %among% c("a", "z"))) | (W %among% "p" & W %among% c("q", "r") | Z %among% "y" & Z %among% "y") & (X %among% "s" & Y %among% "v" | (W %among% c("r", "p") | W %among% "r"))) | ((X %among% "u" | X %among% "u") & (Z %among% c("z", "a") | W %among% "q") & (W %among% "r" | Z %among% c("z", "a") | Y %among% c("w", "v") & Z %among% c("a", "z")) | (W %among% "r" & Y %among% c("v", "w") | (X %among% c("s", "t") | X %among% c("u", "t")) | (Y %among% "w" & X %among% "u" | (Z %among% "y" | Z %among% c("z", "y"))))) & ((W %among% "q" & X %among% c("t", "s") & (Y %among% c("w", "x") & Z %among% c("z", "a")) | (Y %among% "w" | Z %among% "y") & (X %among% c("u", "t") & Z %among% "y")) & ((Z %among% c("a", "y") & Y %among% "x" | (X %among% c("t", "s") | X %among% "t")) & (Z %among% c("a", "y") & Y %among% "x" & (Y %among% "v" & W %among% "p"))))) & (((Z %among% "z" | Z %among% c("z", "a")) & (Y %among% c("w", "x") & Y %among% c("w", "v")) | (Y %among% "x" | Y %among% "v") & (Y %among% c("w", "x") | Y %among% "w")) & (W %among% "p" & Y %among% "w" & (W %among% "r" & W %among% c("r", "q")) | (Z %among% "z" | X %among% "t" | W %among% c("p", "q") & W %among% "r")) & ((W %among% "q" | Y %among% c("w", "v")) & (X %among% "u" & W %among% "p") | (Z %among% c("y", "z") | Y %among% "w") & (Z %among% "z" & W %among% "q") | (Z %among% "y" | Z %among% "y" | Y %among% "x" & Z %among% c("a", "y") | Z %among% c("y", "z") & X %among% c("s", "t") & (Y %among% "x" | Y %among% c("x", "v")))) & (((Z %among% c("y", "a") | W %among% "r") & (Y %among% "x" | X %among% c("t", "u")) | (X %among% c("t", "s") & W %among% "p" | Y %among% c("w", "v") & Z %among% "a") | (X %among% "t" | Y %among% c("x", "w") | (X %among% "t" | Y %among% "v")) & ((Z %among% c("y", "a") | X %among% "t") & (W %among% "q" & Z %among% "a"))) & ((W %among% c("r", "q") | W %among% c("r", "q")) & (W %among% "p" & W %among% "q") | (X %among% c("u", "s") | Y %among% "w") & (X %among% "t" | W %among% "p") | Y %among% "x" & Z %among% "z" & (Z %among% "a" & X %among% c("s", "u")) & (W %among% c("r", "q") & X %among% c("u", "t") | Z %among% c("y", "z") & X %among% c("s", "u")))))) -(W %among% c("p", "q") | W %among% "p" | (Z %among% c("z", "a") | Z %among% "z") | (Y %among% c("w", "x") & W %among% c("p", "r") | Z %among% c("z", "a") & X %among% c("u", "t")) | X %among% "t" & W %among% "p" & (Y %among% c("w", "x") | Z %among% c("y", "a")) & (Z %among% "z" & Z %among% c("y", "a") & (Z %among% "z" | W %among% "q"))) & ((Y %among% "v" | W %among% c("q", "r") | (Y %among% "x" | Z %among% "y") | Z %among% "y" & Z %among% c("z", "a") & (Z %among% c("y", "z") & Y %among% "x")) & ((Y %among% c("v", "w") | Z %among% c("y", "z") | X %among% c("t", "s") & Z %among% "z") & (Y %among% c("x", "v") | W %among% c("r", "p") | W %among% "p" & Y %among% c("x", "v")))) & ((Z %among% c("z", "y") | X %among% c("u", "t") | (W %among% c("q", "r") | Z %among% c("y", "z")) | (Y %among% "x" & X %among% c("t", "s") | (X %among% c("u", "s") | Z %among% "z"))) & ((W %among% c("q", "p") | Y %among% c("w", "v")) & (X %among% "u" & X %among% "t") | Y %among% "v" & Z %among% c("y", "z") & (W %among% c("q", "p") & Y %among% c("v", "w"))) & (((Z %among% "z" | W %among% "r") & (Y %among% c("x", "v") | W %among% "p") | (X %among% "s" & W %among% c("r", "p") | Y %among% c("x", "w") & W %among% "q")) & ((W %among% "r" | Y %among% c("v", "x") | Z %among% "z" & Y %among% "x") & (Z %among% "a" & W %among% c("p", "q") | (W %among% "r" | X %among% c("s", "t")))))) | Y %among% c("v", "w") & Y %among% c("w", "v") & (Y %among% c("v", "w") & Y %among% c("v", "w")) & ((X %among% "s" | W %among% "q") & (W %among% "q" | Y %among% "x")) & (X %among% c("u", "t") & X %among% "u" & (X %among% "u" | W %among% "r") & ((Z %among% c("z", "a") | Y %among% c("w", "v")) & (Y %among% c("x", "v") & Z %among% "z"))) & (W %among% "p" | Z %among% c("a", "z") | Z %among% "a" & X %among% c("s", "u") | W %among% "r" & X %among% c("u", "s") & (Z %among% "y" | Z %among% "z") | (Z %among% c("y", "a") | X %among% c("s", "u") | (X %among% "u" | Y %among% c("w", "v")) | (W %among% "r" | Z %among% "a" | (W %among% c("p", "r") | W %among% "r")))) & (Y %among% "v" & W %among% "q" | Z %among% c("y", "a") & X %among% c("u", "t") | (X %among% "s" | Y %among% "v" | (X %among% "t" | W %among% "q")) | (X %among% c("t", "u") & X %among% c("u", "t") | (Y %among% c("v", "x") | Y %among% c("w", "v")) | (Z %among% "y" | X %among% "t" | (W %among% "p" | X %among% c("t", "u")))) | ((Y %among% c("x", "w") | Y %among% "v") & (W %among% c("p", "q") | Y %among% c("v", "w")) | (Y %among% "v" | X %among% "s") & (X %among% "u" & W %among% c("p", "q" ))) & ((Z %among% "a" & W %among% "r" | X %among% c("t", "u") & X %among% c("t", "u")) & (Y %among% "v" & X %among% "t" | (Y %among% c("v", "w") | W %among% c("p", "q"))))) -(W %among% "q" & X %among% "s" & (Y %among% c("x", "v") & W %among% c("p", "r")) & (Z %among% c("z", "y") & W %among% c("p", "r") | (X %among% "t" | X %among% c("t", "s"))) & ((Y %among% c("w", "x") | Z %among% c("y", "a")) & (Y %among% "x" & Y %among% "x") & (W %among% c("r", "p") & W %among% "q" | (X %among% c("s", "t") | W %among% "r"))) & ((Y %among% c("v", "w") & X %among% "u" & (Z %among% "a" | Z %among% c("y", "z")) | (Z %among% c("z", "y") | Z %among% "y" | X %among% c("u", "s") & Y %among% c("w", "x"))) & ((Y %among% c("x", "v") & Y %among% c("x", "w") | (Z %among% c("a", "z") | W %among% c("q", "r"))) & (X %among% "u" | Z %among% "y" | (Z %among% c("a", "y") | X %among% "s")))) & (((W %among% "r" | Z %among% c("a", "y") | W %among% "p" & W %among% c("r", "q")) & (Z %among% "z" | W %among% c("r", "q") | Z %among% "a" & Y %among% "v") | (X %among% "u" | Z %among% c("z", "y") | (W %among% c("r", "p") | W %among% c("q", "p"))) & (Z %among% c("a", "y") & Z %among% c("a", "y") & (Y %among% "v" | W %among% "p"))) & (((Y %among% c("v", "x") | W %among% "r") & (X %among% c("s", "t") | X %among% c("t", "s")) | (Y %among% c("v", "x") | W %among% c("q", "p")) & (Y %among% c("x", "w") & Z %among% "z")) & (Z %among% c("y", "z") & Z %among% "z" | (X %among% "u" | X %among% c("t", "u")) | X %among% "s" & W %among% c("q", "r") & (Y %among% c("x", "w") | X %among% "s")))) | ((W %among% "q" & Z %among% c("y", "z") | (Z %among% "a" | Y %among% c("w", "v")) | (X %among% c("t", "s") & Z %among% c("a", "z") | Y %among% "x" & Y %among% c("x", "v")) | (Y %among% "v" & Z %among% "a" | (Z %among% "a" | W %among% "q")) & (Z %among% "y" & Y %among% c("v", "w") & (X %among% c("s", "u") & Z %among% "z"))) & ((W %among% c("q", "p") | Z %among% c("a", "z") | X %among% c("t", "s") & W %among% c("q", "r") | (W %among% "r" | Y %among% c("x", "w") | Z %among% c("a", "y") & X %among% c("s", "u"))) & ((X %among% c("t", "s") | X %among% "s" | (Y %among% c("v", "w") | W %among% c("q", "r"))) & ((Z %among% "y" | Z %among% "z") & (W %among% "r" | X %among% "s")))) | (Y %among% "x" & Z %among% "y" & (Y %among% c("w", "x") | X %among% "u") & (X %among% "u" & X %among% c("u", "t") | X %among% "u" & Y %among% c("w", "v")) & (Y %among% c("v", "w") & Z %among% "z" & (Y %among% "w" | X %among% "s") | (Y %among% c("x", "v") & X %among% "u" | (Y %among% c("x", "w") | Y %among% "v"))) | (Y %among% "w" & Z %among% c("a", "y") & (Y %among% c("w", "x") & X %among% c("u", "t")) | Y %among% c("w", "x") & W %among% "q" & (X %among% "t" | X %among% c("s", "t"))) & ((Y %among% "x" | Z %among% "z") & (Z %among% "a" | W %among% "p") & (W %among% "r" & W %among% c("r", "q") | Z %among% "z" & Y %among% "w"))))) & ((Z %among% "y" & W %among% c("r", "p") & (Z %among% "z" & X %among% "u") | (Z %among% "y" | W %among% c("q", "p")) & (X %among% c("u", "s") | Y %among% c("v", "x"))) & ((Z %among% c("z", "y") | X %among% c("s", "u")) & (Y %among% "v" & W 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& (Z %among% "a" & W %among% "r" & (W %among% "r" | Z %among% c("a", "y"))) | (X %among% "u" & Z %among% "z" | X %among% c("u", "t") & Z %among% "z" | (Y %among% "v" | X %among% c("t", "s") | (Z %among% c("a", "z") | Y %among% "v")))))) | ((W %among% "r" | Z %among% c("a", "z")) & (Y %among% "x" | Y %among% "w") & (W %among% c("r", "p") & Z %among% "y" | (W %among% "p" | Z %among% "y")) | (Y %among% c("w", "x") & X %among% c("s", "t") | X %among% c("t", "s") & W %among% c("q", "r")) & (W %among% c("p", "r") & X %among% "u" & (Y %among% c("w", "v") & Z %among% c("z", "y" ))) | ((W %among% "r" | W %among% c("p", "r")) & (X %among% "t" | W %among% c("q", "p")) & (Z %among% c("y", "z") | X %among% "u" | Y %among% c("w", "v") & W %among% "r") | ((Y %among% "w" | Z %among% "a") & (X %among% "s" & Z %among% c("z", "y")) | (X %among% c("s", "u") | Z %among% c("z", "a")) & (Z %among% c("a", "y") & W %among% c("q", "p"))))) & (X %among% c("t", "u") & Z %among% "z" & (X %among% c("s", "u") & W 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c("u", "s") & Z %among% "z" | (W %among% c("p", "q") | X %among% "t") & (W %among% c("p", "r" ) & Z %among% c("a", "y"))) & ((W %among% "p" | X %among% c("t", "s") | (W %among% "q" | Y %among% "x")) & (W %among% c("p", "r") & W %among% c("p", "q") & (X %among% "u" & Y %among% c("x", "w")))) | (Z %among% "y" & X %among% "t" & (Z %among% c("z", "a") | Z %among% "a") & (X %among% "u" & Y %among% c("x", "w") | (W %among% c("p", "q") | X %among% c("u", "t"))) | (W %among% "p" & Z %among% "z" & (Z %among% c("y", "a") & Z %among% c("y", "a")) | W %among% c("r", "p") & Y %among% "w" & (Z %among% c("a", "z") & Z %among% "y"))) & ((X %among% c("s", "t") | W %among% c("r", "q")) & (Y %among% "x" | X %among% "t") | (W %among% "r" | X %among% "t") & (W %among% "p" & Z %among% c("a", "y")) | Z %among% "a" & W %among% c("p", "r") & (Y %among% "x" | X %among% "u") & ((X %among% c("s", "t") | Z %among% c("y", "z")) & (Z %among% "a" | X %among% "u")))) -(Y %among% c("w", "x") | W %among% "q" | X %among% 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| (Z %among% c("z", "y") | W %among% "q")) & (Z %among% "y" & Z %among% c("z", "a") | X %among% c("u", "t") & Y %among% "w" | (Z %among% "z" & Z %among% c("a", "z") | (W %among% c("p", "r") | X %among% c("s", "u")))) & (Z %among% c("y", "z") & Y %among% c("x", "w") & (Y %among% "w" | X %among% c("t", "s")) | (X %among% c("t", "u") | W %among% "q") & (Y %among% "x" & X %among% "t") | (W %among% c("r", "q") | Z %among% "y") & (W %among% c("p", "r") & Y %among% c("x", "w")) & (X %among% c("u", "t") | W %among% c("q", "p") | W %among% "q" & Y %among% "w")))) -((Y %among% c("v", "x") & X %among% "t" | Y %among% "v" & Y %among% c("x", "w") | Z %among% "y" & W %among% c("r", "q") & (W %among% "p" | X %among% c("t", "u")) | (W %among% "q" & X %among% "s" | Z %among% c("y", "z") & Z %among% c("y", "a") | (Z %among% "a" & Y %among% c("w", "v") | (Y %among% c("v", "w") | W %among% "r")))) & (Y %among% c("x", "w") & Y %among% c("v", "x") & (Z %among% c("a", "y") & Z %among% "a") | (Z %among% "y" | 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%among% "w" | Z %among% "a" | Z %among% "y" & Z %among% "y" | (Y %among% c("w", "x") & Y %among% "x" | Y %among% "w" & X %among% c("t", "u")))) & ((Y %among% "x" | X %among% c("u", "t") | (Z %among% c("a", "z") | Z %among% c("a", "y"))) & ((Z %among% "z" | W %among% "r") & (Y %among% c("x", "w") & Y %among% c("x", "w"))) & (Y %among% "w" & Y %among% c("v", "w") | Y %among% c("w", "v") & Y %among% c("w", "x") | (Z %among% "y" | W %among% c("q", "r") | (Z %among% c("a", "z") | Y %among% "v")))))) & ((Z %among% c("a", "y") & Y %among% "w" & (Y %among% c("x", "v") & X %among% "t") & (W %among% c("p", "q") | W %among% "q" | (X %among% "s" | W %among% "r")) | (X %among% c("s", "u") | W %among% "p") & (Y %among% c("w", "x") & X %among% c("t", "u")) & (Y %among% "x" & X %among% c("s", "u") | (W %among% "q" | W %among% "p"))) & (W %among% "r" & Z %among% c("a", "y") | (X %among% c("s", "u") | Y %among% c("x", "w")) | (Z %among% "z" | Y %among% "v") & (X %among% "s" | Y %among% "x") | ((Y 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"v")) | (X %among% c("t", "u") & Z %among% "a" & (W %among% "q" & Z %among% c("y", "a")) | (W %among% c("q", "r") | Z %among% c("a", "y")) & (Y %among% "w" | W %among% "r")) | (W %among% "r" & Z %among% c("y", "a") | (Z %among% c("y", "a") | W %among% c("r", "q")) | (Y %among% "w" | Y %among% "w") & (Y %among% c("x", "v") & W %among% "p") | (Y %among% c("x", "v") & X %among% "t" | (Z %among% c("y", "a") | X %among% c("t", "u"))) & ((X %among% "s" | Y %among% "x") & (W %among% "r" & X %among% c("u", "s"))))))) -(Z %among% "a" & Y %among% "v" & (Z %among% "y" & X %among% "t") & (X %among% c("t", "s") | Z %among% "z" | (Z %among% "a" | X %among% c("t", "u"))) | ((X %among% "s" | Y %among% c("w", "x")) & (X %among% "t" | X %among% "s") | (Z %among% "y" | W %among% "q") & (Y %among% "w" | W %among% c("q", "r")))) & ((Y %among% c("w", "v") | Y %among% c("w", "v")) & (W %among% "p" | W %among% "r") | (Z %among% c("a", "z") & X %among% c("u", "t") | Z %among% "a" & Z %among% "z") | (X %among% 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%among% c("v", "w") | W %among% c("q", "r") | (X %among% c("s", "u") | Z %among% c("z", "a")) | (X %among% c("t", "u") | X %among% "s") & (Z %among% "y" & X %among% c("s", "t")) | (Y %among% c("x", "v") | X %among% "s" | X %among% c("s", "t") & W %among% "q") & (Y %among% "v" | X %among% "t" | Y %among% "x" & Z %among% "z")) | ((X %among% "u" & X %among% c("s", "t") | Z %among% c("a", "y") & X %among% c("u", "s")) & (Y %among% c("v", "x") & Y %among% c("x", "v") | W %among% "p" & W %among% "p") | (Y %among% "w" & W %among% c("r", "p") & (Z %among% c("y", "z") | Z %among% "z") | (Z %among% "a" | W %among% c("r", "q")) & (X %among% c("s", "t") | Y %among% c("w", "x")))) & ((X %among% "s" & Z %among% "y" | (Y %among% c("w", "x") | Z %among% c("z", "a")) | (W %among% "r" | X %among% "u" | W %among% c("q", "p") & Z %among% "z")) & (W %among% "r" & Z %among% c("y", "a") & (Z %among% c("a", "y") & Z %among% c("z", "a")) & (Y %among% c("v", "x") | W %among% c("p", "q") | X %among% c("u", "s") & W %among% c("q", "r")))))) & (((W %among% "p" | Y %among% "x") & (X %among% "t" | X %among% "u") & (W %among% "p" | Y %among% c("w", "v") | X %among% c("s", "t") & Z %among% c("y", "z")) & (W %among% c("q", "p") & Z %among% c("y", "z") | (Z %among% c("a", "z") | Y %among% "w") | (Z %among% c("y", "a") & X %among% "s" | (W %among% "q" | Z %among% "z"))) | (W %among% "p" & X %among% c("s", "u") | X %among% c("u", "t") & X %among% "t" | (Z %among% "a" & Y %among% c("w", "x") | X %among% "u" & X %among% "u")) & (W %among% "p" & X %among% c("u", "s") & (Z %among% "z" | W %among% "r") | Y %among% c("x", "v") & Y %among% "x" & (X %among% c("s", "u") & Z %among% "a"))) & ((X %among% c("s", "t") & Y %among% "v" | Y %among% c("v", "x") & X %among% c("s", "t")) & ((W %among% c("p", "q") | Y %among% c("x", "w")) & (X %among% "t" & X %among% c("t", "u"))) | (W %among% "r" | Z %among% c("a", "y") | W %among% "q" & Y %among% "w") & (Y %among% "w" | X %among% "s" | Z %among% "a" & Z %among% "a") | 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"s" & Z %among% c("a", "y")))) | (Z %among% c("a", "y") & X %among% "t" | (X %among% "u" | W %among% c("r", "q"))) & (X %among% "t" & Y %among% "x" | Y %among% c("x", "w") & Z %among% "z") & (W %among% c("r", "q") & W %among% c("q", "r") & (X %among% c("s", "u") | W %among% "r") & (X %among% c("s", "u") & Y %among% "w" | W %among% c("q", "p") & W %among% "p")) & (X %among% "s" | W %among% c("p", "r") | X %among% c("t", "s") & Y %among% c("x", "w") | (Y %among% c("v", "x") | Y %among% c("v", "w") | (W %among% "p" | W %among% "p")) | (Y %among% "v" & Z %among% "y" & (X %among% "t" | X %among% "t") | (W %among% c("r", "q") | Y %among% c("x", "v")) & (X %among% c("u", "s") & Y %among% "x")))))) -((X %among% "t" | Y %among% c("w", "v") | Y %among% "v" & W %among% "p" | (W %among% "q" & Y %among% c("x", "v") | (Z %among% "y" | X %among% c("s", "t"))) | (X %among% "t" | Y %among% c("w", "v")) & (Y %among% "w" & Z %among% "z") & (Z %among% c("a", "z") & X %among% c("s", "t") | Z %among% "z" & 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& ((((X %among% "s" | X %among% c("s", "t")) & (Y %among% "w" | Z %among% c("a", "y")) | (X %among% c("u", "s") & Z %among% c("z", "a") | W %among% "q" & W %among% "q")) & (X %among% "u" & Z %among% c("a", "z") & (W %among% c("p", "r") | X %among% c("u", "t")) & (Y %among% c("v", "w") & X %among% c("t", "u") | (X %among% "t" | W %among% "p"))) | ((W %among% "r" & Y %among% c("v", "w") | (Y %among% "x" | Z %among% c("z", "a"))) & ((Y %among% c("x", "w") | W %among% c("q", "p")) & (Z %among% "y" & Y %among% "v")) | (Z %among% c("z", "a") & X %among% "t" | Z %among% "y" & Z %among% "a" | (Z %among% c("y", "a") | Y %among% c("x", "v") | X %among% "s" & X %among% "s")))) & ((X %among% "u" | X %among% "t" | (X %among% c("u", "s") | Z %among% "y")) & ((W %among% c("r", "q") | Z %among% "y") & (W %among% c("q", "r") | Y %among% "w")) | (W %among% "p" & W %among% c("q", "r") | Y %among% c("x", "v") & X %among% "t") & (W %among% "q" & X %among% c("t", "s") & (X %among% "t" & W %among% c("q", 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c("z", "y") & W %among% "r" | (Y %among% c("w", "x") | Y %among% "x")) & (W %among% "r" | Z %among% c("z", "a") | Z %among% c("a", "z") & Y %among% c("v", "x")) | (Y %among% c("w", "x") | Z %among% c("y", "a") | Z %among% c("y", "a") & Z %among% c("y", "z")) & (X %among% "s" & Y %among% "v" & (X %among% c("u", "s") & X %among% "s"))) & ((W %among% c("r", "p") & W %among% c("q", "p") | Y %among% "x" & Z %among% c("y", "a")) & ((Z %among% "y" | Y %among% c("x", "w")) & (W %among% c("p", "r") | X %among% c("s", "u"))) & ((W %among% c("p", "r") | W %among% "p") & (W %among% c("r", "q") | W %among% "q") & ((X %among% "t" | Z %among% c("z", "a")) & (W %among% c("p", "q") | W %among% c("r", "p"))))) | (Z %among% c("a", "z") & W %among% c("r", "q") | (Y %among% "x" | W %among% c("p", "q"))) & (X %among% "u" & Y %among% "w" & (Z %among% c("y", "a") & W %among% "r")) & (X %among% c("u", "t") & X %among% c("s", "u") | (X %among% c("u", "t") | Y %among% "x") | (X %among% "u" & W %among% "q" | (Y %among% c("v", "w") | Z %among% "a"))) & (X %among% c("u", "t") | Y %among% c("w", "v") | X %among% "u" & X %among% "u" | (X %among% "u" & Y %among% "w" | (Y %among% "v" | Y %among% c("x", "v"))) | (Y %among% c("x", "v") & X %among% "t" | (Y %among% c("w", "x") | X %among% "s")) & ((Y %among% c("x", "v") | Z %among% "a") & (Z %among% "a" | W %among% "q"))) | ((Y %among% "w" | W %among% "p") & (X %among% c("s", "u") | X %among% c("s", "u")) | Y %among% c("w", "x") & X %among% c("t", "s") & (X %among% c("u", "t") & X %among% c("u", "s"))) & (Y %among% c("x", "w") & W %among% "r" & (Z %among% "a" & Y %among% "w") | (W %among% "p" | X %among% c("t", "s")) & (X %among% c("u", "t") & Z %among% "y")) & ((Y %among% c("x", "v") & W %among% "p" | Y %among% "v" & W %among% c("r", "q") | Y %among% c("w", "v") & X %among% "s" & (W %among% "p" & X %among% c("u", "t"))) & ((X %among% "u" | Z %among% "y" | Z %among% "y" & X %among% "s") & (X %among% c("t", "u") | Z %among% "z" | Y %among% "v" & Y %among% c("w", "v")))) & ((Z %among% "a" & X %among% c("t", "u") & (X %among% c("s", "u") & X %among% "s") & ((X %among% c("u", "t") | Z %among% "z") & (Z %among% "y" & Y %among% "x")) | (Y %among% c("w", "v") | Z %among% "y") & (X %among% "u" & X %among% "s") & ((Y %among% c("w", "x") | Y %among% "v") & (Z %among% c("z", "y") & Y %among% "v"))) & ((W %among% "p" | Z %among% c("z", "a")) & (Y %among% "v" & Y %among% "x") & (W %among% "p" & Y %among% c("x", "v") & (X %among% "u" & X %among% "s")) | (Z %among% c("a", "y") | Z %among% c("a", "y") | W %among% c("r", "q") & Y %among% c("x", "v")) & ((X %among% "t" | W %among% "r") & (W %among% c("r", "q") & Y %among% "x"))))) | ((Y %among% "w" | X %among% c("s", "t")) & (X %among% c("s", "t") | X %among% "t") | (W %among% "q" | W %among% "q") & (Y %among% c("v", "x") & Y %among% "w") | ((W %among% "q" | Z %among% "y") & (Z %among% c("y", "a") & Y %among% c("x", "w")) | (Z %among% c("z", "a") & Y %among% c("x", "v") | W %among% c("q", "r") & W %among% c("r", "p")))) & (Y %among% "w" & X %among% c("s", "t") | (Y %among% c("x", "v") | X %among% "t") | (W %among% "p" | Z %among% "z" | X %among% "s" & W %among% "r") | (Z %among% "a" & Y %among% "v" | W %among% "r" & X %among% c("s", "t")) & (Y %among% c("w", "x") & Z %among% c("z", "a") & (Z %among% "y" & Z %among% c("a", "y")))) & (Z %among% "y" | W %among% "r" | (Z %among% c("z", "y") | Y %among% c("x", "v")) | (X %among% c("t", "s") & W %among% "r" | (X %among% "t" | X %among% "u")) | Y %among% "v" & X %among% "u" & (X %among% c("t", "s") | Y %among% c("w", "x")) & (Y %among% c("x", "v") & Z %among% "z" | Z %among% "y" & W %among% c("q", "r")) | ((W %among% "r" | Y %among% "w" | X %among% "s" & Y %among% c("w", "x")) & (Y %among% "w" | W %among% c("p", "q") | X %among% "t" & X %among% "t") | (Z %among% c("y", "a") & Z %among% c("a", "y") | W %among% "p" & Y %among% c("w", "x")) & ((Y %among% "x" | W %among% "q") & (X %among% c("t", "s") & Y %among% "v")))) & ((Z %among% "y" & Y %among% "w" & (Z %among% c("y", "a") | W %among% c("p", "q")) | (W %among% c("r", "q") | X %among% "t" | Y %among% c("x", "v") & X %among% "s") | (Z %among% c("z", "y") | W %among% "q" | X %among% "u" & W %among% "q" | W %among% "r" & Z %among% "z" & (X %among% "t" & W %among% "q")) | ((Z %among% "z" & W %among% c("p", "q") | (X %among% "s" | W %among% c("p", "r"))) & (Y %among% "v" & X %among% c("t", "u") & (X %among% c("t", "s") | Z %among% c("y", "a"))) | (W %among% "p" | X %among% c("u", "t") | X %among% c("u", "t") & Y %among% c("x", "w") | Y %among% c("w", "x") & W %among% c("q", "p") & (Z %among% c("a", "z") & Z %among% c("z", "a"))))) & (Y %among% "w" | Z %among% "z" | (X %among% "s" | W %among% c("q", "p")) | (Z %among% c("a", "y") | W %among% "q") & (Z %among% c("z", "y") & Y %among% c("v", "w")) | (X %among% "u" & Z %among% "y" & (X %among% "s" | X %among% c("u", "s")) | (Y %among% c("x", "v") | X %among% c("t", "s") | Z %among% c("a", "z") & X %among% c("s", "u"))) | (Z %among% c("a", "y") | W %among% c("p", "q")) & (Y %among% c("v", "x") & Z %among% c("z", "y")) & (Y %among% c("v", "w") & Y %among% "x" & (X %among% "t" & Z %among% "z")) & ((X %among% "u" & W %among% c("r", "p") | (W %among% c("q", "p") | X %among% c("t", "u"))) & (Y %among% "x" & Z %among% "z" | Y %among% c("v", "x") & W %among% "q")))) & ((Y %among% "v" & X %among% "s" | X %among% c("u", "s") & W %among% "q" | Y %among% c("w", "v") & W %among% c("p", "r") & (W %among% "p" | Y %among% "v")) & ((Y %among% c("v", "w") | Z %among% "y") & (Z %among% "y" | X %among% "t") | (W %among% c("q", "r") & Z %among% "y" | X %among% "u" & W %among% "r")) | (X %among% c("s", "t") | Y %among% "w" | W %among% c("p", "q") & Z %among% c("a", "y")) & (Z %among% "a" & Z %among% c("z", "y") | X %among% c("s", "t") & X %among% c("u", "t")) & (X %among% "s" | W %among% c("r", "q") | Z %among% "a" & Z %among% "y" | (Z %among% c("z", "y") | Y %among% "x") & (X %among% c("t", "s") & X %among% "u")) | ((Z %among% "a" & Y %among% c("w", "v") | Y %among% c("w", "x") & W %among% "q" | X %among% "t" & X %among% "s" & (W %among% "p" & Z %among% "z")) & ((X %among% c("s", "u") | Z %among% c("z", "y") | (Y %among% "x" | Y %among% "x")) & (W %among% c("p", "q") | Z %among% "z" | Z %among% "y" & X %among% c("u", "s" ))) | (X %among% c("t", "s") & W %among% c("p", "q") & (W %among% c("p", "q") | Y %among% c("x", "w")) | Y %among% c("v", "x") & X %among% "t" & (X %among% "t" & W %among% c("p", "q")) | (Y %among% "v" & Y %among% "w" | (X %among% "u" | W %among% "p") | Z %among% c("z", "a") & X %among% "s" & (Y %among% "v" | Z %among% c("z", "a"))))) | (((W %among% "p" | X %among% "u" | (W %among% "r" | W %among% c("r", "p"))) & (X %among% c("t", "u") | X %among% c("s", "t") | (X %among% c("s", "u") | Z %among% "a")) | (Y %among% c("w", "v") & W %among% "r" | X %among% "t" & X %among% c("s", "u") | (W %among% c("p", "q") | X %among% "u" | (Z %among% "a" | X %among% c("u", "s"))))) & ((Z %among% "a" | Z %among% "a") & (Z %among% "y" & Y %among% "x") | X %among% "t" & W %among% "q" & (X %among% "u" | Z %among% c("y", "z")) | ((Y %among% c("w", "v") | Z %among% c("z", "a")) & (W %among% "q" & W %among% c("p", "q")) | (Z %among% "y" | Z %among% "z") & (Y %among% c("v", "x") | W %among% c("q", "p")))) | (Z %among% c("y", "z") | X %among% c("s", "u") | Y %among% c("v", "x") & Z %among% "y" | Y %among% "v" & Z %among% c("z", "a") & (Y %among% "w" | Y %among% "v")) & (Z %among% "z" | Y %among% "x" | (W %among% "r" | Y %among% c("w", "x")) | (X %among% "t" | Y %among% c("v", "x") | (W %among% c("p", "q") | Z %among% "y"))) & (Z %among% c("z", "a") & Y %among% "v" | (W %among% c("q", "r") | Y %among% "v") | X %among% "t" & X %among% c("s", "u") & (X %among% "u" & X %among% "s") | X %among% "t" & W %among% "p" & (W %among% c("r", "q") | Z %among% "a") & (W %among% c("r", "p") & Y %among% c("v", "x") | (Y %among% c("v", "x") | X %among% "t"))))) From 9a0b99f06a769070fc86f27ccb42843802400dc3 Mon Sep 17 00:00:00 2001 From: mb706 Date: Fri, 20 Sep 2024 12:34:18 +0200 Subject: [PATCH 52/87] one in ten million bug --- R/CnfFormula_simplify2.R | 1 + 1 file changed, 1 insertion(+) diff --git a/R/CnfFormula_simplify2.R b/R/CnfFormula_simplify2.R index 520c38474..7a3456b9c 100644 --- a/R/CnfFormula_simplify2.R +++ b/R/CnfFormula_simplify2.R @@ -409,6 +409,7 @@ simplify_cnf = function(entries, universe) { ousr = on_updated_subset_relations(meta_idx_inner, meta_idx_outer) if (is.null(ousr)) break if (ousr) return(return_entries(FALSE)) + if (eliminated[[clause_idx_inner]] || is_unit[[clause_idx_inner]]) next # yes this can happen. } if (updated_inso_outer) { ousr = on_updated_subset_relations(meta_idx_outer, meta_idx_inner) From 53a6f379fc897b599cac3b1498b880e13d0aa08b Mon Sep 17 00:00:00 2001 From: mb706 Date: Fri, 20 Sep 2024 17:00:59 +0200 Subject: [PATCH 53/87] slight optimization --- R/CnfFormula_simplify2.R | 84 +++++++++++++++++++++++++++++++++++++++- 1 file changed, 82 insertions(+), 2 deletions(-) diff --git a/R/CnfFormula_simplify2.R b/R/CnfFormula_simplify2.R index 7a3456b9c..65e655e31 100644 --- a/R/CnfFormula_simplify2.R +++ b/R/CnfFormula_simplify2.R @@ -104,9 +104,18 @@ simplify_cnf = function(entries, universe) { entries[[ur]][[1L]] <<- (unit_domains[[nu]] = unit_isct) # update the *old* unit and unit_domains in one go. unit_domains is updated by-reference (environment) eliminated[[unit_idx]] <<- TRUE } - # The symbol registry is empty at the start, this happens when new units are added later + # The symbol registry is empty at the start; the following happens when new units are added later + for (s_clause_idx in symbol_registry[[nu]]) { - if (eliminated[[s_clause_idx]]) next # could have been eliminated by subsumption elimination during unit propagation of another clause + # could have been eliminated by subsumption elimination during unit propagation of another clause + # (we are not afraid of is_unit here, since we are the unit for the symbol here -- everything else that has the + # symbol gets eliminated) + if (eliminated[[s_clause_idx]]) next + if (!is.null(is_not_subset_of)) { + # if we already know that s_clause_idx[[nu]] is a subset of unit_idx, we can skip this + s_clause_idx_meta = available_inverse[[s_clause_idx]] + if (s_clause_idx_meta <= meta_idx_outer && !is_not_subset_of[[s_clause_idx_meta]][available_inverse[[unit_idx]], nu]) next + } adr = apply_domain_restriction(s_clause_idx, nu, unit_domains[[nu]], TRUE) if (identical(adr, TRUE)) return(TRUE) # forward contradiction signal } @@ -420,6 +429,77 @@ simplify_cnf = function(entries, universe) { } } + ## Some thoughts: + # could still do resolution self subsumption: + # given Clause X + # clause A that is mostly subset of X except for one symbol s + # clause B that is complement to A wrt s *outside of X[s]*, otherwise subset of X except for one symbol t, which is also in X + # - implied resolution of A and B is (A + B - s), can do self subsumption w/r/t t -> restrict X[t] to B[t] + # what else do we know? + # - A has rowsum 1; X[s] is therefore already self subsumption restricted to intersection with A[s] + # - B has rowsum 2 -- if it were 1, then we could already do the self subsumption w/r/t t + # - ideally we don't want to check that intersect(A[s], B[s]) is in X[s] too often + # how to do this efficiently? + # - keep matrix of complement relationships? -- would miss out on cases where intersection of A[s] and B[s] is in X[s] + # - if we do this reactively, we have to react every time a new rowsum == 1 OR rowsum == 2 appears? + # - for each entry and each symbol, keep a rowsum == 1 and rowsum == 2 queue? + # - would have to keep a reverse registry as well so we know where to eliminate entries from? or just live with the fact that we have to check for eliminated every time? + # - or just use the symbol registry + # suggestion: + # - when rowsum == 2: check symbol registry, intersect where not_subset w/r/t the symbol is TRUE, check rowsum == 1 on the other side, then check intersection relationship? + # - Maybe cache rowsum somewhere. + # - when rowsum == 1, check symbol registry, intersect where not_subset w/r/t the symbol is TRUE, check rowsum == 2 on the other side, then check intersection relationship? + # What about longer graphs? For hidden lateral addition, we can just build up one clause at a time and see if it gets eliminated. + # - what happens is that rowsum == 1 elements are "plugs" that can reduce rowsums of other elements. + # - reducing rowsums of other rowsum == 1 elements is boring, since HLA will have the same result + # - the weird thing here is that, when doing the intersection part, we want to consider the intersection outside of X wiht maximal symbols, not minimal symbols; + # this is different than in all the other cases, for which we can just greedily reduce symbols. + # - do we, in principle, want to do this with all the hidden tautology eliminated clauses present? + # - maybe what we do is we continue with self subsumption eliminatoin during HLA? + # - YES + # - this changes the HLA loop, however, since now we need to revisit clauses that we have looped over already + # - keep track of the clause+, as well as rowsums, and update them in the on_subset_relations handler + # - question remains: do we want to keep the HLA-eliminated clauses? + # - suppose a clause A is subset of X w/r/t all symbols except s. + # - if it is eliminated by HLA, then this is only interesting if it is eliminated with at least one clause that is subset of A[s] but not X[s]; otherwise, + # X could have been eliminated already. + # - if we are only on about hidden tautology elimination, then X[s] would be filled up to superset A[s] eventually, and whatever eliminated A[s] can still work on X. + # - however, we are looking at a B that is not a subset of X w/r/t s and another symbol t. + # - test case: + # 1 A %among% c("a1", "a2") | B %among% "b1" | C %among% c("c1", "c2") + # 2 B %among% c("b1", "b2") | C %among% c("c1", "c3") + # 3 A %among% c("a1", "a2") | B %among% c("b1", "b3") + # 4 A %among% "a2" | B %among% "b3" | D %among% "d1" + # 5 A %among% "a1" | B %among% "b3" | D %among% c("d2", "d3") + # - clause 3 adds 'b2' to clause 1; clause 2 can then restrict clause 1 to 'c1' + # - however, clauses 4 and 5 eliminate clause 3 through hidden subsumption elimination + # - how can clause 1 be restricted to 'c1' now? + # - I guess here we have a special case not treated above: two clauses that have both rowsum 2, that can be combined to rowsum 1 (w/r/t clause 1 here) + # - test case 2: + # 1 A %among% c("a1", "a2") | B %among% "b1" | C %among% c("c1", "c2") | D %among% "d3" + # 2 B %among% c("b1", "b2") | C %among% c("c1", "c3") + # 3 A %among% c("a1", "a2") | B %among% c("b1", "b3") | D %among% "d3" + # 4 A %among% "a2" | B %among% "b3" | D %among% c("d1", "d3") + # 5 A %among% "a1" | B %among% "b3" | D %among% c("d2", "d3") + # - here, 4 and 5 can also be combined to remove B from clause 1. At the same time, clause 1+ retains B and gains b2 as well. + # - this was not visible from subset relations alone: 4 and 5 could differ in many symbols, only their intersection must be complement w/r/t 1. + # - they don't get built up by clause 1 and they don't build it up. + # - do we have to look at all combinations of all clauses? + # - take two clauses: intersection w/r/t one symbol, union w/r/t all others -- this can do something interesting to a third clause if the# + # intersection is a subset w/r/t the third clause, but they were not subsets before. Also each clause must have have rowsums >= 2, since rowsum 1 + # clauses are already considered. + # - this builds up a clause that these clauses could have eliminated + # - to test all these relationships, maybe we are in exponential time already? + # - how *could* this work? for all pairs of clauses, intersect w/r/t one symbol, union the others? + # - is this still valid if one of the original clauses gets eliminated? Probably yes, if all we use this for is self subsumption elimination. + # testcase: + # (X ∈ {s} | Z ∈ {y}) + # & (Y ∈ {x} | X ∈ {t}) + # & (Y ∈ {x} | Z ∈ {z}) + # (in R-code, that is: `CnfFormula(list(X %among% "s" | Z %among% "y", Y %among% "x" | X %among% "t", Y %among% "x" | Z %among% "z"))` ) + # Here, the first two clauses can restrict the 3rd clause to `Y %among% "x"`, which then subsumption-eliminates clauses 2 and 3. + + # Now for the big one: Asymmetric Hidden Literal Addition (Marijn et al.) # First, we do non-units, then we do units separately. From e6b020e8108a7f17951acb2c656c2383f5206665 Mon Sep 17 00:00:00 2001 From: mb706 Date: Fri, 20 Sep 2024 17:01:03 +0200 Subject: [PATCH 54/87] some thoughts --- attic/mvsat.mv | 72 ++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 72 insertions(+) diff --git a/attic/mvsat.mv b/attic/mvsat.mv index 27fcdcd26..d5ea5e313 100644 --- a/attic/mvsat.mv +++ b/attic/mvsat.mv @@ -110,3 +110,75 @@ # This is because we don't eliminate (C | A) & (!C | B) & (B | A) by removing (B | A) # so, if clause X and clause Y have a symbol in common where the values are disjoint, the disjunction of the rest is implied? + +## Some thoughts: +# could still do resolution self subsumption: +# given Clause X +# clause A that is mostly subset of X except for one symbol s +# clause B that is complement to A wrt s *outside of X[s]*, otherwise subset of X except for one symbol t, which is also in X +# - implied resolution of A and B is (A + B - s), can do self subsumption w/r/t t -> restrict X[t] to B[t] +# what else do we know? +# - A has rowsum 1; X[s] is therefore already self subsumption restricted to intersection with A[s] +# - B has rowsum 2 -- if it were 1, then we could already do the self subsumption w/r/t t +# - ideally we don't want to check that intersect(A[s], B[s]) is in X[s] too often +# how to do this efficiently? +# - keep matrix of complement relationships? -- would miss out on cases where intersection of A[s] and B[s] is in X[s] +# - if we do this reactively, we have to react every time a new rowsum == 1 OR rowsum == 2 appears? +# - for each entry and each symbol, keep a rowsum == 1 and rowsum == 2 queue? +# - would have to keep a reverse registry as well so we know where to eliminate entries from? or just live with the fact that we have to check for eliminated every time? +# - or just use the symbol registry +# suggestion: +# - when rowsum == 2: check symbol registry, intersect where not_subset w/r/t the symbol is TRUE, check rowsum == 1 on the other side, then check intersection relationship? +# - Maybe cache rowsum somewhere. +# - when rowsum == 1, check symbol registry, intersect where not_subset w/r/t the symbol is TRUE, check rowsum == 2 on the other side, then check intersection relationship? +# What about longer graphs? For hidden lateral addition, we can just build up one clause at a time and see if it gets eliminated. +# - what happens is that rowsum == 1 elements are "plugs" that can reduce rowsums of other elements. +# - reducing rowsums of other rowsum == 1 elements is boring, since HLA will have the same result +# - the weird thing here is that, when doing the intersection part, we want to consider the intersection outside of X wiht maximal symbols, not minimal symbols; +# this is different than in all the other cases, for which we can just greedily reduce symbols. +# - do we, in principle, want to do this with all the hidden tautology eliminated clauses present? +# - maybe what we do is we continue with self subsumption eliminatoin during HLA? +# - YES +# - this changes the HLA loop, however, since now we need to revisit clauses that we have looped over already +# - keep track of the clause+, as well as rowsums, and update them in the on_subset_relations handler +# - question remains: do we want to keep the HLA-eliminated clauses? +# - suppose a clause A is subset of X w/r/t all symbols except s. +# - if it is eliminated by HLA, then this is only interesting if it is eliminated with at least one clause that is subset of A[s] but not X[s]; otherwise, +# X could have been eliminated already. +# - if we are only on about hidden tautology elimination, then X[s] would be filled up to superset A[s] eventually, and whatever eliminated A[s] can still work on X. +# - however, we are looking at a B that is not a subset of X w/r/t s and another symbol t. +# - test case: +# 1 A %among% c("a1", "a2") | B %among% "b1" | C %among% c("c1", "c2") +# 2 B %among% c("b1", "b2") | C %among% c("c1", "c3") +# 3 A %among% c("a1", "a2") | B %among% c("b1", "b3") +# 4 A %among% "a2" | B %among% "b3" | D %among% "d1" +# 5 A %among% "a1" | B %among% "b3" | D %among% c("d2", "d3") +# - clause 3 adds 'b2' to clause 1; clause 2 can then restrict clause 1 to 'c1' +# - however, clauses 4 and 5 eliminate clause 3 through hidden subsumption elimination +# - how can clause 1 be restricted to 'c1' now? +# - I guess here we have a special case not treated above: two clauses that have both rowsum 2, that can be combined to rowsum 1 (w/r/t clause 1 here) +# - test case 2: +# 1 A %among% c("a1", "a2") | B %among% "b1" | C %among% c("c1", "c2") | D %among% "d3" +# 2 B %among% c("b1", "b2") | C %among% c("c1", "c3") +# 3 A %among% c("a1", "a2") | B %among% c("b1", "b3") | D %among% "d3" +# 4 A %among% "a2" | B %among% "b3" | D %among% c("d1", "d3") +# 5 A %among% "a1" | B %among% "b3" | D %among% c("d2", "d3") +# - here, 4 and 5 can also be combined to remove B from clause 1. At the same time, clause 1+ retains B and gains b2 as well. +# - this was not visible from subset relations alone: 4 and 5 could differ in many symbols, only their intersection must be complement w/r/t 1. +# - they don't get built up by clause 1 and they don't build it up. +# - do we have to look at all combinations of all clauses? +# - take two clauses: intersection w/r/t one symbol, union w/r/t all others -- this can do something interesting to a third clause if the# +# intersection is a subset w/r/t the third clause, but they were not subsets before. Also each clause must have have rowsums >= 2, since rowsum 1 +# clauses are already considered. +# - this builds up a clause that these clauses could have eliminated +# - to test all these relationships, maybe we are in exponential time already? +# - how *could* this work? for all pairs of clauses, intersect w/r/t one symbol, union the others? +# - is this still valid if one of the original clauses gets eliminated? Probably yes, if all we use this for is self subsumption elimination. +# testcase: +# (X ∈ {s} | Z ∈ {y}) +# & (Y ∈ {x} | X ∈ {t}) +# & (Y ∈ {x} | Z ∈ {z}) +# (in R-code, that is: `CnfFormula(list(X %among% "s" | Z %among% "y", Y %among% "x" | X %among% "t", Y %among% "x" | Z %among% "z"))` ) +# Here, the first two clauses can restrict the 3rd clause to `Y %among% "x"`, which then subsumption-eliminates clauses 2 and 3. + + From 9a59c323483d2d2f6cf51ed8c0b80df5cc0ea627 Mon Sep 17 00:00:00 2001 From: mb706 Date: Fri, 20 Sep 2024 17:19:54 +0200 Subject: [PATCH 55/87] fixed optimization --- R/CnfFormula_simplify2.R | 87 ++++++---------------------------------- 1 file changed, 13 insertions(+), 74 deletions(-) diff --git a/R/CnfFormula_simplify2.R b/R/CnfFormula_simplify2.R index 65e655e31..b370e76b5 100644 --- a/R/CnfFormula_simplify2.R +++ b/R/CnfFormula_simplify2.R @@ -105,16 +105,26 @@ simplify_cnf = function(entries, universe) { eliminated[[unit_idx]] <<- TRUE } # The symbol registry is empty at the start; the following happens when new units are added later - + use_inso = FALSE + if (!is.null(is_not_subset_of)) { + # if we have the is_not_subset_of matrix, we can use it to skip some checks + unit_idx_meta = available_inverse[[unit_idx]] + use_inso = unit_idx_meta <= meta_idx_outer # .. but only if we have built the matrix up to the current index + if (use_inso) { + # if the unit is a subset of the other clause, we will never skip. + inso_column = is_not_subset_of[[unit_idx_meta]][, nu] + } + } for (s_clause_idx in symbol_registry[[nu]]) { # could have been eliminated by subsumption elimination during unit propagation of another clause # (we are not afraid of is_unit here, since we are the unit for the symbol here -- everything else that has the # symbol gets eliminated) if (eliminated[[s_clause_idx]]) next - if (!is.null(is_not_subset_of)) { + if (use_inso) { # if we already know that s_clause_idx[[nu]] is a subset of unit_idx, we can skip this + # exception: unit_idx is *also* a subset, implying equality, in which case we will do subsumption elimination. s_clause_idx_meta = available_inverse[[s_clause_idx]] - if (s_clause_idx_meta <= meta_idx_outer && !is_not_subset_of[[s_clause_idx_meta]][available_inverse[[unit_idx]], nu]) next + if (s_clause_idx_meta <= meta_idx_outer && inso_column[[s_clause_idx_meta]] && !is_not_subset_of[[s_clause_idx_meta]][unit_idx_meta, nu]) next } adr = apply_domain_restriction(s_clause_idx, nu, unit_domains[[nu]], TRUE) if (identical(adr, TRUE)) return(TRUE) # forward contradiction signal @@ -429,77 +439,6 @@ simplify_cnf = function(entries, universe) { } } - ## Some thoughts: - # could still do resolution self subsumption: - # given Clause X - # clause A that is mostly subset of X except for one symbol s - # clause B that is complement to A wrt s *outside of X[s]*, otherwise subset of X except for one symbol t, which is also in X - # - implied resolution of A and B is (A + B - s), can do self subsumption w/r/t t -> restrict X[t] to B[t] - # what else do we know? - # - A has rowsum 1; X[s] is therefore already self subsumption restricted to intersection with A[s] - # - B has rowsum 2 -- if it were 1, then we could already do the self subsumption w/r/t t - # - ideally we don't want to check that intersect(A[s], B[s]) is in X[s] too often - # how to do this efficiently? - # - keep matrix of complement relationships? -- would miss out on cases where intersection of A[s] and B[s] is in X[s] - # - if we do this reactively, we have to react every time a new rowsum == 1 OR rowsum == 2 appears? - # - for each entry and each symbol, keep a rowsum == 1 and rowsum == 2 queue? - # - would have to keep a reverse registry as well so we know where to eliminate entries from? or just live with the fact that we have to check for eliminated every time? - # - or just use the symbol registry - # suggestion: - # - when rowsum == 2: check symbol registry, intersect where not_subset w/r/t the symbol is TRUE, check rowsum == 1 on the other side, then check intersection relationship? - # - Maybe cache rowsum somewhere. - # - when rowsum == 1, check symbol registry, intersect where not_subset w/r/t the symbol is TRUE, check rowsum == 2 on the other side, then check intersection relationship? - # What about longer graphs? For hidden lateral addition, we can just build up one clause at a time and see if it gets eliminated. - # - what happens is that rowsum == 1 elements are "plugs" that can reduce rowsums of other elements. - # - reducing rowsums of other rowsum == 1 elements is boring, since HLA will have the same result - # - the weird thing here is that, when doing the intersection part, we want to consider the intersection outside of X wiht maximal symbols, not minimal symbols; - # this is different than in all the other cases, for which we can just greedily reduce symbols. - # - do we, in principle, want to do this with all the hidden tautology eliminated clauses present? - # - maybe what we do is we continue with self subsumption eliminatoin during HLA? - # - YES - # - this changes the HLA loop, however, since now we need to revisit clauses that we have looped over already - # - keep track of the clause+, as well as rowsums, and update them in the on_subset_relations handler - # - question remains: do we want to keep the HLA-eliminated clauses? - # - suppose a clause A is subset of X w/r/t all symbols except s. - # - if it is eliminated by HLA, then this is only interesting if it is eliminated with at least one clause that is subset of A[s] but not X[s]; otherwise, - # X could have been eliminated already. - # - if we are only on about hidden tautology elimination, then X[s] would be filled up to superset A[s] eventually, and whatever eliminated A[s] can still work on X. - # - however, we are looking at a B that is not a subset of X w/r/t s and another symbol t. - # - test case: - # 1 A %among% c("a1", "a2") | B %among% "b1" | C %among% c("c1", "c2") - # 2 B %among% c("b1", "b2") | C %among% c("c1", "c3") - # 3 A %among% c("a1", "a2") | B %among% c("b1", "b3") - # 4 A %among% "a2" | B %among% "b3" | D %among% "d1" - # 5 A %among% "a1" | B %among% "b3" | D %among% c("d2", "d3") - # - clause 3 adds 'b2' to clause 1; clause 2 can then restrict clause 1 to 'c1' - # - however, clauses 4 and 5 eliminate clause 3 through hidden subsumption elimination - # - how can clause 1 be restricted to 'c1' now? - # - I guess here we have a special case not treated above: two clauses that have both rowsum 2, that can be combined to rowsum 1 (w/r/t clause 1 here) - # - test case 2: - # 1 A %among% c("a1", "a2") | B %among% "b1" | C %among% c("c1", "c2") | D %among% "d3" - # 2 B %among% c("b1", "b2") | C %among% c("c1", "c3") - # 3 A %among% c("a1", "a2") | B %among% c("b1", "b3") | D %among% "d3" - # 4 A %among% "a2" | B %among% "b3" | D %among% c("d1", "d3") - # 5 A %among% "a1" | B %among% "b3" | D %among% c("d2", "d3") - # - here, 4 and 5 can also be combined to remove B from clause 1. At the same time, clause 1+ retains B and gains b2 as well. - # - this was not visible from subset relations alone: 4 and 5 could differ in many symbols, only their intersection must be complement w/r/t 1. - # - they don't get built up by clause 1 and they don't build it up. - # - do we have to look at all combinations of all clauses? - # - take two clauses: intersection w/r/t one symbol, union w/r/t all others -- this can do something interesting to a third clause if the# - # intersection is a subset w/r/t the third clause, but they were not subsets before. Also each clause must have have rowsums >= 2, since rowsum 1 - # clauses are already considered. - # - this builds up a clause that these clauses could have eliminated - # - to test all these relationships, maybe we are in exponential time already? - # - how *could* this work? for all pairs of clauses, intersect w/r/t one symbol, union the others? - # - is this still valid if one of the original clauses gets eliminated? Probably yes, if all we use this for is self subsumption elimination. - # testcase: - # (X ∈ {s} | Z ∈ {y}) - # & (Y ∈ {x} | X ∈ {t}) - # & (Y ∈ {x} | Z ∈ {z}) - # (in R-code, that is: `CnfFormula(list(X %among% "s" | Z %among% "y", Y %among% "x" | X %among% "t", Y %among% "x" | Z %among% "z"))` ) - # Here, the first two clauses can restrict the 3rd clause to `Y %among% "x"`, which then subsumption-eliminates clauses 2 and 3. - - # Now for the big one: Asymmetric Hidden Literal Addition (Marijn et al.) # First, we do non-units, then we do units separately. From c2539f4ee6ee6c6c23894bd66ffe6e539a833641 Mon Sep 17 00:00:00 2001 From: mb706 Date: Fri, 20 Sep 2024 17:39:45 +0200 Subject: [PATCH 56/87] ENOUGH --- attic/mvsat.mv | 6 ++++++ 1 file changed, 6 insertions(+) diff --git a/attic/mvsat.mv b/attic/mvsat.mv index d5ea5e313..1b43d5c7b 100644 --- a/attic/mvsat.mv +++ b/attic/mvsat.mv @@ -174,6 +174,12 @@ # - to test all these relationships, maybe we are in exponential time already? # - how *could* this work? for all pairs of clauses, intersect w/r/t one symbol, union the others? # - is this still valid if one of the original clauses gets eliminated? Probably yes, if all we use this for is self subsumption elimination. +# - how about this: we keep a separate queue of clauses that could be used for self subsumption elimination of clauses that were potentially already eliminated. +# we do this opportunistically, since it could contain information from higher order combinations of other clauses, which we won't bother to check exhaustively. +# Whenever rowsum of something is 2 after maximally expanding clause+, we check if there is something else that also has rowsum 2 w/r/t the same variables +# (for this it must be in the same variable queues) and if so, try to use it for self subsumption elimination. We need to somehow mark that this happened, +# since we don't need to do it again. +# - subsumption-eliminating something from clause X means that clause X could now be subset for something else, so we need to react... # testcase: # (X ∈ {s} | Z ∈ {y}) # & (Y ∈ {x} | X ∈ {t}) From 421965203da0724e1efd5b3cec5cfe6a8bcab674 Mon Sep 17 00:00:00 2001 From: mb706 Date: Sat, 21 Sep 2024 02:25:07 +0200 Subject: [PATCH 57/87] some final thoughts --- attic/mvsat.mv | 6 ++++++ 1 file changed, 6 insertions(+) diff --git a/attic/mvsat.mv b/attic/mvsat.mv index 1b43d5c7b..688cd309b 100644 --- a/attic/mvsat.mv +++ b/attic/mvsat.mv @@ -180,6 +180,12 @@ # (for this it must be in the same variable queues) and if so, try to use it for self subsumption elimination. We need to somehow mark that this happened, # since we don't need to do it again. # - subsumption-eliminating something from clause X means that clause X could now be subset for something else, so we need to react... +# - maybe we should be reactive about clause+ right away: upon constructing the matrix, we also get a subset_count matrix; we build the clause+ right away. +# This way the logic for subsumption elimination after clause+-ing is easier; otherwise the code just needs to get written twice... +# - self-subsumption elimination after clause+ needs to do all the other things as well anyways... +# - check what we are currently doing based on is_not_subset_of -- we would turn it into is_not_subset_of_clause+, effectively. +# - do we need another symbol registry? For clause+, or for eliminated-but-can-still-trigger-self-subsumption? +# - now we need to treat units more like other clauses, as they can get normal clause+ and need normal subset-relationships. # testcase: # (X ∈ {s} | Z ∈ {y}) # & (Y ∈ {x} | X ∈ {t}) From aa6efc308936d2167a1babc3bce517726dc5e32f Mon Sep 17 00:00:00 2001 From: mb706 Date: Sat, 21 Sep 2024 16:17:09 +0200 Subject: [PATCH 58/87] checkpoint --- R/CnfFormula_simplify1.R | 581 +++++++++++++++++++++++++++++++++++++++ 1 file changed, 581 insertions(+) create mode 100644 R/CnfFormula_simplify1.R diff --git a/R/CnfFormula_simplify1.R b/R/CnfFormula_simplify1.R new file mode 100644 index 000000000..b370e76b5 --- /dev/null +++ b/R/CnfFormula_simplify1.R @@ -0,0 +1,581 @@ + + +simplify_cnf = function(entries, universe) { + ################################# + # Some vocabulary: + # - `entries` is a list of `clauses`, which are named lists. + # - `clauses`' names are `symbols`, the values are the `ranges` of the symbols within that clause + # - `unit`: clause with single symbol + # Glossary of operations: + # - `unit propagation`: ranges of a symbol within a unit constitute the entire possible range of that symbol, + # so all clauses with that symbol are restricted to those values + # - `subsumption elimination`: if all ranges of all symbols within one clause are subsets of those ranges in another clause, + # then the other clause can be removed + # - `self-subsumption elimination`: if the ranges of all except one symbol within one clause are a subset of those ranges + # in another clause, then the remaining symbol in the latter clause can be intersected with the remaining symbol. + # - `hidden literal addition` (HLA): if the ranges of all except one symbol within one clause are a subset of those ranges + # in another clause, then the *complement* of the remaining symbol in the former clause can be added to the latter clause. + # This is basically the reverse of self-subsumption elimination. We do not use this to change clauses directly; + # the point here is that the resulting clause, even if applied repeatedly, is logically equivalent to the original clause within the formula: + # - `hidden subsumption elimination`: if applying HLA results in a clause that can be subsumed, the original clause can be removed. + # - `hidden tautology elimination`: if applying HLA results in a clause that is a tautology, the original clause can be removed. + # Note: 'Clause Elimination Procedures for CNF Formulas' by Marijn Heule et al. calls this "Asymmetric Hidden Literal Addition". + ################################# + + ######################## + ## Helper functions ## + ######################## + + # faster intersect, setdiff etc. that rely on x, y being characters with no duplicates + char_intersect = function(x, y) x[x %in% y] + char_setdiff = function(x, y) x[!x %in% y] + + # construct the CnfFormula return object + return_entries = function(entries) { + structure( + if (!length(entries)) TRUE else entries, + universe = universe, + class = "CnfFormula" + ) + } + + if (is.logical(entries)) return(return_entries(entries)) + + ######################## + ## Variable setup ## + ######################## + + entries = entries[order(lengths(entries))] + + is_unit = lengths(entries) == 1L + eliminated = logical(length(entries)) + + # maps symbol name -> the index of unit clauses + unit_registry = new.env(parent = emptyenv()) + + # maps symbol name -> their current domain + unit_domains = new.env(parent = emptyenv()) + + # maps symbol name -> the index of all non-unit clauses that refer to it + symbol_registry = new.env(parent = emptyenv()) + + is_not_subset_of = NULL # see further down + available_inverse = NULL # ditto + + ################################## + ## Event-driven clause handling ## + ################################## + # The following functions process the CNF clauses in various ways, + # depending on the current state of the entries. + # The state of the entries is updated in-place. + # The functions are then called in a loop, but they may also call each other. + # It is therefore important that they make the global state consistent before + # calling other functions, and that they are aware of how the global state *can* + # have changed upon their return. + # - entries[[clause_idx]] should be updated if necessary before other fns are called + # - symbol_registry[[symbol]] could have been updated + # - eliminated[[clause_idx]] could have been set to TRUE + # Since functions can call each other in different ways, `eliminated` could have changed even for clauses + # for which the other functions were not called. + + # Register a clause as a unit: + # - check if there is already a unit for this symbol + # - if not, add it to the unit registry + # - otherwise, intersect unit domains (and exit on contradiction) + # - apply unit propagation + # - We do *not* update the sybmol registry here; if the clause is registered for a given symbol, + # it has to be removed from there *before* calling this function. + register_unit = function(unit_idx) { + unit = entries[[unit_idx]] + nu = names(unit) + ur = unit_registry[[nu]] + if (is.null(ur)) { + unit_registry[[nu]] = unit_idx # environment assignment + unit_domains[[nu]] = unit[[1L]] # environment assignment + # this is init'd TRUE for those w/ length 1 at the start, we set it to TRUE for clauses where symbols were eliminated + is_unit[[unit_idx]] <<- TRUE + } else { + # two units refer to the same symbol + # -> we keep the one we saw before but update it to the intersection. + # the current one is eliminated + prev_unit = unit_domains[[nu]] + unit_isct = prev_unit[prev_unit %in% unit[[1L]]] + if (!length(unit_isct)) return(TRUE) # signal that we have a contradiction and can exit + entries[[ur]][[1L]] <<- (unit_domains[[nu]] = unit_isct) # update the *old* unit and unit_domains in one go. unit_domains is updated by-reference (environment) + eliminated[[unit_idx]] <<- TRUE + } + # The symbol registry is empty at the start; the following happens when new units are added later + use_inso = FALSE + if (!is.null(is_not_subset_of)) { + # if we have the is_not_subset_of matrix, we can use it to skip some checks + unit_idx_meta = available_inverse[[unit_idx]] + use_inso = unit_idx_meta <= meta_idx_outer # .. but only if we have built the matrix up to the current index + if (use_inso) { + # if the unit is a subset of the other clause, we will never skip. + inso_column = is_not_subset_of[[unit_idx_meta]][, nu] + } + } + for (s_clause_idx in symbol_registry[[nu]]) { + # could have been eliminated by subsumption elimination during unit propagation of another clause + # (we are not afraid of is_unit here, since we are the unit for the symbol here -- everything else that has the + # symbol gets eliminated) + if (eliminated[[s_clause_idx]]) next + if (use_inso) { + # if we already know that s_clause_idx[[nu]] is a subset of unit_idx, we can skip this + # exception: unit_idx is *also* a subset, implying equality, in which case we will do subsumption elimination. + s_clause_idx_meta = available_inverse[[s_clause_idx]] + if (s_clause_idx_meta <= meta_idx_outer && inso_column[[s_clause_idx_meta]] && !is_not_subset_of[[s_clause_idx_meta]][unit_idx_meta, nu]) next + } + adr = apply_domain_restriction(s_clause_idx, nu, unit_domains[[nu]], TRUE) + if (identical(adr, TRUE)) return(TRUE) # forward contradiction signal + } + FALSE # no contradiction + } + + # restrict the symbol in the clause to a given domain, e.g. a unit + # - clause_idx: index in entries + # - symbol: name of symbol to restrict + # - restringent: domain to restrict to + # returns TRUE if a contradiction was detected, NULL if the clause was eliminated + apply_domain_restriction = function(clause_idx, symbol, restringent, is_unit_propagation) { + clause = entries[[clause_idx]] + symbol_idx = match(symbol, names(clause)) + if (is.na(symbol_idx)) return(FALSE) + + clause_symbol_length_before = length(clause[[symbol_idx]]) + clause[[symbol_idx]] = char_intersect(clause[[symbol_idx]], restringent) + if (length(clause[[symbol_idx]]) == length(restringent)) { + # If the lengths match, then the clause is a superset of the unit (since the intersections are equal) + # the clause is therefore subsumed by the unit + eliminate_clause_update_sr(clause_idx) + return(NULL) + } + # clause was not changed + if (length(clause[[symbol_idx]]) == clause_symbol_length_before) return(FALSE) + if (!length(clause[[symbol_idx]])) { + # the symbol is not in the clause anymore + return(eliminate_symbol_from_clause(clause_idx, symbol)) + } + # clause was changed. + # We don't need to do this when we go the eliminate_symbol_from_clause route, since that will update the clause in any case. + entries[[clause_idx]] <<- clause + + # We need to update the subset relations matrix, if it exists + if (is.null(is_not_subset_of)) return(FALSE) + + meta_idx = available_inverse[[clause_idx]] + # meta_idx_outer is the index up to which we have built is_not_subset_of; if meta_idx > meta_idx_outer, then we haven't seen the clause yet. + # we are not relying on the fact that as soon as is_not_subset_of is non-null, we will only get here for clauses for which + # is_not_subset_of was built, because unit-propagation could be cascading from a unit elimination. + if (meta_idx > meta_idx_outer) return(FALSE) + + if (!is_unit_propagation) { + # we are not propagating units, so we need to update the subset relations in the other direction. + # we do this first, in case on_updated_subset_relations gets too eager later + idx_to_check = which(available[seq_len(meta_idx_outer)] %in% symbol_registry[[symbol]]) + for (other_meta_idx in idx_to_check) { + # was the other a subset of us before? that could have changed now. + if (!is_not_subset_of[[other_meta_idx]][meta_idx, symbol] && !all(entries[[available[[other_meta_idx]]]][[symbol]] %in% entries[[clause_idx]][[symbol]])) { + is_not_subset_of[[other_meta_idx]][meta_idx, symbol] <<- TRUE + # no need to call on_updated_subset_relations, since we are increasing rowsums, not decreasing them + } + } + } + + is_not_subset_of_col = match(symbol, colnames(is_not_subset_of[[meta_idx]])) + # * We could now be a subset of things that we were not a subset of before, so we only need to check the TRUE entries and may be setting them to FALSE. + # --> hence `is_not_subset_of[meta_idx][is_not_subset_of[meta_idx]` + # Note: we cannot address is_not_subset_of by symbol_idx, since clauses may get shorter but is_not_subset_of stays the same! + # * If this is unit propagation, we do not need to check other entries, since apply_domain_restriction happens to all clauses in a row, so the counter-side is updated in time. + # In particular, we do not need to worry that some other clause that was formerly our subset ceases to be our subset, since that other clause + # will also be restricted by the unit. + # * We can only ever set those entries to FALSE for which the other clause is in the symbol registry for the current symbol + # --> hence `available %in% symbol_registry[[symbol]]` + # * We only need to check up to the point where we have built is_not_subset_of + # --> hence `available <= meta_idx_outer` + rows_to_check = which((is_not_subset_of[[meta_idx]][, is_not_subset_of_col] & available %in% symbol_registry[[symbol]])[seq_len(meta_idx_outer)]) + for (other_meta_idx in rows_to_check) { + clause_idx_other = available[[other_meta_idx]] + # while we only get here for rows that are in the symbol_registry and therefore not eliminated / units, we need to check again since on_update_subset_relations() + # can change this during the loop. + if (eliminated[[clause_idx_other]] || is_unit[[clause_idx_other]]) next + + # when we get here, that means that the symbol exists both in clause_idx and in other_ref_this symbol, *and* we have seen both clauses + # in the is_not_subset_of building process. + # If this were not the case, then we would not need to change anything. + other_clause_range = entries[[available[[other_meta_idx]]]][[symbol]] + if (!all(entries[[clause_idx]][[symbol]] %in% other_clause_range)) next + + # we are now a subset (and most likely were not before) + # ("most likely" because it could probably happen that we re-enter this part through some cascading elimination / propagation) + is_not_subset_of[[meta_idx]][other_meta_idx, is_not_subset_of_col] <<- FALSE + ousr = on_updated_subset_relations(meta_idx, other_meta_idx) + if (identical(ousr, TRUE)) return(TRUE) # forward contradiction signal. We don't care if other_meta_idx was eliminated. + if (eliminated[[clause_idx]]) return(NULL) # need to check more directly if things escalated somehow and clause_idx was eliminated indirectly + } + FALSE # no contradiction + } + + # eliminate `symbol` from `clause_idx` + # returns 'NULL' for turned into a unit or eliminated, 'TRUE' for contradiction, 'FALSE' for nothing happened + eliminate_symbol_from_clause = function(clause_idx, symbol) { + clause = entries[[clause_idx]] + clause[[symbol]] = NULL + if (!length(clause)) return(TRUE) # signal that we have a contradiction and can exit + # remove from symbol registry of the symbol that went to 0 + sr = symbol_registry[[symbol]] + symbol_registry[[symbol]] = sr[sr != clause_idx] + + entries[[clause_idx]] <<- clause + if (length(clause) == 1) { + # new unit ahoy + # remove from symbol registry of the symbol that remains in the clause + # (since it is now a unit) + sr = symbol_registry[[names(clause)]] + symbol_registry[[names(clause)]] = sr[sr != clause_idx] + if (register_unit(clause_idx)) return(TRUE) # forward signal from register_unit: contradiction + return(NULL) # clause was turned into a unit + } + # clause was not turned into a unit, so we need to fill in is_not_subset_of + if (is.null(is_not_subset_of)) return(FALSE) # we have not started filling this one in + + meta_idx = available_inverse[[clause_idx]] + # meta_idx_outer is the index up to which we have built is_not_subset_of; if meta_idx > meta_idx_outer, then we haven't seen the clause yet. + # we are not relying on the fact that as soon as is_not_subset_of is non-null, we will only get here for clauses for which + # this was built, because it could be cascading from a unit elimination. + if (meta_idx > meta_idx_outer) return(FALSE) + + is_not_subset_of_col = match(symbol, colnames(is_not_subset_of[[meta_idx]])) + rows_changed = which(is_not_subset_of[[meta_idx]][, is_not_subset_of_col]) + is_not_subset_of[[meta_idx]][, is_not_subset_of_col] <<- FALSE + for (others_ref_this_symbol in available_inverse[sr]) { + if (others_ref_this_symbol <= meta_idx_outer) { # meta_idx_outer is the index up to which we have built is_not_subset_of + is_not_subset_of[[others_ref_this_symbol]][meta_idx, symbol] <<- TRUE + } + } + # we could have some leftover TRUEs from eliminated or unit-ed clauses + rows_changed_ids = available[rows_changed] + for (meta_idx_other in rows_changed[!eliminated[rows_changed_ids] & !is_unit[rows_changed_ids] & rows_changed <= meta_idx_outer]) { + # We have to do this *after* we set the corresponding values to TRUE for others_ref_this_symbol, + # since calling this could realistically change the symbol registry (e.g. if it leads to a symbol + # being eliminated from other clauses). + clause_idx_other = available[[meta_idx_other]] + # while we *do* restrict meta_idx_other in the for loop already, eliminated and is_unit can still change during the loop, so check here again + if (eliminated[[clause_idx_other]] || is_unit[[clause_idx_other]]) next + ousr = on_updated_subset_relations(meta_idx, meta_idx_other) + if (identical(ousr, TRUE)) return(TRUE) + # on_updated_subset_relations could cascade down to eliminating meta_idx (i.e. clause_idx) + if (eliminated[[clause_idx]]) return(NULL) + } + FALSE + } + + # returns 'NULL' when meta_idx_other was eliminated (or possibly turned into a unit), + # 'TRUE' for contradiction, 'FALSE' for nothing changed + on_updated_subset_relations = function(meta_idx, meta_idx_other) { + # the row `meta_idx_other` of `is_not_subset_of[[meta_idx]]` has been updated. + # we now check whether we can apply subsumption elimination, or at least self-subsumption elimination, on `meta_idx`. + rowsum = sum(is_not_subset_of[[meta_idx]][meta_idx_other, ]) + if (rowsum > 1) return(FALSE) # nothing to do + if (rowsum == 0) { + eliminate_clause_update_sr(available[[meta_idx_other]]) + return(NULL) + } + # rowsum == 1 + symbol_to_restrict = colnames(is_not_subset_of[[meta_idx]])[is_not_subset_of[[meta_idx]][meta_idx_other, ]] + # update clause and sc! + + # note we update meta_idx_other: we are currently subset of that other clause w/r/t all except one symbol. + # we can therefore intersect that last symbol in the other clause with the range of that symbol in the current clause. + # apply_domain_restriction will take care of eliminating the symbol if the range becomes empty. + # It could in theory even do subsumption, but we have already taken care of that above. + apply_domain_restriction(available[[meta_idx_other]], symbol_to_restrict, entries[[available[[meta_idx]]]][[symbol_to_restrict]], FALSE) + + } + + # mark a clause as eliminated and update symbol registry + # This is relatively safe to call, since it does not modify any other clauses and does not create new units or subset relationships. + eliminate_clause_update_sr = function(clause_idx) { + if (is_unit[[clause_idx]]) stop("Bug in the code, this should never happen.") + eliminated[[clause_idx]] <<- TRUE + for (s in names(entries[[clause_idx]])) { + sr = symbol_registry[[s]] + symbol_registry[[s]] = sr[sr != clause_idx] + } + } + + # process units: + # - populate unit_domains + # - start populating symbol_registry; it gets finished later down with non-units + # - also reduce duplicate units and replace them with their intersection + unit_queue = which(is_unit) + for (unit_idx in unit_queue) { + if (register_unit(unit_idx)) return(return_entries(FALSE)) + } + + # if there were only units, we are done + if (length(unit_queue) == length(entries)) return(return_entries(entries[!eliminated])) + + # process non-units: + # - eliminate entries subsumed by units + # - populate symbol_registry + # we sorted clauses by length, so we can skip ahead by length(unit_queue) + # At this point, everything after the unit_queue is not (yet) a unit. + # The seq.int here is "dangerous" and only allowed because we checked for length(unit_queue) == length(entries) above. + for (clause_idx in seq.int(length(unit_queue) + 1L, length(entries))) { + + # intersect with units and eliminate subsumed clauses + clause_symbol_isct = char_intersect(names(entries[[clause_idx]]), names(unit_domains)) + # apply unit-propagation early, since we otherwise run the risk of adding the clause + # to lots of symbol registry entries, only to remove it again right away + for (symbol in clause_symbol_isct) { + adr = apply_domain_restriction(clause_idx, symbol, unit_domains[[symbol]], TRUE) + if (is.null(adr)) break + if (adr) return(return_entries(FALSE)) + } + + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) next # could happen from unit propagation + + # do cache `clause = entries[[clause_idx]]` and refer to names(clause) here, + # since apply_domain_restriction might have removed symbols from the clause + for (symbol in names(entries[[clause_idx]])) { + sr_entry = symbol_registry[[symbol]] + if (is.null(sr_entry)) { + symbol_registry[[symbol]] = clause_idx + } else { + symbol_registry[[symbol]][[length(sr_entry) + 1L]] = clause_idx + } + } + } + + + # let's start with (self)-subsumption. + # this can also create new units etc. + + # we don't need to check for units, upon registration they are automatically removed, and they cannot help with self-subsumption or HLA + available = which(!(eliminated | is_unit)) + available_inverse = match(seq_along(entries), available) + + # record for each clause whether it is a subset of another clause. + # we record this for each symbol separately, so when a symbol gets self-subsumed, we can re-check others more quickly. + # Default is FALSE (not not a subset, i.e. it is a subset), this aligns with absent columns (which are subsets of everything) + # + # note that as soon as is_not_subset_of is non-null, some other functions assume that meta_idx_outer is also defined. + is_not_subset_of = vector("list", length(available)) + + for (meta_idx_outer in seq_along(available)) { + clause_idx = available[[meta_idx_outer]] + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) next # may happen if we somehow turn something into a unit that eliminates a later clause + clause = entries[[clause_idx]] + + # is_not_subset_of[[i]][j, k] records whether for symbol k, clause i is not a subset of clause j + # If k is not in clause i, then var(i, k) is trivially a subset of var(j, k), so this is interpreted as FALSE. + # If k is not in clause j but is in clause i, then var(i, k) is not a subset of var(j, k), so this is interpreted as TRUE. + # We initialize with TRUE and then search for instances where a symbol k is in both clauses i and j, and where var(i, k) *is* a subset of var(j, k). + # In that case, we set the entry to FALSE. + is_not_subset_of[[meta_idx_outer]] = matrix( + TRUE, + nrow = length(available), # indexed by meta_idx! + ncol = length(clause), + dimnames = list(NULL, names(clause)) + ) + # we are not a subset of ourselves + # (this prevents us from checking this later in on_updated_subset_relations; if we do check it there, we would eliminate the clause from itself) + is_not_subset_of[[meta_idx_outer]][meta_idx_outer, ] = FALSE + + for (meta_idx_inner in seq_len(meta_idx_outer - 1L)) { + ## need to refresh clause here, since it might have been shortened by unit propagation in an earlier iteration + clause = entries[[clause_idx]] + clause_idx_inner = available[[meta_idx_inner]] + if (eliminated[[clause_idx_inner]] || is_unit[[clause_idx_inner]]) next + clause_inner = entries[[clause_idx_inner]] + # note that even though we sort entries at the beginning, we can *not* rely on clause_inner to have smaller or equal length than clause, + # since unit elimination can change the length of clauses + + sci = names(clause_inner) + sci_sc_map = match(sci, names(clause), nomatch = 0L) + sci_names_in_common = which(sci_sc_map != 0L) + + # symbols that are not in common trivially get the matrix entry TRUE + # (they are not subsets of their counterpart in the other clause, since the other ones are empty) + updated_inso_inner = FALSE + updated_inso_outer = FALSE + + for (symbol_idx_inner in sci_names_in_common) { + symbol_idx_outer = sci_sc_map[[symbol_idx_inner]] + symbol = sci[[symbol_idx_inner]] + + range_inner = clause_inner[[symbol_idx_inner]] + range_outer = clause[[symbol_idx_outer]] + + inner_subset_of_outer = all(range_inner %in% range_outer) + outer_subset_of_inner = (inner_subset_of_outer && length(range_outer) == length(range_inner)) || all(range_outer %in% range_inner) + if (inner_subset_of_outer) { + updated_inso_inner = TRUE + # Avoid assigning TRUE to matrix that is initialized with TRUE. + # We index by column name here, since it is possible that clauses were shortened by + # unit propagation or self subsumption elimination somewhere on the way here + is_not_subset_of[[meta_idx_inner]][meta_idx_outer, symbol] = FALSE + } + if (outer_subset_of_inner) { + updated_inso_outer = TRUE + is_not_subset_of[[meta_idx_outer]][meta_idx_inner, symbol] = FALSE + } + } + # prefer to eliminate the outer loopo clause first, since we have already + # done more work for the inner loop clause (which comes earlier in 'entries') + if (updated_inso_inner) { + ousr = on_updated_subset_relations(meta_idx_inner, meta_idx_outer) + if (is.null(ousr)) break + if (ousr) return(return_entries(FALSE)) + if (eliminated[[clause_idx_inner]] || is_unit[[clause_idx_inner]]) next # yes this can happen. + } + if (updated_inso_outer) { + ousr = on_updated_subset_relations(meta_idx_outer, meta_idx_inner) + if (identical(ousr, TRUE)) return(return_entries(FALSE)) + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) break # probably this can happen if things cascade onwards when updating clause_inner + if (is.null(ousr)) next + } + } + } + + # Now for the big one: Asymmetric Hidden Literal Addition (Marijn et al.) + + # First, we do non-units, then we do units separately. + # We go big to small, since eliminating one clause could prevent us from eliminating other clauses, and all things being equal, we prefer eliminating long ones. + + # We only loop over the entries that have not been eliminated yet. + # We update `remaining_nonunit_entries` inside the loop whenever a clause is eliminated. + remaining_entries = which(!eliminated)[order(lengths(entries[!eliminated]), decreasing = TRUE)] + remaining_nonunit_entries = remaining_entries[seq_len(length(remaining_entries) - length(unit_domains))] + remaining_unit_entries = if (length(unit_domains)) remaining_entries[seq.int(length(remaining_entries) - length(unit_domains) + 1L, length(remaining_entries))] + + # iterating from large to small entries + for (clause_idx in remaining_nonunit_entries) { + clause = entries[[clause_idx]] + + # index inside `is_not_subset_of` + meta_idx = available_inverse[[clause_idx]] + remaining_other_entries = remaining_nonunit_entries[remaining_nonunit_entries != clause_idx] + + # we keep track of which clauses were used for HLA, since every other clause can only do that once. + was_used = logical(length(remaining_other_entries)) + + # for each of the other clauses, how many of their symbols are not a subset of the current clause? + not_subset_count = integer(length(remaining_other_entries)) + for (roe_idx in seq_along(remaining_other_entries)) { + # if we had set up is_not_subset_of as a 3-dim array, then the following could just have been a colSums over is_not_subset_of[, meta_idx, ] + # However, that array would take a lot of memory: N_clauses^2 x N_all_symbols; The current setup has N_clauses^2 x max(N_symbols_per_clause) + other_clause_idx = remaining_other_entries[[roe_idx]] + meta_idx_other = available_inverse[[other_clause_idx]] + not_subset_count[[roe_idx]] = sum(is_not_subset_of[[meta_idx_other]][meta_idx, ]) + } + repeat { + # we do HLA by looking for a clause that is a subset of the current clause w/r/t all except one symbol. + # We also only consider every clause at most once, since it won't have anything else to add a second time. + # No need to check for == 0 here: if it was the case before, then we eliminated the clause already. If it becomes the case during the loop, we check + # for it further down. + hla_clause_idx = match(TRUE, not_subset_count == 1L & !was_used) + if (is.na(hla_clause_idx)) break # no more clauses to consider: all are either used or have no_subset_count > 1 + clause_idx_other = remaining_other_entries[[hla_clause_idx]] + meta_idx_other = available_inverse[[clause_idx_other]] + symbol = colnames(is_not_subset_of[[meta_idx_other]])[is_not_subset_of[[meta_idx_other]][meta_idx, ]] + range_old = clause[[symbol]] + # new range of the symbol inside the clause: Union of old range and complement of that symbol's range in the other clause. + range_new = c(range_old, char_setdiff(universe[[symbol]], c(range_old, entries[[clause_idx_other]][[symbol]]))) + if (length(range_new) == length(universe[[symbol]])) { + # hidden tautology elimination + + # We still need the symbol registry (see below), so this can not be replaced by just `eliminated[[clause_idx]] = TRUE` + eliminate_clause_update_sr(clause_idx) + remaining_nonunit_entries = remaining_other_entries + break + } + # Now loop over clauses that also use the symbol, checking if they have one less `not_subset_count` because of that + # Note we do not need to check subsumption w/r/t units any more: All symbols are proper subsets w/r/t units at this point, + # so if adding the complement of one symbol to another made it a superset of a unit, the result was a tautology already. + for (updating_clause_meta_idx in available_inverse[symbol_registry[[symbol]]]) { + # we don't want to skip 'was_used' here, since we might still do hidden subsumption elimination with them. + if (is_not_subset_of[[updating_clause_meta_idx]][meta_idx, symbol] && + all(entries[[available[[updating_clause_meta_idx]]]][[symbol]] %in% range_new)) { + is_not_subset_of[[updating_clause_meta_idx]][meta_idx, symbol] = FALSE + roe_idx = match(available[[updating_clause_meta_idx]], remaining_other_entries) # I wished I didn't have to do this + not_subset_count[[roe_idx]] = not_subset_count[[roe_idx]] - 1L + if (not_subset_count[[roe_idx]] == 0L) { + # hidden subsumption elimination + eliminate_clause_update_sr(clause_idx) + remaining_nonunit_entries = remaining_other_entries + break + } + } + } + if (eliminated[[clause_idx]]) break # the break inside the for-loop above will not break the repeat loop + was_used[[hla_clause_idx]] = TRUE + clause[[symbol]] = range_new + } + } + + # We now do the same thing as above, only for units. + # Units are different, because they don't have the `is_not_subset_of` matrices. These are trivially constructed from + # The symbol registry: "is_not_subset_of" for unit relating to symbol `s` is TRUE for all symbols in a clause that are not `s`. + # We deliberately make use of `remaining_nonunit_entries` here, which has been updated in the loop above as nonunit-clauses were eliminated + delayedAssign("roe_inverse", match(seq_along(entries), remaining_nonunit_entries)) # only do this match()-call if it is actually needed + for (clause_idx in remaining_unit_entries) { + clause = entries[[clause_idx]] + unitsymbol = names(clause) + was_used = logical(length(remaining_nonunit_entries)) + # every clause that is not yet eliminated is a proper subset of the current unit. + # If it is length N and contains the unit symbol, then N - 1 of its symbols are not subsets; + # otherwise (if it does not contain the unit symbol), all N symbols are not subsets. + not_subset_count = lengths(entries[remaining_nonunit_entries]) - (remaining_nonunit_entries %in% symbol_registry[[unitsymbol]]) + + # corresponding to `is_not_subset_of` matrix; only construct this for entries where it is needed. + is_not_subset_of_unit = vector("list", length(remaining_nonunit_entries)) + + # The following loop is mostly identical to the loop above, only for units. + repeat { + hla_clause_idx = match(TRUE, not_subset_count == 1L & !was_used) + if (is.na(hla_clause_idx)) break # no more clauses to consider: all are either used or have no_subset_count > 1 + clause_idx_other = remaining_nonunit_entries[[hla_clause_idx]] + clause_other = entries[[clause_idx_other]] + if (is.null(is_not_subset_of_unit[[hla_clause_idx]])) { + is_not_subset_of_unit[[hla_clause_idx]] = structure(names(clause_other) != unitsymbol, names = names(clause_other)) + } + is_not_subset_entry = is_not_subset_of_unit[[hla_clause_idx]] + symbol = names(is_not_subset_entry)[is_not_subset_entry] + range_old = clause[[symbol]] + range_new = c(range_old, char_setdiff(universe[[symbol]], c(range_old, clause_other[[symbol]]))) + if (length(range_new) == length(universe[[symbol]])) { + # hidden tautology elimination + # no more need to update the unit registry + eliminated[[clause_idx]] = TRUE + break + } + # Now loop over clauses that also use the symbol, checking if they have one less `not_subset_count` because of that + for (updating_clause_idx in symbol_registry[[symbol]]) { + updating_hla_clause_idx = roe_inverse[[updating_clause_idx]] + if (is.null(is_not_subset_of_unit[[updating_hla_clause_idx]])) { + # Dynamically construct this entry if it is not set yet. + # We could delay this further, but that would make things even more complicated + updating_clause = entries[[updating_clause_idx]] + is_not_subset_of_unit[[updating_hla_clause_idx]] = structure(names(updating_clause) != unitsymbol, names = names(updating_clause)) + } + if (is_not_subset_of_unit[[updating_hla_clause_idx]][[symbol]] && + all(entries[[updating_clause_idx]][[symbol]] %in% range_new)) { + is_not_subset_of_unit[[updating_hla_clause_idx]][[symbol]] = FALSE + not_subset_count[[updating_hla_clause_idx]] = not_subset_count[[updating_hla_clause_idx]] - 1L + if (not_subset_count[[updating_hla_clause_idx]] == 0) { + # hidden subsumption elimination + eliminated[[clause_idx]] = TRUE + break + } + } + } + if (eliminated[[clause_idx]]) break # the break inside the for-loop above will not break the repeat loop + was_used[[hla_clause_idx]] = TRUE + clause[[symbol]] = range_new + } + } + + return_entries(entries[!eliminated]) +} From ccdca30d4afafc42090245bf4cca83848e70e240 Mon Sep 17 00:00:00 2001 From: mb706 Date: Sat, 21 Sep 2024 23:52:57 +0200 Subject: [PATCH 59/87] lets see where this got us --- R/CnfFormula_simplify2.R | 475 ++++++++++++++++++++------------------- 1 file changed, 240 insertions(+), 235 deletions(-) diff --git a/R/CnfFormula_simplify2.R b/R/CnfFormula_simplify2.R index b370e76b5..c22bcae24 100644 --- a/R/CnfFormula_simplify2.R +++ b/R/CnfFormula_simplify2.R @@ -60,7 +60,7 @@ simplify_cnf = function(entries, universe) { symbol_registry = new.env(parent = emptyenv()) is_not_subset_of = NULL # see further down - available_inverse = NULL # ditto + symbol_registry_ext = NULL # see further down ################################## ## Event-driven clause handling ## @@ -89,7 +89,10 @@ simplify_cnf = function(entries, universe) { unit = entries[[unit_idx]] nu = names(unit) ur = unit_registry[[nu]] - if (is.null(ur)) { + # it may be possible that we hidden subsumption eliminate a unit but get a new unit; for this case, we check whether ur is eliminated. + # In the eliminated-and-new-unit case, we do not need to worry about intersecting ranges, since the new unit will have been made a subset + # through unit propagation at this point. + if (is.null(ur) || eliminated[[ur]]) { unit_registry[[nu]] = unit_idx # environment assignment unit_domains[[nu]] = unit[[1L]] # environment assignment # this is init'd TRUE for those w/ length 1 at the start, we set it to TRUE for clauses where symbols were eliminated @@ -99,11 +102,17 @@ simplify_cnf = function(entries, universe) { # -> we keep the one we saw before but update it to the intersection. # the current one is eliminated prev_unit = unit_domains[[nu]] - unit_isct = prev_unit[prev_unit %in% unit[[1L]]] + # if we reached the is_not_subset_of part, we have the symbol registry set up and do unit propagation already, so + # we know the new unit is a subset of the old one. + unit_isct = if (is.null(is_not_subset_of)) prev_unit[prev_unit %in% unit[[1L]]] else unit[[1L]] if (!length(unit_isct)) return(TRUE) # signal that we have a contradiction and can exit entries[[ur]][[1L]] <<- (unit_domains[[nu]] = unit_isct) # update the *old* unit and unit_domains in one go. unit_domains is updated by-reference (environment) eliminated[[unit_idx]] <<- TRUE } + update_unit_range(unit_idx, nu) + } + + update_unit_range = function(unit_idx, unit_name) { # The symbol registry is empty at the start; the following happens when new units are added later use_inso = FALSE if (!is.null(is_not_subset_of)) { @@ -112,10 +121,10 @@ simplify_cnf = function(entries, universe) { use_inso = unit_idx_meta <= meta_idx_outer # .. but only if we have built the matrix up to the current index if (use_inso) { # if the unit is a subset of the other clause, we will never skip. - inso_column = is_not_subset_of[[unit_idx_meta]][, nu] + inso_column = is_not_subset_of[[unit_idx_meta]][, unit_name] } } - for (s_clause_idx in symbol_registry[[nu]]) { + for (s_clause_idx in symbol_registry[[unit_name]]) { # could have been eliminated by subsumption elimination during unit propagation of another clause # (we are not afraid of is_unit here, since we are the unit for the symbol here -- everything else that has the # symbol gets eliminated) @@ -124,11 +133,23 @@ simplify_cnf = function(entries, universe) { # if we already know that s_clause_idx[[nu]] is a subset of unit_idx, we can skip this # exception: unit_idx is *also* a subset, implying equality, in which case we will do subsumption elimination. s_clause_idx_meta = available_inverse[[s_clause_idx]] - if (s_clause_idx_meta <= meta_idx_outer && inso_column[[s_clause_idx_meta]] && !is_not_subset_of[[s_clause_idx_meta]][unit_idx_meta, nu]) next + if (s_clause_idx_meta <= meta_idx_outer && inso_column[[s_clause_idx_meta]] && !is_not_subset_of[[s_clause_idx_meta]][unit_idx_meta, unit_name]) next } - adr = apply_domain_restriction(s_clause_idx, nu, unit_domains[[nu]], TRUE) + adr = apply_domain_restriction(s_clause_idx, unit_name, unit_domains[[unit_name]], TRUE) if (identical(adr, TRUE)) return(TRUE) # forward contradiction signal } + if (!is.null(symbol_registry_ext)) { + ## we do not need to do unit propagation for the plus clauses, but we *do* need to check for unit subsumption. + # We do this here since eliminate_symbol_from_clause will not do this when a unit was generated. + unit_meta_idx = available_inverse[[unit_idx]] + for (meta_idx_plus in symbol_registry_ext[[unit_name]]) { + if (meta_idx_plus == unit_meta_idx) next + if (all(entries_ext[[meta_idx_plus]][[unit_name]] %in% unit_domains[[unit_name]])) { + # we are a subset of the other clause + eliminate_clause_update_sr(available[[meta_idx_plus]]) + } + } + } FALSE # no contradiction } @@ -145,8 +166,8 @@ simplify_cnf = function(entries, universe) { clause_symbol_length_before = length(clause[[symbol_idx]]) clause[[symbol_idx]] = char_intersect(clause[[symbol_idx]], restringent) if (length(clause[[symbol_idx]]) == length(restringent)) { - # If the lengths match, then the clause is a superset of the unit (since the intersections are equal) - # the clause is therefore subsumed by the unit + # If the lengths match, then the clause is a superset of the restringent (since the intersections are equal) + # the clause is therefore subsumed by the restringent -- unit elimination or (hidden) subsumption elimination eliminate_clause_update_sr(clause_idx) return(NULL) } @@ -154,6 +175,7 @@ simplify_cnf = function(entries, universe) { if (length(clause[[symbol_idx]]) == clause_symbol_length_before) return(FALSE) if (!length(clause[[symbol_idx]])) { # the symbol is not in the clause anymore + if (is_unit[[clause_idx]]) return(TRUE) # unit contradiction return(eliminate_symbol_from_clause(clause_idx, symbol)) } # clause was changed. @@ -163,24 +185,32 @@ simplify_cnf = function(entries, universe) { # We need to update the subset relations matrix, if it exists if (is.null(is_not_subset_of)) return(FALSE) + if (is_unit[[clause_idx]]) { + # restricting units only happens if the unit has a clause+, so we + # only worry about this once is_not_subset_of exists + # update_unit_range will check updated subset relations for unit subsumption elimination + return(update_unit_range(clause_idx, symbol)) + } + meta_idx = available_inverse[[clause_idx]] # meta_idx_outer is the index up to which we have built is_not_subset_of; if meta_idx > meta_idx_outer, then we haven't seen the clause yet. # we are not relying on the fact that as soon as is_not_subset_of is non-null, we will only get here for clauses for which # is_not_subset_of was built, because unit-propagation could be cascading from a unit elimination. if (meta_idx > meta_idx_outer) return(FALSE) - if (!is_unit_propagation) { - # we are not propagating units, so we need to update the subset relations in the other direction. - # we do this first, in case on_updated_subset_relations gets too eager later - idx_to_check = which(available[seq_len(meta_idx_outer)] %in% symbol_registry[[symbol]]) - for (other_meta_idx in idx_to_check) { - # was the other a subset of us before? that could have changed now. - if (!is_not_subset_of[[other_meta_idx]][meta_idx, symbol] && !all(entries[[available[[other_meta_idx]]]][[symbol]] %in% entries[[clause_idx]][[symbol]])) { - is_not_subset_of[[other_meta_idx]][meta_idx, symbol] <<- TRUE - # no need to call on_updated_subset_relations, since we are increasing rowsums, not decreasing them - } - } - } + ### TODO: I *THINK* this is not needed, since we only care about subset relations between clause and clause+, which only ever updates towards FALSE. + # if (!is_unit_propagation) { + # # we are not propagating units, so we need to update the subset relations in the other direction. + # # we do this first, in case on_updated_subset_relations gets too eager later + # idx_to_check = which(available[seq_len(meta_idx_outer)] %in% symbol_registry[[symbol]]) + # for (other_meta_idx in idx_to_check) { + # # was the other a subset of us before? that could have changed now. + # if (!is_not_subset_of[[other_meta_idx]][meta_idx, symbol] && !all(entries[[available[[other_meta_idx]]]][[symbol]] %in% entries[[clause_idx]][[symbol]])) { + # is_not_subset_of[[other_meta_idx]][meta_idx, symbol] <<- TRUE + # # no need to call on_updated_subset_relations, since we are increasing rowsums, not decreasing them + # } + # } + # } is_not_subset_of_col = match(symbol, colnames(is_not_subset_of[[meta_idx]])) # * We could now be a subset of things that we were not a subset of before, so we only need to check the TRUE entries and may be setting them to FALSE. @@ -193,25 +223,28 @@ simplify_cnf = function(entries, universe) { # --> hence `available %in% symbol_registry[[symbol]]` # * We only need to check up to the point where we have built is_not_subset_of # --> hence `available <= meta_idx_outer` - rows_to_check = which((is_not_subset_of[[meta_idx]][, is_not_subset_of_col] & available %in% symbol_registry[[symbol]])[seq_len(meta_idx_outer)]) - for (other_meta_idx in rows_to_check) { - clause_idx_other = available[[other_meta_idx]] + # * We do not need to check that meta_idx != other_meta_plus, since that row is initialized as FALSE + rows_to_check = which(is_not_subset_of[[meta_idx]][, is_not_subset_of_col] & available %in% symbol_registry_ext[[symbol]] & !is.na(not_subset_count[meta_idx, ])) + for (meta_idx_plus in rows_to_check) { + clause_idx_other = available[[meta_idx_plus]] # while we only get here for rows that are in the symbol_registry and therefore not eliminated / units, we need to check again since on_update_subset_relations() # can change this during the loop. - if (eliminated[[clause_idx_other]] || is_unit[[clause_idx_other]]) next + if (eliminated[[clause_idx_other]]) next + if (!is_not_subset_of[[meta_idx]][meta_idx_plus, is_not_subset_of_col]) next # check again, since on_update_subset_relations() can change this # when we get here, that means that the symbol exists both in clause_idx and in other_ref_this symbol, *and* we have seen both clauses # in the is_not_subset_of building process. # If this were not the case, then we would not need to change anything. - other_clause_range = entries[[available[[other_meta_idx]]]][[symbol]] + other_clause_range = entries_ext[[meta_idx_plus]][[symbol]] if (!all(entries[[clause_idx]][[symbol]] %in% other_clause_range)) next - # we are now a subset (and most likely were not before) - # ("most likely" because it could probably happen that we re-enter this part through some cascading elimination / propagation) - is_not_subset_of[[meta_idx]][other_meta_idx, is_not_subset_of_col] <<- FALSE - ousr = on_updated_subset_relations(meta_idx, other_meta_idx) - if (identical(ousr, TRUE)) return(TRUE) # forward contradiction signal. We don't care if other_meta_idx was eliminated. - if (eliminated[[clause_idx]]) return(NULL) # need to check more directly if things escalated somehow and clause_idx was eliminated indirectly + # we are now a subset and were not before. We know this, since we check that is TRUE *inside the loop* + is_not_subset_of[[meta_idx]][meta_idx_plus, is_not_subset_of_col] <<- FALSE + not_subset_count[meta_idx, meta_idx_plus] <<- (rowsum = not_subset_count[meta_idx, meta_idx_plus] - 1L) + if (rowsum > 2L) next + ousr = on_updated_subset_relations(meta_idx, meta_idx_plus, rowsum) + if (identical(ousr, TRUE)) return(TRUE) # forward contradiction signal. We don't care if meta_idx_plus was eliminated. + if (eliminated[[clause_idx]]) return(NULL) # need to check if things escalated somehow and clause_idx was eliminated indirectly } FALSE # no contradiction } @@ -246,23 +279,28 @@ simplify_cnf = function(entries, universe) { if (meta_idx > meta_idx_outer) return(FALSE) is_not_subset_of_col = match(symbol, colnames(is_not_subset_of[[meta_idx]])) - rows_changed = which(is_not_subset_of[[meta_idx]][, is_not_subset_of_col]) + rows_changed = which(is_not_subset_of[[meta_idx]][, is_not_subset_of_col] & available %in% symbol_registry_ext[[symbol]] & !is.na(not_subset_count[meta_idx, ])) + not_subset_count[meta_idx, rows_changed] <<- not_subset_count[meta_idx, rows_changed] - 1L is_not_subset_of[[meta_idx]][, is_not_subset_of_col] <<- FALSE - for (others_ref_this_symbol in available_inverse[sr]) { - if (others_ref_this_symbol <= meta_idx_outer) { # meta_idx_outer is the index up to which we have built is_not_subset_of - is_not_subset_of[[others_ref_this_symbol]][meta_idx, symbol] <<- TRUE - } - } + ## TODO: I think this is not necessary, since we only care about subset relations between clause and clause+, which only ever updates towards FALSE. + # for (others_ref_this_symbol in available_inverse[sr]) { + # if (others_ref_this_symbol <= meta_idx_outer) { # meta_idx_outer is the index up to which we have built is_not_subset_of + # is_not_subset_of[[others_ref_this_symbol]][meta_idx, symbol] <<- TRUE + # } + # } # we could have some leftover TRUEs from eliminated or unit-ed clauses - rows_changed_ids = available[rows_changed] - for (meta_idx_other in rows_changed[!eliminated[rows_changed_ids] & !is_unit[rows_changed_ids] & rows_changed <= meta_idx_outer]) { + + for (meta_idx_plus in rows_changed) { + ## TODO: maybe the following comment is obsolete, see above # We have to do this *after* we set the corresponding values to TRUE for others_ref_this_symbol, # since calling this could realistically change the symbol registry (e.g. if it leads to a symbol # being eliminated from other clauses). - clause_idx_other = available[[meta_idx_other]] + clause_idx_other = available[[meta_idx_plus]] # while we *do* restrict meta_idx_other in the for loop already, eliminated and is_unit can still change during the loop, so check here again - if (eliminated[[clause_idx_other]] || is_unit[[clause_idx_other]]) next - ousr = on_updated_subset_relations(meta_idx, meta_idx_other) + if (eliminated[[clause_idx_other]]) next + rowsum = not_subset_count[meta_idx, meta_idx_plus] + if (rowsum > 2L) next + ousr = on_updated_subset_relations(meta_idx, meta_idx_plus, rowsum) if (identical(ousr, TRUE)) return(TRUE) # on_updated_subset_relations could cascade down to eliminating meta_idx (i.e. clause_idx) if (eliminated[[clause_idx]]) return(NULL) @@ -270,37 +308,106 @@ simplify_cnf = function(entries, universe) { FALSE } + apply_hidden_literal_addition = function(meta_idx_plus, symbol, other_range) { + fullrange = unit_domains[[symbol]] + # The following is not necessary; the plus-clauses are only imaginary, and everything + # for which we add the complement will be a proper subset of the unit. + #> if (is.null(fullrange)) fullrange = universe[[symbol]] + #> range_old = entries_ext[[meta_idx_plus]][[symbol]] + + # hidden literal addition: we add the complement of the restricting symbol to the other clause. + if (is.null(range_old)) { + range_new = char_setdiff(fullrange, other_range) + # add to symbol_registry_ext + if (is.null(symbol_registry_ext[[symbol]])) { + symbol_registry_ext[[symbol]] = meta_idx_plus + } else { + symbol_registry_ext[[symbol]][[length(symbol_registry_ext[[symbol]]) + 1L]] = meta_idx_plus + } + } else { + range_new = c(range_old, char_setdiff(fullrange, c(range_old, other_range))) + if (length(range_new) == length(fullrange)) { + # hidden tautology elimination + eliminate_clause_update_sr(available[[meta_idx_plus]]) + return(NULL) + } + } + if (length(range_new) == length(range_old)) return(FALSE) + + entries_ext[[meta_idx_plus]][[symbol]] = range_new + + # update subset relations matrix. HLA only starts when the matrix exists, so no need to check for is.null(is_not_subset_of) + other_ref_symbol = available_inverse[symbol_registry[[symbol]]] + + # don't bother updating the ones we have not seen yet + for (meta_idx_other in other_ref_symbol[!is.na(not_subset_count[other_ref_symbol, meta_idx_plus]) & other_ref_symbol != meta_idx_plus]) { + idx_other = available[[meta_idx_other]] + if (eliminated[[idx_other]] || is_unit[[idx_other]]) next + if (!is_not_subset_of[[meta_idx_other]][meta_idx_plus, symbol]) next + + if (all(entries[[idx_other]][[symbol]] %in% entries[[meta_idx_plus]][[symbol]])) { + # we are a new subset of the other clause + is_not_subset_of[[meta_idx_other]][meta_idx_plus, symbol] <<- FALSE + not_subset_count[meta_idx_other, meta_idx_plus] <<- (rowsum = not_subset_count[meta_idx_other, meta_idx_plus] - 1L) + if (rowsum > 2L) next + ousr = on_updated_subset_relations(meta_idx_other, meta_idx_plus, rowsum) + if (is.null(ousr)) return(NULL) + if (ousr) return(TRUE) + } + } + + FALSE + } + # returns 'NULL' when meta_idx_other was eliminated (or possibly turned into a unit), # 'TRUE' for contradiction, 'FALSE' for nothing changed - on_updated_subset_relations = function(meta_idx, meta_idx_other) { - # the row `meta_idx_other` of `is_not_subset_of[[meta_idx]]` has been updated. + on_updated_subset_relations = function(meta_idx, meta_idx_plus, rowsum) { + # the row `meta_idx_plus` of `is_not_subset_of[[meta_idx]]` has been updated. # we now check whether we can apply subsumption elimination, or at least self-subsumption elimination, on `meta_idx`. - rowsum = sum(is_not_subset_of[[meta_idx]][meta_idx_other, ]) - if (rowsum > 1) return(FALSE) # nothing to do - if (rowsum == 0) { - eliminate_clause_update_sr(available[[meta_idx_other]]) + # rowsum = sum(is_not_subset_of[[meta_idx]][meta_idx_plus, ]) + if (rowsum > 2L) return(FALSE) # nothing to do + if (rowsum == 0L) { + eliminate_clause_update_sr(available[[meta_idx_plus]]) return(NULL) } - # rowsum == 1 - symbol_to_restrict = colnames(is_not_subset_of[[meta_idx]])[is_not_subset_of[[meta_idx]][meta_idx_other, ]] - # update clause and sc! - - # note we update meta_idx_other: we are currently subset of that other clause w/r/t all except one symbol. - # we can therefore intersect that last symbol in the other clause with the range of that symbol in the current clause. - # apply_domain_restriction will take care of eliminating the symbol if the range becomes empty. - # It could in theory even do subsumption, but we have already taken care of that above. - apply_domain_restriction(available[[meta_idx_other]], symbol_to_restrict, entries[[available[[meta_idx]]]][[symbol_to_restrict]], FALSE) - + if (rowsum == 1L) { + symbol_to_restrict = colnames(is_not_subset_of[[meta_idx]])[is_not_subset_of[[meta_idx]][meta_idx_plus, ]] + range_restricting = entries[[available[[meta_idx]]]][[symbol_to_restrict]] + + ahla = apply_hidden_literal_addition(meta_idx_plus, symbol_to_restrict, range_restricting) + if (is.null(ahla)) return(NULL) + if (ahla) return(TRUE) + + # update clause and sc! + # note we update meta_idx_plus: we are currently subset of that other clause w/r/t all except one symbol. + # we can therefore intersect that last symbol in the other clause with the range of that symbol in the current clause. + # apply_domain_restriction will take care of eliminating the symbol if the range becomes empty. + # It could in theory even do subsumption, but we have already taken care of that above. + return(apply_domain_restriction(available[[meta_idx_plus]], symbol_to_restrict, range_restricting, FALSE)) + } + # rowsum == 2 + # TODO + FALSE } # mark a clause as eliminated and update symbol registry # This is relatively safe to call, since it does not modify any other clauses and does not create new units or subset relationships. eliminate_clause_update_sr = function(clause_idx) { - if (is_unit[[clause_idx]]) stop("Bug in the code, this should never happen.") eliminated[[clause_idx]] <<- TRUE - for (s in names(entries[[clause_idx]])) { - sr = symbol_registry[[s]] - symbol_registry[[s]] = sr[sr != clause_idx] + # we could actually be a unit, after hidden literal addition. In that case, + # the unit is not entered in the symbol_registry, but it is in the symbol_registry_ext. + if (!is_unit[[clause_idx]]) { + for (s in names(entries[[clause_idx]])) { + sr = symbol_registry[[s]] + symbol_registry[[s]] = sr[sr != clause_idx] + } + } + if (!is.null(symbol_registry_ext)) { + meta_idx = available_inverse[[clause_idx]] + for (s in names(entries[[clause_idx]])) { + sr = symbol_registry_ext[[s]] + symbol_registry_ext[[s]] = sr[sr != meta_idx] + } } } @@ -354,7 +461,8 @@ simplify_cnf = function(entries, universe) { # we don't need to check for units, upon registration they are automatically removed, and they cannot help with self-subsumption or HLA available = which(!(eliminated | is_unit)) - available_inverse = match(seq_along(entries), available) + available_ext = c(available, which(is_unit)) + available_inverse = match(seq_along(entries), available_ext) # record for each clause whether it is a subset of another clause. # we record this for each symbol separately, so when a symbol gets self-subsumed, we can re-check others more quickly. @@ -363,6 +471,28 @@ simplify_cnf = function(entries, universe) { # note that as soon as is_not_subset_of is non-null, some other functions assume that meta_idx_outer is also defined. is_not_subset_of = vector("list", length(available)) + # not_subset_count[i, j]: how many symbols of clause i are not subset of clause_ext j? + # if this is 1, we can do self-subsumption elimination and HLA. + # if this is 2, we can do self-subsumption with a resolution. + not_subset_count = matrix(NA_integer_, nrow = length(available), ncol = length(available_ext)) + + # symbol registry for 'extended' clauses + symbol_registry_ext = new.env(hash = TRUE, parent = emptyenv(), size = length(length(symbol_registry) + 10)) + for (n in names(symbol_registry)) { + symbol_registry_ext[[n]] = available_inverse[symbol_registry[[n]]] + } + + for (su in names(unit_registry)) { + unit_idx = available_inverse[[unit_registry[[su]]]] + if (is.null(symbol_registry_ext[[su]])) { + symbol_registry_ext[[su]] = unit_idx + } else { + symbol_registry_ext[[su]][[length(symbol_registry_ext[[su]]) + 1L]] = unit_idx + } + } + + entries_ext = entries[available_ext] + for (meta_idx_outer in seq_along(available)) { clause_idx = available[[meta_idx_outer]] if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) next # may happen if we somehow turn something into a unit that eliminates a later clause @@ -374,7 +504,7 @@ simplify_cnf = function(entries, universe) { # We initialize with TRUE and then search for instances where a symbol k is in both clauses i and j, and where var(i, k) *is* a subset of var(j, k). # In that case, we set the entry to FALSE. is_not_subset_of[[meta_idx_outer]] = matrix( - TRUE, + NA, nrow = length(available), # indexed by meta_idx! ncol = length(clause), dimnames = list(NULL, names(clause)) @@ -383,197 +513,72 @@ simplify_cnf = function(entries, universe) { # (this prevents us from checking this later in on_updated_subset_relations; if we do check it there, we would eliminate the clause from itself) is_not_subset_of[[meta_idx_outer]][meta_idx_outer, ] = FALSE - for (meta_idx_inner in seq_len(meta_idx_outer - 1L)) { - ## need to refresh clause here, since it might have been shortened by unit propagation in an earlier iteration - clause = entries[[clause_idx]] - clause_idx_inner = available[[meta_idx_inner]] - if (eliminated[[clause_idx_inner]] || is_unit[[clause_idx_inner]]) next - clause_inner = entries[[clause_idx_inner]] + not_subset_count[meta_idx_outer, meta_idx_outer] = 0L + for (symbol_idx in seq_along(clause)) { + symbol = names(clause)[[symbol_idx]] + unit_idx = unit_registry[[symbol]] + if (!is.null(unit_idx)) { + not_subset_count[meta_idx_outer, available_inverse[[unit_idx]]] = length(clause) - 1L + is_not_subset_of[[meta_idx_outer]][available_inverse[[unit_idx]], symbol_idx] = FALSE + } + } + } + + for (meta_idx_outer in seq_along(available)) { + clause_idx = available[[meta_idx_outer]] + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) next # may happen if we somehow turn something into a unit that eliminates a later clause + + for (meta_idx_plus in seq_len(available)) { + if (meta_idx_plus == meta_idx_outer) next + clause_idx_inner = available[[meta_idx_plus]] + + if (eliminated[[clause_idx_inner]] || !is.na(not_subset_count[meta_idx_outer, meta_idx_plus])) next + clause_ext_inner = entries_ext[[meta_idx_plus]] # note that even though we sort entries at the beginning, we can *not* rely on clause_inner to have smaller or equal length than clause, # since unit elimination can change the length of clauses - sci = names(clause_inner) + ## need to refresh clause here, since it might have been shortened by unit propagation in an earlier iteration + clause = entries[[clause_idx]] + + sci = names(clause_ext_inner) sci_sc_map = match(sci, names(clause), nomatch = 0L) sci_names_in_common = which(sci_sc_map != 0L) + is_not_subset_of[[meta_idx_outer]][meta_idx_plus, !colnames(is_not_subset_of[[meta_idx_outer]]) %in% sci] = TRUE # symbols that are not in common trivially get the matrix entry TRUE # (they are not subsets of their counterpart in the other clause, since the other ones are empty) - updated_inso_inner = FALSE - updated_inso_outer = FALSE - + any_updated = FALSE for (symbol_idx_inner in sci_names_in_common) { symbol_idx_outer = sci_sc_map[[symbol_idx_inner]] symbol = sci[[symbol_idx_inner]] + if (!is.na(is_not_subset_of[[meta_idx_outer]][meta_idx_plus, symbol])) next + any_updated = TRUE - range_inner = clause_inner[[symbol_idx_inner]] + range_inner = clause_ext_inner[[symbol_idx_inner]] range_outer = clause[[symbol_idx_outer]] - inner_subset_of_outer = all(range_inner %in% range_outer) - outer_subset_of_inner = (inner_subset_of_outer && length(range_outer) == length(range_inner)) || all(range_outer %in% range_inner) - if (inner_subset_of_outer) { - updated_inso_inner = TRUE - # Avoid assigning TRUE to matrix that is initialized with TRUE. + outer_subset_of_inner = all(range_outer %in% range_inner) + inner_subset_of_outer = outer_subset_of_inner && meta_idx_plus > meta_idx_outer && !is_unit[[clause_idx_inner]] && length(range_outer) == length(range_inner) + if (inner_subset_of_outer && is.na(is_not_subset_of[[meta_idx_plus]][meta_idx_outer, symbol])) { + # We only assign FALSE here if we find equality (which we get for basically free from range_outer %in% range_inner && lengths are equal). + # Otherwise we leave the entry NA and set this value when meta_idx_plus is processed in the outer loop. # We index by column name here, since it is possible that clauses were shortened by # unit propagation or self subsumption elimination somewhere on the way here - is_not_subset_of[[meta_idx_inner]][meta_idx_outer, symbol] = FALSE - } - if (outer_subset_of_inner) { - updated_inso_outer = TRUE - is_not_subset_of[[meta_idx_outer]][meta_idx_inner, symbol] = FALSE + is_not_subset_of[[meta_idx_plus]][meta_idx_outer, symbol] = FALSE } + is_not_subset_of[[meta_idx_outer]][meta_idx_plus, symbol] = !outer_subset_of_inner } + if (!any_updated) next # prefer to eliminate the outer loopo clause first, since we have already # done more work for the inner loop clause (which comes earlier in 'entries') - if (updated_inso_inner) { - ousr = on_updated_subset_relations(meta_idx_inner, meta_idx_outer) - if (is.null(ousr)) break - if (ousr) return(return_entries(FALSE)) - if (eliminated[[clause_idx_inner]] || is_unit[[clause_idx_inner]]) next # yes this can happen. - } - if (updated_inso_outer) { - ousr = on_updated_subset_relations(meta_idx_outer, meta_idx_inner) - if (identical(ousr, TRUE)) return(return_entries(FALSE)) - if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) break # probably this can happen if things cascade onwards when updating clause_inner - if (is.null(ousr)) next - } - } - } - - # Now for the big one: Asymmetric Hidden Literal Addition (Marijn et al.) - - # First, we do non-units, then we do units separately. - # We go big to small, since eliminating one clause could prevent us from eliminating other clauses, and all things being equal, we prefer eliminating long ones. + rowsum = sum(is_not_subset_of[[meta_idx_outer]][meta_idx_plus, ]) + not_subset_count[meta_idx_outer, meta_idx_plus] = rowsum + if (rowsum > 2L) next + ousr = on_updated_subset_relations(meta_idx_outer, meta_idx_plus, rowsum) + if (is.null(ousr)) break + if (ousr) return(return_entries(FALSE)) + if (eliminated[[clause_idx_inner]] || is_unit[[clause_idx_inner]]) next # yes this can happen. - # We only loop over the entries that have not been eliminated yet. - # We update `remaining_nonunit_entries` inside the loop whenever a clause is eliminated. - remaining_entries = which(!eliminated)[order(lengths(entries[!eliminated]), decreasing = TRUE)] - remaining_nonunit_entries = remaining_entries[seq_len(length(remaining_entries) - length(unit_domains))] - remaining_unit_entries = if (length(unit_domains)) remaining_entries[seq.int(length(remaining_entries) - length(unit_domains) + 1L, length(remaining_entries))] - - # iterating from large to small entries - for (clause_idx in remaining_nonunit_entries) { - clause = entries[[clause_idx]] - - # index inside `is_not_subset_of` - meta_idx = available_inverse[[clause_idx]] - remaining_other_entries = remaining_nonunit_entries[remaining_nonunit_entries != clause_idx] - - # we keep track of which clauses were used for HLA, since every other clause can only do that once. - was_used = logical(length(remaining_other_entries)) - - # for each of the other clauses, how many of their symbols are not a subset of the current clause? - not_subset_count = integer(length(remaining_other_entries)) - for (roe_idx in seq_along(remaining_other_entries)) { - # if we had set up is_not_subset_of as a 3-dim array, then the following could just have been a colSums over is_not_subset_of[, meta_idx, ] - # However, that array would take a lot of memory: N_clauses^2 x N_all_symbols; The current setup has N_clauses^2 x max(N_symbols_per_clause) - other_clause_idx = remaining_other_entries[[roe_idx]] - meta_idx_other = available_inverse[[other_clause_idx]] - not_subset_count[[roe_idx]] = sum(is_not_subset_of[[meta_idx_other]][meta_idx, ]) - } - repeat { - # we do HLA by looking for a clause that is a subset of the current clause w/r/t all except one symbol. - # We also only consider every clause at most once, since it won't have anything else to add a second time. - # No need to check for == 0 here: if it was the case before, then we eliminated the clause already. If it becomes the case during the loop, we check - # for it further down. - hla_clause_idx = match(TRUE, not_subset_count == 1L & !was_used) - if (is.na(hla_clause_idx)) break # no more clauses to consider: all are either used or have no_subset_count > 1 - clause_idx_other = remaining_other_entries[[hla_clause_idx]] - meta_idx_other = available_inverse[[clause_idx_other]] - symbol = colnames(is_not_subset_of[[meta_idx_other]])[is_not_subset_of[[meta_idx_other]][meta_idx, ]] - range_old = clause[[symbol]] - # new range of the symbol inside the clause: Union of old range and complement of that symbol's range in the other clause. - range_new = c(range_old, char_setdiff(universe[[symbol]], c(range_old, entries[[clause_idx_other]][[symbol]]))) - if (length(range_new) == length(universe[[symbol]])) { - # hidden tautology elimination - - # We still need the symbol registry (see below), so this can not be replaced by just `eliminated[[clause_idx]] = TRUE` - eliminate_clause_update_sr(clause_idx) - remaining_nonunit_entries = remaining_other_entries - break - } - # Now loop over clauses that also use the symbol, checking if they have one less `not_subset_count` because of that - # Note we do not need to check subsumption w/r/t units any more: All symbols are proper subsets w/r/t units at this point, - # so if adding the complement of one symbol to another made it a superset of a unit, the result was a tautology already. - for (updating_clause_meta_idx in available_inverse[symbol_registry[[symbol]]]) { - # we don't want to skip 'was_used' here, since we might still do hidden subsumption elimination with them. - if (is_not_subset_of[[updating_clause_meta_idx]][meta_idx, symbol] && - all(entries[[available[[updating_clause_meta_idx]]]][[symbol]] %in% range_new)) { - is_not_subset_of[[updating_clause_meta_idx]][meta_idx, symbol] = FALSE - roe_idx = match(available[[updating_clause_meta_idx]], remaining_other_entries) # I wished I didn't have to do this - not_subset_count[[roe_idx]] = not_subset_count[[roe_idx]] - 1L - if (not_subset_count[[roe_idx]] == 0L) { - # hidden subsumption elimination - eliminate_clause_update_sr(clause_idx) - remaining_nonunit_entries = remaining_other_entries - break - } - } - } - if (eliminated[[clause_idx]]) break # the break inside the for-loop above will not break the repeat loop - was_used[[hla_clause_idx]] = TRUE - clause[[symbol]] = range_new - } - } - - # We now do the same thing as above, only for units. - # Units are different, because they don't have the `is_not_subset_of` matrices. These are trivially constructed from - # The symbol registry: "is_not_subset_of" for unit relating to symbol `s` is TRUE for all symbols in a clause that are not `s`. - # We deliberately make use of `remaining_nonunit_entries` here, which has been updated in the loop above as nonunit-clauses were eliminated - delayedAssign("roe_inverse", match(seq_along(entries), remaining_nonunit_entries)) # only do this match()-call if it is actually needed - for (clause_idx in remaining_unit_entries) { - clause = entries[[clause_idx]] - unitsymbol = names(clause) - was_used = logical(length(remaining_nonunit_entries)) - # every clause that is not yet eliminated is a proper subset of the current unit. - # If it is length N and contains the unit symbol, then N - 1 of its symbols are not subsets; - # otherwise (if it does not contain the unit symbol), all N symbols are not subsets. - not_subset_count = lengths(entries[remaining_nonunit_entries]) - (remaining_nonunit_entries %in% symbol_registry[[unitsymbol]]) - - # corresponding to `is_not_subset_of` matrix; only construct this for entries where it is needed. - is_not_subset_of_unit = vector("list", length(remaining_nonunit_entries)) - - # The following loop is mostly identical to the loop above, only for units. - repeat { - hla_clause_idx = match(TRUE, not_subset_count == 1L & !was_used) - if (is.na(hla_clause_idx)) break # no more clauses to consider: all are either used or have no_subset_count > 1 - clause_idx_other = remaining_nonunit_entries[[hla_clause_idx]] - clause_other = entries[[clause_idx_other]] - if (is.null(is_not_subset_of_unit[[hla_clause_idx]])) { - is_not_subset_of_unit[[hla_clause_idx]] = structure(names(clause_other) != unitsymbol, names = names(clause_other)) - } - is_not_subset_entry = is_not_subset_of_unit[[hla_clause_idx]] - symbol = names(is_not_subset_entry)[is_not_subset_entry] - range_old = clause[[symbol]] - range_new = c(range_old, char_setdiff(universe[[symbol]], c(range_old, clause_other[[symbol]]))) - if (length(range_new) == length(universe[[symbol]])) { - # hidden tautology elimination - # no more need to update the unit registry - eliminated[[clause_idx]] = TRUE - break - } - # Now loop over clauses that also use the symbol, checking if they have one less `not_subset_count` because of that - for (updating_clause_idx in symbol_registry[[symbol]]) { - updating_hla_clause_idx = roe_inverse[[updating_clause_idx]] - if (is.null(is_not_subset_of_unit[[updating_hla_clause_idx]])) { - # Dynamically construct this entry if it is not set yet. - # We could delay this further, but that would make things even more complicated - updating_clause = entries[[updating_clause_idx]] - is_not_subset_of_unit[[updating_hla_clause_idx]] = structure(names(updating_clause) != unitsymbol, names = names(updating_clause)) - } - if (is_not_subset_of_unit[[updating_hla_clause_idx]][[symbol]] && - all(entries[[updating_clause_idx]][[symbol]] %in% range_new)) { - is_not_subset_of_unit[[updating_hla_clause_idx]][[symbol]] = FALSE - not_subset_count[[updating_hla_clause_idx]] = not_subset_count[[updating_hla_clause_idx]] - 1L - if (not_subset_count[[updating_hla_clause_idx]] == 0) { - # hidden subsumption elimination - eliminated[[clause_idx]] = TRUE - break - } - } - } - if (eliminated[[clause_idx]]) break # the break inside the for-loop above will not break the repeat loop - was_used[[hla_clause_idx]] = TRUE - clause[[symbol]] = range_new } } From e75ae091590a68cd5446d2f8bab8e49fb68d8ff5 Mon Sep 17 00:00:00 2001 From: mb706 Date: Sun, 22 Sep 2024 01:29:15 +0200 Subject: [PATCH 60/87] passing the easy tests --- R/CnfFormula_simplify.R | 2 +- R/CnfFormula_simplify1.R | 2 +- R/CnfFormula_simplify2.R | 64 +++++++++++++---------- tests/testthat/test_CnfFormula.R | 2 +- tests/testthat/test_CnfFormula_simplify.R | 1 + 5 files changed, 39 insertions(+), 32 deletions(-) diff --git a/R/CnfFormula_simplify.R b/R/CnfFormula_simplify.R index c422c7d4e..f3661001d 100644 --- a/R/CnfFormula_simplify.R +++ b/R/CnfFormula_simplify.R @@ -3,7 +3,7 @@ -simplify_cnf_old = function(entries, universe) { +simplify_cnf_1 = function(entries, universe) { return_false = structure( FALSE, universe = universe, diff --git a/R/CnfFormula_simplify1.R b/R/CnfFormula_simplify1.R index b370e76b5..4fd03867e 100644 --- a/R/CnfFormula_simplify1.R +++ b/R/CnfFormula_simplify1.R @@ -1,6 +1,6 @@ -simplify_cnf = function(entries, universe) { +simplify_cnf_2 = function(entries, universe) { ################################# # Some vocabulary: # - `entries` is a list of `clauses`, which are named lists. diff --git a/R/CnfFormula_simplify2.R b/R/CnfFormula_simplify2.R index c22bcae24..081ae6539 100644 --- a/R/CnfFormula_simplify2.R +++ b/R/CnfFormula_simplify2.R @@ -107,7 +107,8 @@ simplify_cnf = function(entries, universe) { unit_isct = if (is.null(is_not_subset_of)) prev_unit[prev_unit %in% unit[[1L]]] else unit[[1L]] if (!length(unit_isct)) return(TRUE) # signal that we have a contradiction and can exit entries[[ur]][[1L]] <<- (unit_domains[[nu]] = unit_isct) # update the *old* unit and unit_domains in one go. unit_domains is updated by-reference (environment) - eliminated[[unit_idx]] <<- TRUE + eliminate_clause_update_sr(unit_idx) + unit_idx = ur } update_unit_range(unit_idx, nu) } @@ -144,9 +145,9 @@ simplify_cnf = function(entries, universe) { unit_meta_idx = available_inverse[[unit_idx]] for (meta_idx_plus in symbol_registry_ext[[unit_name]]) { if (meta_idx_plus == unit_meta_idx) next - if (all(entries_ext[[meta_idx_plus]][[unit_name]] %in% unit_domains[[unit_name]])) { + if (all(unit_domains[[unit_name]] %in% entries_ext[[meta_idx_plus]][[unit_name]])) { # we are a subset of the other clause - eliminate_clause_update_sr(available[[meta_idx_plus]]) + eliminate_clause_update_sr(available_ext[[meta_idx_plus]]) } } } @@ -224,13 +225,13 @@ simplify_cnf = function(entries, universe) { # * We only need to check up to the point where we have built is_not_subset_of # --> hence `available <= meta_idx_outer` # * We do not need to check that meta_idx != other_meta_plus, since that row is initialized as FALSE - rows_to_check = which(is_not_subset_of[[meta_idx]][, is_not_subset_of_col] & available %in% symbol_registry_ext[[symbol]] & !is.na(not_subset_count[meta_idx, ])) + rows_to_check = which(is_not_subset_of[[meta_idx]][, is_not_subset_of_col] & available_ext %in% symbol_registry_ext[[symbol]] & !is.na(not_subset_count[meta_idx, ])) for (meta_idx_plus in rows_to_check) { - clause_idx_other = available[[meta_idx_plus]] - # while we only get here for rows that are in the symbol_registry and therefore not eliminated / units, we need to check again since on_update_subset_relations() + clause_idx_other = available_ext[[meta_idx_plus]] + # while we only get here for rows that are in the symbol_registry and therefore not eliminated / units, we need to check again since on_updated_subset_relations() # can change this during the loop. if (eliminated[[clause_idx_other]]) next - if (!is_not_subset_of[[meta_idx]][meta_idx_plus, is_not_subset_of_col]) next # check again, since on_update_subset_relations() can change this + if (!is_not_subset_of[[meta_idx]][meta_idx_plus, is_not_subset_of_col]) next # check again, since on_updated_subset_relations() can change this # when we get here, that means that the symbol exists both in clause_idx and in other_ref_this symbol, *and* we have seen both clauses # in the is_not_subset_of building process. @@ -279,7 +280,7 @@ simplify_cnf = function(entries, universe) { if (meta_idx > meta_idx_outer) return(FALSE) is_not_subset_of_col = match(symbol, colnames(is_not_subset_of[[meta_idx]])) - rows_changed = which(is_not_subset_of[[meta_idx]][, is_not_subset_of_col] & available %in% symbol_registry_ext[[symbol]] & !is.na(not_subset_count[meta_idx, ])) + rows_changed = which(is_not_subset_of[[meta_idx]][, is_not_subset_of_col] & available_ext %in% symbol_registry_ext[[symbol]] & !is.na(not_subset_count[meta_idx, ])) not_subset_count[meta_idx, rows_changed] <<- not_subset_count[meta_idx, rows_changed] - 1L is_not_subset_of[[meta_idx]][, is_not_subset_of_col] <<- FALSE ## TODO: I think this is not necessary, since we only care about subset relations between clause and clause+, which only ever updates towards FALSE. @@ -295,7 +296,7 @@ simplify_cnf = function(entries, universe) { # We have to do this *after* we set the corresponding values to TRUE for others_ref_this_symbol, # since calling this could realistically change the symbol registry (e.g. if it leads to a symbol # being eliminated from other clauses). - clause_idx_other = available[[meta_idx_plus]] + clause_idx_other = available_ext[[meta_idx_plus]] # while we *do* restrict meta_idx_other in the for loop already, eliminated and is_unit can still change during the loop, so check here again if (eliminated[[clause_idx_other]]) next rowsum = not_subset_count[meta_idx, meta_idx_plus] @@ -309,11 +310,12 @@ simplify_cnf = function(entries, universe) { } apply_hidden_literal_addition = function(meta_idx_plus, symbol, other_range) { - fullrange = unit_domains[[symbol]] + fullrange = universe[[symbol]] # The following is not necessary; the plus-clauses are only imaginary, and everything # for which we add the complement will be a proper subset of the unit. + #> fullrange = unit_domains[[symbol]] #> if (is.null(fullrange)) fullrange = universe[[symbol]] - #> range_old = entries_ext[[meta_idx_plus]][[symbol]] + range_old = entries_ext[[meta_idx_plus]][[symbol]] # hidden literal addition: we add the complement of the restricting symbol to the other clause. if (is.null(range_old)) { @@ -328,13 +330,13 @@ simplify_cnf = function(entries, universe) { range_new = c(range_old, char_setdiff(fullrange, c(range_old, other_range))) if (length(range_new) == length(fullrange)) { # hidden tautology elimination - eliminate_clause_update_sr(available[[meta_idx_plus]]) + eliminate_clause_update_sr(available_ext[[meta_idx_plus]]) return(NULL) } } if (length(range_new) == length(range_old)) return(FALSE) - entries_ext[[meta_idx_plus]][[symbol]] = range_new + entries_ext[[meta_idx_plus]][[symbol]] <<- range_new # update subset relations matrix. HLA only starts when the matrix exists, so no need to check for is.null(is_not_subset_of) other_ref_symbol = available_inverse[symbol_registry[[symbol]]] @@ -345,7 +347,7 @@ simplify_cnf = function(entries, universe) { if (eliminated[[idx_other]] || is_unit[[idx_other]]) next if (!is_not_subset_of[[meta_idx_other]][meta_idx_plus, symbol]) next - if (all(entries[[idx_other]][[symbol]] %in% entries[[meta_idx_plus]][[symbol]])) { + if (all(entries[[idx_other]][[symbol]] %in% entries_ext[[meta_idx_plus]][[symbol]])) { # we are a new subset of the other clause is_not_subset_of[[meta_idx_other]][meta_idx_plus, symbol] <<- FALSE not_subset_count[meta_idx_other, meta_idx_plus] <<- (rowsum = not_subset_count[meta_idx_other, meta_idx_plus] - 1L) @@ -367,7 +369,7 @@ simplify_cnf = function(entries, universe) { # rowsum = sum(is_not_subset_of[[meta_idx]][meta_idx_plus, ]) if (rowsum > 2L) return(FALSE) # nothing to do if (rowsum == 0L) { - eliminate_clause_update_sr(available[[meta_idx_plus]]) + eliminate_clause_update_sr(available_ext[[meta_idx_plus]]) return(NULL) } if (rowsum == 1L) { @@ -383,7 +385,7 @@ simplify_cnf = function(entries, universe) { # we can therefore intersect that last symbol in the other clause with the range of that symbol in the current clause. # apply_domain_restriction will take care of eliminating the symbol if the range becomes empty. # It could in theory even do subsumption, but we have already taken care of that above. - return(apply_domain_restriction(available[[meta_idx_plus]], symbol_to_restrict, range_restricting, FALSE)) + return(apply_domain_restriction(available_ext[[meta_idx_plus]], symbol_to_restrict, range_restricting, FALSE)) } # rowsum == 2 # TODO @@ -505,7 +507,7 @@ simplify_cnf = function(entries, universe) { # In that case, we set the entry to FALSE. is_not_subset_of[[meta_idx_outer]] = matrix( NA, - nrow = length(available), # indexed by meta_idx! + nrow = length(available_ext), # indexed by meta_idx! ncol = length(clause), dimnames = list(NULL, names(clause)) ) @@ -514,21 +516,27 @@ simplify_cnf = function(entries, universe) { is_not_subset_of[[meta_idx_outer]][meta_idx_outer, ] = FALSE not_subset_count[meta_idx_outer, meta_idx_outer] = 0L + } + + for (meta_idx_outer in seq_along(available)) { + clause_idx = available[[meta_idx_outer]] + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) next # may happen if we somehow turn something into a unit that eliminates a later clause + for (symbol_idx in seq_along(clause)) { symbol = names(clause)[[symbol_idx]] unit_idx = unit_registry[[symbol]] if (!is.null(unit_idx)) { - not_subset_count[meta_idx_outer, available_inverse[[unit_idx]]] = length(clause) - 1L - is_not_subset_of[[meta_idx_outer]][available_inverse[[unit_idx]], symbol_idx] = FALSE + meta_idx_plus = available_inverse[[unit_idx]] + not_subset_count[meta_idx_outer, meta_idx_plus] = rowsum = length(clause) - 1L + is_not_subset_of[[meta_idx_outer]][meta_idx_plus, ] = TRUE + is_not_subset_of[[meta_idx_outer]][meta_idx_plus, symbol_idx] = FALSE + ousr = on_updated_subset_relations(meta_idx_outer, meta_idx_plus, rowsum) + if (identical(ousr, TRUE)) return(return_entries(FALSE)) + if (is.null(ousr)) break } } - } - - for (meta_idx_outer in seq_along(available)) { - clause_idx = available[[meta_idx_outer]] - if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) next # may happen if we somehow turn something into a unit that eliminates a later clause - for (meta_idx_plus in seq_len(available)) { + for (meta_idx_plus in seq_along(available)) { if (meta_idx_plus == meta_idx_outer) next clause_idx_inner = available[[meta_idx_plus]] @@ -575,10 +583,8 @@ simplify_cnf = function(entries, universe) { not_subset_count[meta_idx_outer, meta_idx_plus] = rowsum if (rowsum > 2L) next ousr = on_updated_subset_relations(meta_idx_outer, meta_idx_plus, rowsum) - if (is.null(ousr)) break - if (ousr) return(return_entries(FALSE)) - if (eliminated[[clause_idx_inner]] || is_unit[[clause_idx_inner]]) next # yes this can happen. - + if (identical(ousr, TRUE)) return(return_entries(FALSE)) + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) break # yes this can happen. } } diff --git a/tests/testthat/test_CnfFormula.R b/tests/testthat/test_CnfFormula.R index d605f03a1..5ab4ec491 100644 --- a/tests/testthat/test_CnfFormula.R +++ b/tests/testthat/test_CnfFormula.R @@ -570,7 +570,7 @@ test_that("CnfFormula performs all simplifications in a complex formula", { test_that("Brute-force test", { skip_on_cran() - +skip() u = CnfUniverse() W = CnfSymbol(u, "W", c("p", "q", "r")) X = CnfSymbol(u, "X", c("s", "t", "u")) diff --git a/tests/testthat/test_CnfFormula_simplify.R b/tests/testthat/test_CnfFormula_simplify.R index fae8fe3f9..6c9aebd69 100644 --- a/tests/testthat/test_CnfFormula_simplify.R +++ b/tests/testthat/test_CnfFormula_simplify.R @@ -4,6 +4,7 @@ test_that("CnfFormula Regression Tests", { skip_on_cran() + skip() testfile = xzfile(test_path("testdata", "cnf.xz")) testcases = readLines(testfile) close(testfile) From 731506ca9905246b478d597214819453605a2480 Mon Sep 17 00:00:00 2001 From: mb706 Date: Sun, 22 Sep 2024 05:35:11 +0200 Subject: [PATCH 61/87] turns out this is a dead end :shrug: --- R/CnfFormula_simplify1.R | 2 +- R/CnfFormula_simplify2.R | 42 +++++---- attic/experiments.R | 106 ++++++++++++++++++++++ attic/mvsat.mv | 18 +++- tests/testthat/test_CnfFormula.R | 9 +- tests/testthat/test_CnfFormula_simplify.R | 1 - 6 files changed, 155 insertions(+), 23 deletions(-) diff --git a/R/CnfFormula_simplify1.R b/R/CnfFormula_simplify1.R index 4fd03867e..b370e76b5 100644 --- a/R/CnfFormula_simplify1.R +++ b/R/CnfFormula_simplify1.R @@ -1,6 +1,6 @@ -simplify_cnf_2 = function(entries, universe) { +simplify_cnf = function(entries, universe) { ################################# # Some vocabulary: # - `entries` is a list of `clauses`, which are named lists. diff --git a/R/CnfFormula_simplify2.R b/R/CnfFormula_simplify2.R index 081ae6539..d2c76469e 100644 --- a/R/CnfFormula_simplify2.R +++ b/R/CnfFormula_simplify2.R @@ -1,6 +1,6 @@ -simplify_cnf = function(entries, universe) { +simplify_cnf_broken = function(entries, universe) { ################################# # Some vocabulary: # - `entries` is a list of `clauses`, which are named lists. @@ -379,7 +379,7 @@ simplify_cnf = function(entries, universe) { ahla = apply_hidden_literal_addition(meta_idx_plus, symbol_to_restrict, range_restricting) if (is.null(ahla)) return(NULL) if (ahla) return(TRUE) - + return(FALSE) # update clause and sc! # note we update meta_idx_plus: we are currently subset of that other clause w/r/t all except one symbol. # we can therefore intersect that last symbol in the other clause with the range of that symbol in the current clause. @@ -522,19 +522,27 @@ simplify_cnf = function(entries, universe) { clause_idx = available[[meta_idx_outer]] if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) next # may happen if we somehow turn something into a unit that eliminates a later clause - for (symbol_idx in seq_along(clause)) { - symbol = names(clause)[[symbol_idx]] + clause = entries[[clause_idx]] + colnames_inso = colnames(is_not_subset_of[[meta_idx_outer]]) + for (inso_idx in seq_along(colnames_inso)) { + symbol = colnames_inso[[inso_idx]] unit_idx = unit_registry[[symbol]] if (!is.null(unit_idx)) { meta_idx_plus = available_inverse[[unit_idx]] - not_subset_count[meta_idx_outer, meta_idx_plus] = rowsum = length(clause) - 1L is_not_subset_of[[meta_idx_outer]][meta_idx_plus, ] = TRUE - is_not_subset_of[[meta_idx_outer]][meta_idx_plus, symbol_idx] = FALSE + if (symbol %in% names(clause)) { + is_not_subset_of[[meta_idx_outer]][meta_idx_plus, symbol] = FALSE + not_subset_count[meta_idx_outer, meta_idx_plus] = rowsum = length(colnames_inso) - 1L + } else { + not_subset_count[meta_idx_outer, meta_idx_plus] = rowsum = length(colnames_inso) + } + if (rowsum > 2L) next ousr = on_updated_subset_relations(meta_idx_outer, meta_idx_plus, rowsum) if (identical(ousr, TRUE)) return(return_entries(FALSE)) - if (is.null(ousr)) break + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) break } } + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) break for (meta_idx_plus in seq_along(available)) { if (meta_idx_plus == meta_idx_outer) next @@ -551,32 +559,32 @@ simplify_cnf = function(entries, universe) { sci = names(clause_ext_inner) sci_sc_map = match(sci, names(clause), nomatch = 0L) sci_names_in_common = which(sci_sc_map != 0L) - is_not_subset_of[[meta_idx_outer]][meta_idx_plus, !colnames(is_not_subset_of[[meta_idx_outer]]) %in% sci] = TRUE + is_not_subset_of[[meta_idx_outer]][meta_idx_plus, !colnames(is_not_subset_of[[meta_idx_outer]]) %in% sci[sci_names_in_common]] = TRUE # symbols that are not in common trivially get the matrix entry TRUE # (they are not subsets of their counterpart in the other clause, since the other ones are empty) - any_updated = FALSE for (symbol_idx_inner in sci_names_in_common) { symbol_idx_outer = sci_sc_map[[symbol_idx_inner]] symbol = sci[[symbol_idx_inner]] if (!is.na(is_not_subset_of[[meta_idx_outer]][meta_idx_plus, symbol])) next - any_updated = TRUE range_inner = clause_ext_inner[[symbol_idx_inner]] range_outer = clause[[symbol_idx_outer]] outer_subset_of_inner = all(range_outer %in% range_inner) inner_subset_of_outer = outer_subset_of_inner && meta_idx_plus > meta_idx_outer && !is_unit[[clause_idx_inner]] && length(range_outer) == length(range_inner) - if (inner_subset_of_outer && is.na(is_not_subset_of[[meta_idx_plus]][meta_idx_outer, symbol])) { - # We only assign FALSE here if we find equality (which we get for basically free from range_outer %in% range_inner && lengths are equal). - # Otherwise we leave the entry NA and set this value when meta_idx_plus is processed in the outer loop. - # We index by column name here, since it is possible that clauses were shortened by - # unit propagation or self subsumption elimination somewhere on the way here - is_not_subset_of[[meta_idx_plus]][meta_idx_outer, symbol] = FALSE + if (inner_subset_of_outer) { + symbol_idx_inner = match(symbol, colnames(is_not_subset_of[[meta_idx_plus]])) + if (!is.na(symbol_idx_inner) && is.na(is_not_subset_of[[meta_idx_plus]][meta_idx_outer, symbol_idx_inner])) { + # We only assign FALSE here if we find equality (which we get for basically free from range_outer %in% range_inner && lengths are equal). + # Otherwise we leave the entry NA and set this value when meta_idx_plus is processed in the outer loop. + # We index by column name here, since it is possible that clauses were shortened by + # unit propagation or self subsumption elimination somewhere on the way here + is_not_subset_of[[meta_idx_plus]][meta_idx_outer, symbol_idx_inner] = FALSE + } } is_not_subset_of[[meta_idx_outer]][meta_idx_plus, symbol] = !outer_subset_of_inner } - if (!any_updated) next # prefer to eliminate the outer loopo clause first, since we have already # done more work for the inner loop clause (which comes earlier in 'entries') rowsum = sum(is_not_subset_of[[meta_idx_outer]][meta_idx_plus, ]) diff --git a/attic/experiments.R b/attic/experiments.R index 9791cfb04..33d5f8e30 100644 --- a/attic/experiments.R +++ b/attic/experiments.R @@ -983,5 +983,111 @@ quote( ) |> evaluate_expression(assignment) +# W X Y Z +# 28 p s v z +X %among% "s" & X %among% "u" & (Z %among% c("y", "a") | Z %among% "a") | +(Z %among% "a" & W %among% c("p", "r") | X %among% c("t", "s") & Z %among% "y") +evaluate_expression(formula_to_expression(X %among% "s" & X %among% "u" & (Z %among% c("y", "a") | Z %among% "a")), assignment) +evaluate_expression(formula_to_expression(Z %among% "a" & W %among% c("p", "r") | X %among% c("t", "s") & Z %among% "y"), assignment) + +evaluate_expression(formula_to_expression(Z %among% "a" & W %among% c("p", "r")), assignment) +evaluate_expression(formula_to_expression(X %among% c("t", "s") & Z %among% "y"), assignment) + +clause1 = Z %among% "a" & W %among% c("p", "r") +clause2 = X %among% c("t", "s") & Z %among% "y" + +evaluate_expression(formula_to_expression(clause1), assignment) +evaluate_expression(formula_to_expression(clause2), assignment) +evaluate_expression(formula_to_expression(clause1 | clause2), assignment) + +quote( +(Y %among% "w" & W %among% c("r", "q") | (X %among% "t" | Y %among% "v")) & (X %among% c("t", "s") | Z %among% "y" | W %among% "p" & Z %among% c("y", "z")) | +(W %among% c("p", "r") & Z %among% c("z", "a") | (W %among% "q" | W %among% "p")) & ((X %among% c("t", "s") | Y %among% "x") & (Z %among% "z" & X %among% c("u", "s"))) +) |> evaluate_expression(assignment) + +( +(Y %among% "w" & W %among% c("r", "q") | (X %among% "t" | Y %among% "v")) & (X %among% c("t", "s") | Z %among% "y" | W %among% "p" & Z %among% c("y", "z")) | +(W %among% c("p", "r") & Z %among% c("z", "a") | (W %among% "q" | W %among% "p")) & ((X %among% c("t", "s") | Y %among% "x") & (Z %among% "z" & X %among% c("u", "s"))) +) |> formula_to_expression() |> evaluate_expression(assignment) + + +c1 = (Y %among% "w" & W %among% c("r", "q") | (X %among% "t" | Y %among% "v")) & (X %among% c("t", "s") | Z %among% "y" | W %among% "p" & Z %among% c("y", "z")) +c2 = (W %among% c("p", "r") & Z %among% c("z", "a") | (W %among% "q" | W %among% "p")) & ((X %among% c("t", "s") | Y %among% "x") & (Z %among% "z" & X %among% c("u", "s"))) + +evaluate_expression(formula_to_expression(c1), assignment) +evaluate_expression(formula_to_expression(c2), assignment) +evaluate_expression(formula_to_expression(c1 | c2), assignment) +# W X Y Z +#17 q u w y + (Z ∈ {z, y} | X ∈ {t, s}) + & (Y ∈ {v, w} | X ∈ {t} | Z ∈ {z}) + & (X ∈ {s, t} | Y ∈ {x, v}) # !!! + & (W ∈ {r, q} | X ∈ {t} | Y ∈ {v} | Z ∈ {z}) + & (W ∈ {p} | X ∈ {s, t} | Z ∈ {y} | Y ∈ {x}) + + +[[1]] +CnfClause: + Z ∈ {z, y} | X ∈ {t, s} + +[[2]] +CnfClause: + Y ∈ {v, w} | X ∈ {t} | Z ∈ {z} + +[[3]] +CnfClause: + W ∈ {p} | X ∈ {t, s} | Z ∈ {z, y} + +[[4]] +CnfClause: + Z ∈ {y, z} | X ∈ {s, t} | Y ∈ {x} + +[[5]] +CnfClause: + W ∈ {r, q} | X ∈ {s, t} | Y ∈ {x, v} # this one removes W + +[[6]] +CnfClause: + W ∈ {r, q} | X ∈ {t} | Y ∈ {v} | Z ∈ {z} + +[[7]] +CnfClause: + W ∈ {p} | X ∈ {s, t} | Z ∈ {y} | Y ∈ {x} + +# W X Y Z +# 5 q t v y +quote( +Y %among% c("w", "x") & X %among% "t" | W %among% "p" & X %among% "u" | +(Z %among% c("y", "z") | Y %among% "x") & (Z %among% "z" & W %among% "q") +) |> # |> evaluate_expression(assignment) +eval() |> formula_to_expression() |> evaluate_expression(assignment) + +c1 = Y %among% c("w", "x") & X %among% "t" | W %among% "p" & X %among% "u" +c2 = (Z %among% c("y", "z") | Y %among% "x") & (Z %among% "z" & W %among% "q") + +evaluate_expression(formula_to_expression(c1), assignment) +evaluate_expression(formula_to_expression(c2), assignment) +evaluate_expression(formula_to_expression(c1 | c2), assignment) + + +> c1 +CnfFormula: + (X ∈ {t, u}) + & (W ∈ {p} | Y ∈ {w, x}) + & (X ∈ {u} | Y ∈ {w, x}) + & (W ∈ {p} | X ∈ {t}) +> c2 +CnfFormula: + (Z ∈ {z}) + & (W ∈ {q}) +> c1 | c2 +CnfFormula: + (X ∈ {t, u} | Z ∈ {z}) + & (X ∈ {t, u} | W ∈ {q}) + & (W ∈ {q, p} | X ∈ {t}) + & (W ∈ {p} | X ∈ {t} | Z ∈ {z}) + & (X ∈ {u} | Y ∈ {w, x} | W ∈ {q}) + + 5, 6, diff --git a/attic/mvsat.mv b/attic/mvsat.mv index 688cd309b..aa3faaa96 100644 --- a/attic/mvsat.mv +++ b/attic/mvsat.mv @@ -192,5 +192,21 @@ # & (Y ∈ {x} | Z ∈ {z}) # (in R-code, that is: `CnfFormula(list(X %among% "s" | Z %among% "y", Y %among% "x" | X %among% "t", Y %among% "x" | Z %among% "z"))` ) # Here, the first two clauses can restrict the 3rd clause to `Y %among% "x"`, which then subsumption-eliminates clauses 2 and 3. - +# +# Problems with this: +# - 1 (A %among% "a1" | B %among% c("b1", "b2")) & +# 2 (A %among% "a1" | B %among% "b2" | C %among% "c1") & +# 3 (A %among% "a2" | C %among% "c2") +# 2 will add C %among% c2 to 1+, which will let 3 remove A %among% "a1" from 1 by self-subsumption. +# The problem here is that, without A %among% "a1", the necessary C %among% c2 could not have been added. +# - 1 (A %among% "a1" | B %among% "b1" | D %among% "d1") & +# 2 (A %among% "a1" | C %among% "c1" | D %among% "d1") & +# 3 (A %among% "a1" | B %among% "b1" | C %among% "c2") & +# 4 (B %among% "b2" | C %among% "c1" | D %among% "d1") +# Clause 2 adds C %among% "c2" to clause 1, which then gets eliminated by 3. +# Clause 1 adds B %among% "b1" to clause 2, which then also gets eliminated by 4. +# However, the assignment A = "a2", B = "b2", C = "c2", D = "d2" is TRUE after removing clauses 1 and 2. +# The problem is that 2 and 3 imply 1, and 4 and 1 imply 2, but one cannot remove both. +# Int he old implementation, this is solved by the fact that we do HLA for one clause at a time, either +# eliminating it or not. diff --git a/tests/testthat/test_CnfFormula.R b/tests/testthat/test_CnfFormula.R index 5ab4ec491..26482332f 100644 --- a/tests/testthat/test_CnfFormula.R +++ b/tests/testthat/test_CnfFormula.R @@ -501,8 +501,11 @@ test_that("CnfFormula performs self-subsumption elimination correctly", { clause3 = CnfClause(list(CnfAtom(X, c("a")), CnfAtom(Y, c("e")))) # X ∈ {a} | Y ∈ {e} # Expected: self-subsumption should simplify the formula - expected_formula = CnfFormula(list(CnfClause(list(CnfAtom(X, c("a", "b")))), - CnfClause(list(CnfAtom(X, c("a", "c")))), CnfClause(list(CnfAtom(X, c("a")), CnfAtom(Y, c("e")))))) + expected_formula = CnfFormula(list( + CnfClause(list(CnfAtom(X, c("a", "b")))), + CnfClause(list(CnfAtom(X, c("a", "c")))), + CnfClause(list(CnfAtom(X, c("a")), CnfAtom(Y, c("e")))) + )) expect_true(all.equal(CnfFormula(list(clause1, clause2, clause3)), expected_formula)) expect_true(all.equal(CnfFormula(list(clause3, clause2, clause1)), expected_formula)) @@ -570,7 +573,7 @@ test_that("CnfFormula performs all simplifications in a complex formula", { test_that("Brute-force test", { skip_on_cran() -skip() + u = CnfUniverse() W = CnfSymbol(u, "W", c("p", "q", "r")) X = CnfSymbol(u, "X", c("s", "t", "u")) diff --git a/tests/testthat/test_CnfFormula_simplify.R b/tests/testthat/test_CnfFormula_simplify.R index 6c9aebd69..fae8fe3f9 100644 --- a/tests/testthat/test_CnfFormula_simplify.R +++ b/tests/testthat/test_CnfFormula_simplify.R @@ -4,7 +4,6 @@ test_that("CnfFormula Regression Tests", { skip_on_cran() - skip() testfile = xzfile(test_path("testdata", "cnf.xz")) testcases = readLines(testfile) close(testfile) From 27868a542ad2c02e9d98cc4915bde65e01d7cdb7 Mon Sep 17 00:00:00 2001 From: mb706 Date: Sun, 22 Sep 2024 18:19:27 +0200 Subject: [PATCH 62/87] remove broken version --- .../CnfFormula_simplify_greedy.R | 21 +++++++++++++++++-- 1 file changed, 19 insertions(+), 2 deletions(-) rename R/CnfFormula_simplify2.R => attic/CnfFormula_simplify_greedy.R (96%) diff --git a/R/CnfFormula_simplify2.R b/attic/CnfFormula_simplify_greedy.R similarity index 96% rename from R/CnfFormula_simplify2.R rename to attic/CnfFormula_simplify_greedy.R index d2c76469e..00d64bad2 100644 --- a/R/CnfFormula_simplify2.R +++ b/attic/CnfFormula_simplify_greedy.R @@ -1,6 +1,23 @@ - -simplify_cnf_broken = function(entries, universe) { +# this does not work: +# Problems with this: +# - 1 (A %among% "a1" | B %among% c("b1", "b2")) & +# 2 (A %among% "a1" | B %among% "b2" | C %among% "c1") & +# 3 (A %among% "a2" | C %among% "c2") +# 2 will add C %among% c2 to 1+, which will let 3 remove A %among% "a1" from 1 by self-subsumption. +# The problem here is that, without A %among% "a1", the necessary C %among% c2 could not have been added. +# - 1 (A %among% "a1" | B %among% "b1" | D %among% "d1") & +# 2 (A %among% "a1" | C %among% "c1" | D %among% "d1") & +# 3 (A %among% "a1" | B %among% "b1" | C %among% "c2") & +# 4 (B %among% "b2" | C %among% "c1" | D %among% "d1") +# Clause 2 adds C %among% "c2" to clause 1, which then gets eliminated by 3. +# Clause 1 adds B %among% "b1" to clause 2, which then also gets eliminated by 4. +# However, the assignment A = "a2", B = "b2", C = "c2", D = "d2" is TRUE after removing clauses 1 and 2. +# The problem is that 2 and 3 imply 1, and 4 and 1 imply 2, but one cannot remove both. +# Int he old implementation, this is solved by the fact that we do HLA for one clause at a time, either +# eliminating it or not. + +simplify_cnf_greedy = function(entries, universe) { ################################# # Some vocabulary: # - `entries` is a list of `clauses`, which are named lists. From 6e0ed18253fec62487d09fff51a5d3af59f19c66 Mon Sep 17 00:00:00 2001 From: mb706 Date: Sun, 22 Sep 2024 18:20:06 +0200 Subject: [PATCH 63/87] checkpoint --- R/CnfFormula_simplify2.R | 581 +++++++++++++++++++++++++++++++++++++++ 1 file changed, 581 insertions(+) create mode 100644 R/CnfFormula_simplify2.R diff --git a/R/CnfFormula_simplify2.R b/R/CnfFormula_simplify2.R new file mode 100644 index 000000000..b370e76b5 --- /dev/null +++ b/R/CnfFormula_simplify2.R @@ -0,0 +1,581 @@ + + +simplify_cnf = function(entries, universe) { + ################################# + # Some vocabulary: + # - `entries` is a list of `clauses`, which are named lists. + # - `clauses`' names are `symbols`, the values are the `ranges` of the symbols within that clause + # - `unit`: clause with single symbol + # Glossary of operations: + # - `unit propagation`: ranges of a symbol within a unit constitute the entire possible range of that symbol, + # so all clauses with that symbol are restricted to those values + # - `subsumption elimination`: if all ranges of all symbols within one clause are subsets of those ranges in another clause, + # then the other clause can be removed + # - `self-subsumption elimination`: if the ranges of all except one symbol within one clause are a subset of those ranges + # in another clause, then the remaining symbol in the latter clause can be intersected with the remaining symbol. + # - `hidden literal addition` (HLA): if the ranges of all except one symbol within one clause are a subset of those ranges + # in another clause, then the *complement* of the remaining symbol in the former clause can be added to the latter clause. + # This is basically the reverse of self-subsumption elimination. We do not use this to change clauses directly; + # the point here is that the resulting clause, even if applied repeatedly, is logically equivalent to the original clause within the formula: + # - `hidden subsumption elimination`: if applying HLA results in a clause that can be subsumed, the original clause can be removed. + # - `hidden tautology elimination`: if applying HLA results in a clause that is a tautology, the original clause can be removed. + # Note: 'Clause Elimination Procedures for CNF Formulas' by Marijn Heule et al. calls this "Asymmetric Hidden Literal Addition". + ################################# + + ######################## + ## Helper functions ## + ######################## + + # faster intersect, setdiff etc. that rely on x, y being characters with no duplicates + char_intersect = function(x, y) x[x %in% y] + char_setdiff = function(x, y) x[!x %in% y] + + # construct the CnfFormula return object + return_entries = function(entries) { + structure( + if (!length(entries)) TRUE else entries, + universe = universe, + class = "CnfFormula" + ) + } + + if (is.logical(entries)) return(return_entries(entries)) + + ######################## + ## Variable setup ## + ######################## + + entries = entries[order(lengths(entries))] + + is_unit = lengths(entries) == 1L + eliminated = logical(length(entries)) + + # maps symbol name -> the index of unit clauses + unit_registry = new.env(parent = emptyenv()) + + # maps symbol name -> their current domain + unit_domains = new.env(parent = emptyenv()) + + # maps symbol name -> the index of all non-unit clauses that refer to it + symbol_registry = new.env(parent = emptyenv()) + + is_not_subset_of = NULL # see further down + available_inverse = NULL # ditto + + ################################## + ## Event-driven clause handling ## + ################################## + # The following functions process the CNF clauses in various ways, + # depending on the current state of the entries. + # The state of the entries is updated in-place. + # The functions are then called in a loop, but they may also call each other. + # It is therefore important that they make the global state consistent before + # calling other functions, and that they are aware of how the global state *can* + # have changed upon their return. + # - entries[[clause_idx]] should be updated if necessary before other fns are called + # - symbol_registry[[symbol]] could have been updated + # - eliminated[[clause_idx]] could have been set to TRUE + # Since functions can call each other in different ways, `eliminated` could have changed even for clauses + # for which the other functions were not called. + + # Register a clause as a unit: + # - check if there is already a unit for this symbol + # - if not, add it to the unit registry + # - otherwise, intersect unit domains (and exit on contradiction) + # - apply unit propagation + # - We do *not* update the sybmol registry here; if the clause is registered for a given symbol, + # it has to be removed from there *before* calling this function. + register_unit = function(unit_idx) { + unit = entries[[unit_idx]] + nu = names(unit) + ur = unit_registry[[nu]] + if (is.null(ur)) { + unit_registry[[nu]] = unit_idx # environment assignment + unit_domains[[nu]] = unit[[1L]] # environment assignment + # this is init'd TRUE for those w/ length 1 at the start, we set it to TRUE for clauses where symbols were eliminated + is_unit[[unit_idx]] <<- TRUE + } else { + # two units refer to the same symbol + # -> we keep the one we saw before but update it to the intersection. + # the current one is eliminated + prev_unit = unit_domains[[nu]] + unit_isct = prev_unit[prev_unit %in% unit[[1L]]] + if (!length(unit_isct)) return(TRUE) # signal that we have a contradiction and can exit + entries[[ur]][[1L]] <<- (unit_domains[[nu]] = unit_isct) # update the *old* unit and unit_domains in one go. unit_domains is updated by-reference (environment) + eliminated[[unit_idx]] <<- TRUE + } + # The symbol registry is empty at the start; the following happens when new units are added later + use_inso = FALSE + if (!is.null(is_not_subset_of)) { + # if we have the is_not_subset_of matrix, we can use it to skip some checks + unit_idx_meta = available_inverse[[unit_idx]] + use_inso = unit_idx_meta <= meta_idx_outer # .. but only if we have built the matrix up to the current index + if (use_inso) { + # if the unit is a subset of the other clause, we will never skip. + inso_column = is_not_subset_of[[unit_idx_meta]][, nu] + } + } + for (s_clause_idx in symbol_registry[[nu]]) { + # could have been eliminated by subsumption elimination during unit propagation of another clause + # (we are not afraid of is_unit here, since we are the unit for the symbol here -- everything else that has the + # symbol gets eliminated) + if (eliminated[[s_clause_idx]]) next + if (use_inso) { + # if we already know that s_clause_idx[[nu]] is a subset of unit_idx, we can skip this + # exception: unit_idx is *also* a subset, implying equality, in which case we will do subsumption elimination. + s_clause_idx_meta = available_inverse[[s_clause_idx]] + if (s_clause_idx_meta <= meta_idx_outer && inso_column[[s_clause_idx_meta]] && !is_not_subset_of[[s_clause_idx_meta]][unit_idx_meta, nu]) next + } + adr = apply_domain_restriction(s_clause_idx, nu, unit_domains[[nu]], TRUE) + if (identical(adr, TRUE)) return(TRUE) # forward contradiction signal + } + FALSE # no contradiction + } + + # restrict the symbol in the clause to a given domain, e.g. a unit + # - clause_idx: index in entries + # - symbol: name of symbol to restrict + # - restringent: domain to restrict to + # returns TRUE if a contradiction was detected, NULL if the clause was eliminated + apply_domain_restriction = function(clause_idx, symbol, restringent, is_unit_propagation) { + clause = entries[[clause_idx]] + symbol_idx = match(symbol, names(clause)) + if (is.na(symbol_idx)) return(FALSE) + + clause_symbol_length_before = length(clause[[symbol_idx]]) + clause[[symbol_idx]] = char_intersect(clause[[symbol_idx]], restringent) + if (length(clause[[symbol_idx]]) == length(restringent)) { + # If the lengths match, then the clause is a superset of the unit (since the intersections are equal) + # the clause is therefore subsumed by the unit + eliminate_clause_update_sr(clause_idx) + return(NULL) + } + # clause was not changed + if (length(clause[[symbol_idx]]) == clause_symbol_length_before) return(FALSE) + if (!length(clause[[symbol_idx]])) { + # the symbol is not in the clause anymore + return(eliminate_symbol_from_clause(clause_idx, symbol)) + } + # clause was changed. + # We don't need to do this when we go the eliminate_symbol_from_clause route, since that will update the clause in any case. + entries[[clause_idx]] <<- clause + + # We need to update the subset relations matrix, if it exists + if (is.null(is_not_subset_of)) return(FALSE) + + meta_idx = available_inverse[[clause_idx]] + # meta_idx_outer is the index up to which we have built is_not_subset_of; if meta_idx > meta_idx_outer, then we haven't seen the clause yet. + # we are not relying on the fact that as soon as is_not_subset_of is non-null, we will only get here for clauses for which + # is_not_subset_of was built, because unit-propagation could be cascading from a unit elimination. + if (meta_idx > meta_idx_outer) return(FALSE) + + if (!is_unit_propagation) { + # we are not propagating units, so we need to update the subset relations in the other direction. + # we do this first, in case on_updated_subset_relations gets too eager later + idx_to_check = which(available[seq_len(meta_idx_outer)] %in% symbol_registry[[symbol]]) + for (other_meta_idx in idx_to_check) { + # was the other a subset of us before? that could have changed now. + if (!is_not_subset_of[[other_meta_idx]][meta_idx, symbol] && !all(entries[[available[[other_meta_idx]]]][[symbol]] %in% entries[[clause_idx]][[symbol]])) { + is_not_subset_of[[other_meta_idx]][meta_idx, symbol] <<- TRUE + # no need to call on_updated_subset_relations, since we are increasing rowsums, not decreasing them + } + } + } + + is_not_subset_of_col = match(symbol, colnames(is_not_subset_of[[meta_idx]])) + # * We could now be a subset of things that we were not a subset of before, so we only need to check the TRUE entries and may be setting them to FALSE. + # --> hence `is_not_subset_of[meta_idx][is_not_subset_of[meta_idx]` + # Note: we cannot address is_not_subset_of by symbol_idx, since clauses may get shorter but is_not_subset_of stays the same! + # * If this is unit propagation, we do not need to check other entries, since apply_domain_restriction happens to all clauses in a row, so the counter-side is updated in time. + # In particular, we do not need to worry that some other clause that was formerly our subset ceases to be our subset, since that other clause + # will also be restricted by the unit. + # * We can only ever set those entries to FALSE for which the other clause is in the symbol registry for the current symbol + # --> hence `available %in% symbol_registry[[symbol]]` + # * We only need to check up to the point where we have built is_not_subset_of + # --> hence `available <= meta_idx_outer` + rows_to_check = which((is_not_subset_of[[meta_idx]][, is_not_subset_of_col] & available %in% symbol_registry[[symbol]])[seq_len(meta_idx_outer)]) + for (other_meta_idx in rows_to_check) { + clause_idx_other = available[[other_meta_idx]] + # while we only get here for rows that are in the symbol_registry and therefore not eliminated / units, we need to check again since on_update_subset_relations() + # can change this during the loop. + if (eliminated[[clause_idx_other]] || is_unit[[clause_idx_other]]) next + + # when we get here, that means that the symbol exists both in clause_idx and in other_ref_this symbol, *and* we have seen both clauses + # in the is_not_subset_of building process. + # If this were not the case, then we would not need to change anything. + other_clause_range = entries[[available[[other_meta_idx]]]][[symbol]] + if (!all(entries[[clause_idx]][[symbol]] %in% other_clause_range)) next + + # we are now a subset (and most likely were not before) + # ("most likely" because it could probably happen that we re-enter this part through some cascading elimination / propagation) + is_not_subset_of[[meta_idx]][other_meta_idx, is_not_subset_of_col] <<- FALSE + ousr = on_updated_subset_relations(meta_idx, other_meta_idx) + if (identical(ousr, TRUE)) return(TRUE) # forward contradiction signal. We don't care if other_meta_idx was eliminated. + if (eliminated[[clause_idx]]) return(NULL) # need to check more directly if things escalated somehow and clause_idx was eliminated indirectly + } + FALSE # no contradiction + } + + # eliminate `symbol` from `clause_idx` + # returns 'NULL' for turned into a unit or eliminated, 'TRUE' for contradiction, 'FALSE' for nothing happened + eliminate_symbol_from_clause = function(clause_idx, symbol) { + clause = entries[[clause_idx]] + clause[[symbol]] = NULL + if (!length(clause)) return(TRUE) # signal that we have a contradiction and can exit + # remove from symbol registry of the symbol that went to 0 + sr = symbol_registry[[symbol]] + symbol_registry[[symbol]] = sr[sr != clause_idx] + + entries[[clause_idx]] <<- clause + if (length(clause) == 1) { + # new unit ahoy + # remove from symbol registry of the symbol that remains in the clause + # (since it is now a unit) + sr = symbol_registry[[names(clause)]] + symbol_registry[[names(clause)]] = sr[sr != clause_idx] + if (register_unit(clause_idx)) return(TRUE) # forward signal from register_unit: contradiction + return(NULL) # clause was turned into a unit + } + # clause was not turned into a unit, so we need to fill in is_not_subset_of + if (is.null(is_not_subset_of)) return(FALSE) # we have not started filling this one in + + meta_idx = available_inverse[[clause_idx]] + # meta_idx_outer is the index up to which we have built is_not_subset_of; if meta_idx > meta_idx_outer, then we haven't seen the clause yet. + # we are not relying on the fact that as soon as is_not_subset_of is non-null, we will only get here for clauses for which + # this was built, because it could be cascading from a unit elimination. + if (meta_idx > meta_idx_outer) return(FALSE) + + is_not_subset_of_col = match(symbol, colnames(is_not_subset_of[[meta_idx]])) + rows_changed = which(is_not_subset_of[[meta_idx]][, is_not_subset_of_col]) + is_not_subset_of[[meta_idx]][, is_not_subset_of_col] <<- FALSE + for (others_ref_this_symbol in available_inverse[sr]) { + if (others_ref_this_symbol <= meta_idx_outer) { # meta_idx_outer is the index up to which we have built is_not_subset_of + is_not_subset_of[[others_ref_this_symbol]][meta_idx, symbol] <<- TRUE + } + } + # we could have some leftover TRUEs from eliminated or unit-ed clauses + rows_changed_ids = available[rows_changed] + for (meta_idx_other in rows_changed[!eliminated[rows_changed_ids] & !is_unit[rows_changed_ids] & rows_changed <= meta_idx_outer]) { + # We have to do this *after* we set the corresponding values to TRUE for others_ref_this_symbol, + # since calling this could realistically change the symbol registry (e.g. if it leads to a symbol + # being eliminated from other clauses). + clause_idx_other = available[[meta_idx_other]] + # while we *do* restrict meta_idx_other in the for loop already, eliminated and is_unit can still change during the loop, so check here again + if (eliminated[[clause_idx_other]] || is_unit[[clause_idx_other]]) next + ousr = on_updated_subset_relations(meta_idx, meta_idx_other) + if (identical(ousr, TRUE)) return(TRUE) + # on_updated_subset_relations could cascade down to eliminating meta_idx (i.e. clause_idx) + if (eliminated[[clause_idx]]) return(NULL) + } + FALSE + } + + # returns 'NULL' when meta_idx_other was eliminated (or possibly turned into a unit), + # 'TRUE' for contradiction, 'FALSE' for nothing changed + on_updated_subset_relations = function(meta_idx, meta_idx_other) { + # the row `meta_idx_other` of `is_not_subset_of[[meta_idx]]` has been updated. + # we now check whether we can apply subsumption elimination, or at least self-subsumption elimination, on `meta_idx`. + rowsum = sum(is_not_subset_of[[meta_idx]][meta_idx_other, ]) + if (rowsum > 1) return(FALSE) # nothing to do + if (rowsum == 0) { + eliminate_clause_update_sr(available[[meta_idx_other]]) + return(NULL) + } + # rowsum == 1 + symbol_to_restrict = colnames(is_not_subset_of[[meta_idx]])[is_not_subset_of[[meta_idx]][meta_idx_other, ]] + # update clause and sc! + + # note we update meta_idx_other: we are currently subset of that other clause w/r/t all except one symbol. + # we can therefore intersect that last symbol in the other clause with the range of that symbol in the current clause. + # apply_domain_restriction will take care of eliminating the symbol if the range becomes empty. + # It could in theory even do subsumption, but we have already taken care of that above. + apply_domain_restriction(available[[meta_idx_other]], symbol_to_restrict, entries[[available[[meta_idx]]]][[symbol_to_restrict]], FALSE) + + } + + # mark a clause as eliminated and update symbol registry + # This is relatively safe to call, since it does not modify any other clauses and does not create new units or subset relationships. + eliminate_clause_update_sr = function(clause_idx) { + if (is_unit[[clause_idx]]) stop("Bug in the code, this should never happen.") + eliminated[[clause_idx]] <<- TRUE + for (s in names(entries[[clause_idx]])) { + sr = symbol_registry[[s]] + symbol_registry[[s]] = sr[sr != clause_idx] + } + } + + # process units: + # - populate unit_domains + # - start populating symbol_registry; it gets finished later down with non-units + # - also reduce duplicate units and replace them with their intersection + unit_queue = which(is_unit) + for (unit_idx in unit_queue) { + if (register_unit(unit_idx)) return(return_entries(FALSE)) + } + + # if there were only units, we are done + if (length(unit_queue) == length(entries)) return(return_entries(entries[!eliminated])) + + # process non-units: + # - eliminate entries subsumed by units + # - populate symbol_registry + # we sorted clauses by length, so we can skip ahead by length(unit_queue) + # At this point, everything after the unit_queue is not (yet) a unit. + # The seq.int here is "dangerous" and only allowed because we checked for length(unit_queue) == length(entries) above. + for (clause_idx in seq.int(length(unit_queue) + 1L, length(entries))) { + + # intersect with units and eliminate subsumed clauses + clause_symbol_isct = char_intersect(names(entries[[clause_idx]]), names(unit_domains)) + # apply unit-propagation early, since we otherwise run the risk of adding the clause + # to lots of symbol registry entries, only to remove it again right away + for (symbol in clause_symbol_isct) { + adr = apply_domain_restriction(clause_idx, symbol, unit_domains[[symbol]], TRUE) + if (is.null(adr)) break + if (adr) return(return_entries(FALSE)) + } + + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) next # could happen from unit propagation + + # do cache `clause = entries[[clause_idx]]` and refer to names(clause) here, + # since apply_domain_restriction might have removed symbols from the clause + for (symbol in names(entries[[clause_idx]])) { + sr_entry = symbol_registry[[symbol]] + if (is.null(sr_entry)) { + symbol_registry[[symbol]] = clause_idx + } else { + symbol_registry[[symbol]][[length(sr_entry) + 1L]] = clause_idx + } + } + } + + + # let's start with (self)-subsumption. + # this can also create new units etc. + + # we don't need to check for units, upon registration they are automatically removed, and they cannot help with self-subsumption or HLA + available = which(!(eliminated | is_unit)) + available_inverse = match(seq_along(entries), available) + + # record for each clause whether it is a subset of another clause. + # we record this for each symbol separately, so when a symbol gets self-subsumed, we can re-check others more quickly. + # Default is FALSE (not not a subset, i.e. it is a subset), this aligns with absent columns (which are subsets of everything) + # + # note that as soon as is_not_subset_of is non-null, some other functions assume that meta_idx_outer is also defined. + is_not_subset_of = vector("list", length(available)) + + for (meta_idx_outer in seq_along(available)) { + clause_idx = available[[meta_idx_outer]] + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) next # may happen if we somehow turn something into a unit that eliminates a later clause + clause = entries[[clause_idx]] + + # is_not_subset_of[[i]][j, k] records whether for symbol k, clause i is not a subset of clause j + # If k is not in clause i, then var(i, k) is trivially a subset of var(j, k), so this is interpreted as FALSE. + # If k is not in clause j but is in clause i, then var(i, k) is not a subset of var(j, k), so this is interpreted as TRUE. + # We initialize with TRUE and then search for instances where a symbol k is in both clauses i and j, and where var(i, k) *is* a subset of var(j, k). + # In that case, we set the entry to FALSE. + is_not_subset_of[[meta_idx_outer]] = matrix( + TRUE, + nrow = length(available), # indexed by meta_idx! + ncol = length(clause), + dimnames = list(NULL, names(clause)) + ) + # we are not a subset of ourselves + # (this prevents us from checking this later in on_updated_subset_relations; if we do check it there, we would eliminate the clause from itself) + is_not_subset_of[[meta_idx_outer]][meta_idx_outer, ] = FALSE + + for (meta_idx_inner in seq_len(meta_idx_outer - 1L)) { + ## need to refresh clause here, since it might have been shortened by unit propagation in an earlier iteration + clause = entries[[clause_idx]] + clause_idx_inner = available[[meta_idx_inner]] + if (eliminated[[clause_idx_inner]] || is_unit[[clause_idx_inner]]) next + clause_inner = entries[[clause_idx_inner]] + # note that even though we sort entries at the beginning, we can *not* rely on clause_inner to have smaller or equal length than clause, + # since unit elimination can change the length of clauses + + sci = names(clause_inner) + sci_sc_map = match(sci, names(clause), nomatch = 0L) + sci_names_in_common = which(sci_sc_map != 0L) + + # symbols that are not in common trivially get the matrix entry TRUE + # (they are not subsets of their counterpart in the other clause, since the other ones are empty) + updated_inso_inner = FALSE + updated_inso_outer = FALSE + + for (symbol_idx_inner in sci_names_in_common) { + symbol_idx_outer = sci_sc_map[[symbol_idx_inner]] + symbol = sci[[symbol_idx_inner]] + + range_inner = clause_inner[[symbol_idx_inner]] + range_outer = clause[[symbol_idx_outer]] + + inner_subset_of_outer = all(range_inner %in% range_outer) + outer_subset_of_inner = (inner_subset_of_outer && length(range_outer) == length(range_inner)) || all(range_outer %in% range_inner) + if (inner_subset_of_outer) { + updated_inso_inner = TRUE + # Avoid assigning TRUE to matrix that is initialized with TRUE. + # We index by column name here, since it is possible that clauses were shortened by + # unit propagation or self subsumption elimination somewhere on the way here + is_not_subset_of[[meta_idx_inner]][meta_idx_outer, symbol] = FALSE + } + if (outer_subset_of_inner) { + updated_inso_outer = TRUE + is_not_subset_of[[meta_idx_outer]][meta_idx_inner, symbol] = FALSE + } + } + # prefer to eliminate the outer loopo clause first, since we have already + # done more work for the inner loop clause (which comes earlier in 'entries') + if (updated_inso_inner) { + ousr = on_updated_subset_relations(meta_idx_inner, meta_idx_outer) + if (is.null(ousr)) break + if (ousr) return(return_entries(FALSE)) + if (eliminated[[clause_idx_inner]] || is_unit[[clause_idx_inner]]) next # yes this can happen. + } + if (updated_inso_outer) { + ousr = on_updated_subset_relations(meta_idx_outer, meta_idx_inner) + if (identical(ousr, TRUE)) return(return_entries(FALSE)) + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) break # probably this can happen if things cascade onwards when updating clause_inner + if (is.null(ousr)) next + } + } + } + + # Now for the big one: Asymmetric Hidden Literal Addition (Marijn et al.) + + # First, we do non-units, then we do units separately. + # We go big to small, since eliminating one clause could prevent us from eliminating other clauses, and all things being equal, we prefer eliminating long ones. + + # We only loop over the entries that have not been eliminated yet. + # We update `remaining_nonunit_entries` inside the loop whenever a clause is eliminated. + remaining_entries = which(!eliminated)[order(lengths(entries[!eliminated]), decreasing = TRUE)] + remaining_nonunit_entries = remaining_entries[seq_len(length(remaining_entries) - length(unit_domains))] + remaining_unit_entries = if (length(unit_domains)) remaining_entries[seq.int(length(remaining_entries) - length(unit_domains) + 1L, length(remaining_entries))] + + # iterating from large to small entries + for (clause_idx in remaining_nonunit_entries) { + clause = entries[[clause_idx]] + + # index inside `is_not_subset_of` + meta_idx = available_inverse[[clause_idx]] + remaining_other_entries = remaining_nonunit_entries[remaining_nonunit_entries != clause_idx] + + # we keep track of which clauses were used for HLA, since every other clause can only do that once. + was_used = logical(length(remaining_other_entries)) + + # for each of the other clauses, how many of their symbols are not a subset of the current clause? + not_subset_count = integer(length(remaining_other_entries)) + for (roe_idx in seq_along(remaining_other_entries)) { + # if we had set up is_not_subset_of as a 3-dim array, then the following could just have been a colSums over is_not_subset_of[, meta_idx, ] + # However, that array would take a lot of memory: N_clauses^2 x N_all_symbols; The current setup has N_clauses^2 x max(N_symbols_per_clause) + other_clause_idx = remaining_other_entries[[roe_idx]] + meta_idx_other = available_inverse[[other_clause_idx]] + not_subset_count[[roe_idx]] = sum(is_not_subset_of[[meta_idx_other]][meta_idx, ]) + } + repeat { + # we do HLA by looking for a clause that is a subset of the current clause w/r/t all except one symbol. + # We also only consider every clause at most once, since it won't have anything else to add a second time. + # No need to check for == 0 here: if it was the case before, then we eliminated the clause already. If it becomes the case during the loop, we check + # for it further down. + hla_clause_idx = match(TRUE, not_subset_count == 1L & !was_used) + if (is.na(hla_clause_idx)) break # no more clauses to consider: all are either used or have no_subset_count > 1 + clause_idx_other = remaining_other_entries[[hla_clause_idx]] + meta_idx_other = available_inverse[[clause_idx_other]] + symbol = colnames(is_not_subset_of[[meta_idx_other]])[is_not_subset_of[[meta_idx_other]][meta_idx, ]] + range_old = clause[[symbol]] + # new range of the symbol inside the clause: Union of old range and complement of that symbol's range in the other clause. + range_new = c(range_old, char_setdiff(universe[[symbol]], c(range_old, entries[[clause_idx_other]][[symbol]]))) + if (length(range_new) == length(universe[[symbol]])) { + # hidden tautology elimination + + # We still need the symbol registry (see below), so this can not be replaced by just `eliminated[[clause_idx]] = TRUE` + eliminate_clause_update_sr(clause_idx) + remaining_nonunit_entries = remaining_other_entries + break + } + # Now loop over clauses that also use the symbol, checking if they have one less `not_subset_count` because of that + # Note we do not need to check subsumption w/r/t units any more: All symbols are proper subsets w/r/t units at this point, + # so if adding the complement of one symbol to another made it a superset of a unit, the result was a tautology already. + for (updating_clause_meta_idx in available_inverse[symbol_registry[[symbol]]]) { + # we don't want to skip 'was_used' here, since we might still do hidden subsumption elimination with them. + if (is_not_subset_of[[updating_clause_meta_idx]][meta_idx, symbol] && + all(entries[[available[[updating_clause_meta_idx]]]][[symbol]] %in% range_new)) { + is_not_subset_of[[updating_clause_meta_idx]][meta_idx, symbol] = FALSE + roe_idx = match(available[[updating_clause_meta_idx]], remaining_other_entries) # I wished I didn't have to do this + not_subset_count[[roe_idx]] = not_subset_count[[roe_idx]] - 1L + if (not_subset_count[[roe_idx]] == 0L) { + # hidden subsumption elimination + eliminate_clause_update_sr(clause_idx) + remaining_nonunit_entries = remaining_other_entries + break + } + } + } + if (eliminated[[clause_idx]]) break # the break inside the for-loop above will not break the repeat loop + was_used[[hla_clause_idx]] = TRUE + clause[[symbol]] = range_new + } + } + + # We now do the same thing as above, only for units. + # Units are different, because they don't have the `is_not_subset_of` matrices. These are trivially constructed from + # The symbol registry: "is_not_subset_of" for unit relating to symbol `s` is TRUE for all symbols in a clause that are not `s`. + # We deliberately make use of `remaining_nonunit_entries` here, which has been updated in the loop above as nonunit-clauses were eliminated + delayedAssign("roe_inverse", match(seq_along(entries), remaining_nonunit_entries)) # only do this match()-call if it is actually needed + for (clause_idx in remaining_unit_entries) { + clause = entries[[clause_idx]] + unitsymbol = names(clause) + was_used = logical(length(remaining_nonunit_entries)) + # every clause that is not yet eliminated is a proper subset of the current unit. + # If it is length N and contains the unit symbol, then N - 1 of its symbols are not subsets; + # otherwise (if it does not contain the unit symbol), all N symbols are not subsets. + not_subset_count = lengths(entries[remaining_nonunit_entries]) - (remaining_nonunit_entries %in% symbol_registry[[unitsymbol]]) + + # corresponding to `is_not_subset_of` matrix; only construct this for entries where it is needed. + is_not_subset_of_unit = vector("list", length(remaining_nonunit_entries)) + + # The following loop is mostly identical to the loop above, only for units. + repeat { + hla_clause_idx = match(TRUE, not_subset_count == 1L & !was_used) + if (is.na(hla_clause_idx)) break # no more clauses to consider: all are either used or have no_subset_count > 1 + clause_idx_other = remaining_nonunit_entries[[hla_clause_idx]] + clause_other = entries[[clause_idx_other]] + if (is.null(is_not_subset_of_unit[[hla_clause_idx]])) { + is_not_subset_of_unit[[hla_clause_idx]] = structure(names(clause_other) != unitsymbol, names = names(clause_other)) + } + is_not_subset_entry = is_not_subset_of_unit[[hla_clause_idx]] + symbol = names(is_not_subset_entry)[is_not_subset_entry] + range_old = clause[[symbol]] + range_new = c(range_old, char_setdiff(universe[[symbol]], c(range_old, clause_other[[symbol]]))) + if (length(range_new) == length(universe[[symbol]])) { + # hidden tautology elimination + # no more need to update the unit registry + eliminated[[clause_idx]] = TRUE + break + } + # Now loop over clauses that also use the symbol, checking if they have one less `not_subset_count` because of that + for (updating_clause_idx in symbol_registry[[symbol]]) { + updating_hla_clause_idx = roe_inverse[[updating_clause_idx]] + if (is.null(is_not_subset_of_unit[[updating_hla_clause_idx]])) { + # Dynamically construct this entry if it is not set yet. + # We could delay this further, but that would make things even more complicated + updating_clause = entries[[updating_clause_idx]] + is_not_subset_of_unit[[updating_hla_clause_idx]] = structure(names(updating_clause) != unitsymbol, names = names(updating_clause)) + } + if (is_not_subset_of_unit[[updating_hla_clause_idx]][[symbol]] && + all(entries[[updating_clause_idx]][[symbol]] %in% range_new)) { + is_not_subset_of_unit[[updating_hla_clause_idx]][[symbol]] = FALSE + not_subset_count[[updating_hla_clause_idx]] = not_subset_count[[updating_hla_clause_idx]] - 1L + if (not_subset_count[[updating_hla_clause_idx]] == 0) { + # hidden subsumption elimination + eliminated[[clause_idx]] = TRUE + break + } + } + } + if (eliminated[[clause_idx]]) break # the break inside the for-loop above will not break the repeat loop + was_used[[hla_clause_idx]] = TRUE + clause[[symbol]] = range_new + } + } + + return_entries(entries[!eliminated]) +} From a41e60ccd35f9328c0c8ac6a6bc1df9e0f9d91f5 Mon Sep 17 00:00:00 2001 From: mb706 Date: Sun, 22 Sep 2024 20:52:40 +0200 Subject: [PATCH 64/87] tests pass --- R/CnfFormula_simplify1.R | 77 ++++++++++++++++++++++++---------------- R/CnfFormula_simplify2.R | 2 +- attic/experiments.R | 7 ++++ 3 files changed, 55 insertions(+), 31 deletions(-) diff --git a/R/CnfFormula_simplify1.R b/R/CnfFormula_simplify1.R index b370e76b5..e8bef9161 100644 --- a/R/CnfFormula_simplify1.R +++ b/R/CnfFormula_simplify1.R @@ -60,7 +60,6 @@ simplify_cnf = function(entries, universe) { symbol_registry = new.env(parent = emptyenv()) is_not_subset_of = NULL # see further down - available_inverse = NULL # ditto ################################## ## Event-driven clause handling ## @@ -172,12 +171,15 @@ simplify_cnf = function(entries, universe) { if (!is_unit_propagation) { # we are not propagating units, so we need to update the subset relations in the other direction. # we do this first, in case on_updated_subset_relations gets too eager later - idx_to_check = which(available[seq_len(meta_idx_outer)] %in% symbol_registry[[symbol]]) + # No need to compare against meta_idx_outer, since not_subset_count will be NA for larger indices.. + idx_to_check = which(!is.na(not_subset_count[, meta_idx]) & available %in% symbol_registry[[symbol]]) for (other_meta_idx in idx_to_check) { # was the other a subset of us before? that could have changed now. if (!is_not_subset_of[[other_meta_idx]][meta_idx, symbol] && !all(entries[[available[[other_meta_idx]]]][[symbol]] %in% entries[[clause_idx]][[symbol]])) { is_not_subset_of[[other_meta_idx]][meta_idx, symbol] <<- TRUE # no need to call on_updated_subset_relations, since we are increasing rowsums, not decreasing them + not_subset_count[other_meta_idx, meta_idx] <<- not_subset_count[other_meta_idx, meta_idx] + 1L + # no need to call the higher order self subsumption elimination handler here, since we need to do this anyways further down. } } } @@ -192,11 +194,11 @@ simplify_cnf = function(entries, universe) { # * We can only ever set those entries to FALSE for which the other clause is in the symbol registry for the current symbol # --> hence `available %in% symbol_registry[[symbol]]` # * We only need to check up to the point where we have built is_not_subset_of - # --> hence `available <= meta_idx_outer` - rows_to_check = which((is_not_subset_of[[meta_idx]][, is_not_subset_of_col] & available %in% symbol_registry[[symbol]])[seq_len(meta_idx_outer)]) + # --> hence the is.na() + rows_to_check = which(!is.na(not_subset_count[meta_idx, ]) & is_not_subset_of[[meta_idx]][, is_not_subset_of_col] & available %in% symbol_registry[[symbol]]) for (other_meta_idx in rows_to_check) { clause_idx_other = available[[other_meta_idx]] - # while we only get here for rows that are in the symbol_registry and therefore not eliminated / units, we need to check again since on_update_subset_relations() + # while we only get here for rows that are in the symbol_registry and therefore not eliminated / units, we need to check again since on_updated_subset_relations() # can change this during the loop. if (eliminated[[clause_idx_other]] || is_unit[[clause_idx_other]]) next @@ -209,10 +211,15 @@ simplify_cnf = function(entries, universe) { # we are now a subset (and most likely were not before) # ("most likely" because it could probably happen that we re-enter this part through some cascading elimination / propagation) is_not_subset_of[[meta_idx]][other_meta_idx, is_not_subset_of_col] <<- FALSE + not_subset_count[meta_idx, other_meta_idx] <<- (rowsum = not_subset_count[meta_idx, other_meta_idx] - 1L) + if (rowsum > 2L) next ousr = on_updated_subset_relations(meta_idx, other_meta_idx) if (identical(ousr, TRUE)) return(TRUE) # forward contradiction signal. We don't care if other_meta_idx was eliminated. if (eliminated[[clause_idx]]) return(NULL) # need to check more directly if things escalated somehow and clause_idx was eliminated indirectly } + # TODO: call on_domain_changed_handle_2nd_order_sse + # it is not a waste w/r/t the 'on_updated_subset_relations' call, since that one only deals with clauses for which the symbol is set to FALSE now, + # i.e. precisely the other clauses. FALSE # no contradiction } @@ -246,11 +253,15 @@ simplify_cnf = function(entries, universe) { if (meta_idx > meta_idx_outer) return(FALSE) is_not_subset_of_col = match(symbol, colnames(is_not_subset_of[[meta_idx]])) - rows_changed = which(is_not_subset_of[[meta_idx]][, is_not_subset_of_col]) + rows_changed = which(is_not_subset_of[[meta_idx]][, is_not_subset_of_col] & !is.na(not_subset_count[meta_idx, ])) is_not_subset_of[[meta_idx]][, is_not_subset_of_col] <<- FALSE - for (others_ref_this_symbol in available_inverse[sr]) { - if (others_ref_this_symbol <= meta_idx_outer) { # meta_idx_outer is the index up to which we have built is_not_subset_of - is_not_subset_of[[others_ref_this_symbol]][meta_idx, symbol] <<- TRUE + not_subset_count[meta_idx, rows_changed] <<- not_subset_count[meta_idx, rows_changed] - 1L + others_ref_this_symbol = available_inverse[sr] + # only where we have already set up is_not_subset_of + for (meta_idx_other in others_ref_this_symbol[!is.na(not_subset_count[others_ref_this_symbol, meta_idx])]) { + if (!is_not_subset_of[[meta_idx_other]][meta_idx, symbol]) { + is_not_subset_of[[meta_idx_other]][meta_idx, symbol] <<- TRUE + not_subset_count[meta_idx_other, meta_idx] <<- not_subset_count[meta_idx_other, meta_idx] + 1L } } # we could have some leftover TRUEs from eliminated or unit-ed clauses @@ -262,6 +273,7 @@ simplify_cnf = function(entries, universe) { clause_idx_other = available[[meta_idx_other]] # while we *do* restrict meta_idx_other in the for loop already, eliminated and is_unit can still change during the loop, so check here again if (eliminated[[clause_idx_other]] || is_unit[[clause_idx_other]]) next + if (not_subset_count[meta_idx, meta_idx_other] > 2L) next ousr = on_updated_subset_relations(meta_idx, meta_idx_other) if (identical(ousr, TRUE)) return(TRUE) # on_updated_subset_relations could cascade down to eliminating meta_idx (i.e. clause_idx) @@ -275,7 +287,7 @@ simplify_cnf = function(entries, universe) { on_updated_subset_relations = function(meta_idx, meta_idx_other) { # the row `meta_idx_other` of `is_not_subset_of[[meta_idx]]` has been updated. # we now check whether we can apply subsumption elimination, or at least self-subsumption elimination, on `meta_idx`. - rowsum = sum(is_not_subset_of[[meta_idx]][meta_idx_other, ]) + rowsum = not_subset_count[meta_idx, meta_idx_other] if (rowsum > 1) return(FALSE) # nothing to do if (rowsum == 0) { eliminate_clause_update_sr(available[[meta_idx_other]]) @@ -290,7 +302,7 @@ simplify_cnf = function(entries, universe) { # apply_domain_restriction will take care of eliminating the symbol if the range becomes empty. # It could in theory even do subsumption, but we have already taken care of that above. apply_domain_restriction(available[[meta_idx_other]], symbol_to_restrict, entries[[available[[meta_idx]]]][[symbol_to_restrict]], FALSE) - + # TODO: handle == 2 case } # mark a clause as eliminated and update symbol registry @@ -362,6 +374,12 @@ simplify_cnf = function(entries, universe) { # # note that as soon as is_not_subset_of is non-null, some other functions assume that meta_idx_outer is also defined. is_not_subset_of = vector("list", length(available)) + # not_subset_count[i, j]: how many symbols of clause i are not subset of clause j? + # if this is 1, we can do self-subsumption elimination and HLA. + # if this is 2, we can do self-subsumption with resolution. + # This is the same as sum(is_not_subset_of[[i]][j, ]) + not_subset_count = matrix(NA_integer_, nrow = length(available), ncol = length(available)) + for (meta_idx_outer in seq_along(available)) { clause_idx = available[[meta_idx_outer]] @@ -398,8 +416,6 @@ simplify_cnf = function(entries, universe) { # symbols that are not in common trivially get the matrix entry TRUE # (they are not subsets of their counterpart in the other clause, since the other ones are empty) - updated_inso_inner = FALSE - updated_inso_outer = FALSE for (symbol_idx_inner in sci_names_in_common) { symbol_idx_outer = sci_sc_map[[symbol_idx_inner]] @@ -411,26 +427,28 @@ simplify_cnf = function(entries, universe) { inner_subset_of_outer = all(range_inner %in% range_outer) outer_subset_of_inner = (inner_subset_of_outer && length(range_outer) == length(range_inner)) || all(range_outer %in% range_inner) if (inner_subset_of_outer) { - updated_inso_inner = TRUE # Avoid assigning TRUE to matrix that is initialized with TRUE. # We index by column name here, since it is possible that clauses were shortened by # unit propagation or self subsumption elimination somewhere on the way here is_not_subset_of[[meta_idx_inner]][meta_idx_outer, symbol] = FALSE } if (outer_subset_of_inner) { - updated_inso_outer = TRUE is_not_subset_of[[meta_idx_outer]][meta_idx_inner, symbol] = FALSE } } # prefer to eliminate the outer loopo clause first, since we have already # done more work for the inner loop clause (which comes earlier in 'entries') - if (updated_inso_inner) { + rowsum = sum(is_not_subset_of[[meta_idx_inner]][meta_idx_outer, ]) + not_subset_count[meta_idx_inner, meta_idx_outer] = rowsum + if (rowsum <= 2) { ousr = on_updated_subset_relations(meta_idx_inner, meta_idx_outer) if (is.null(ousr)) break if (ousr) return(return_entries(FALSE)) if (eliminated[[clause_idx_inner]] || is_unit[[clause_idx_inner]]) next # yes this can happen. } - if (updated_inso_outer) { + rowsum = sum(is_not_subset_of[[meta_idx_outer]][meta_idx_inner, ]) + not_subset_count[meta_idx_outer, meta_idx_inner] = rowsum + if (rowsum <= 2) { ousr = on_updated_subset_relations(meta_idx_outer, meta_idx_inner) if (identical(ousr, TRUE)) return(return_entries(FALSE)) if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) break # probably this can happen if things cascade onwards when updating clause_inner @@ -438,7 +456,6 @@ simplify_cnf = function(entries, universe) { } } } - # Now for the big one: Asymmetric Hidden Literal Addition (Marijn et al.) # First, we do non-units, then we do units separately. @@ -462,20 +479,20 @@ simplify_cnf = function(entries, universe) { was_used = logical(length(remaining_other_entries)) # for each of the other clauses, how many of their symbols are not a subset of the current clause? - not_subset_count = integer(length(remaining_other_entries)) - for (roe_idx in seq_along(remaining_other_entries)) { - # if we had set up is_not_subset_of as a 3-dim array, then the following could just have been a colSums over is_not_subset_of[, meta_idx, ] - # However, that array would take a lot of memory: N_clauses^2 x N_all_symbols; The current setup has N_clauses^2 x max(N_symbols_per_clause) - other_clause_idx = remaining_other_entries[[roe_idx]] - meta_idx_other = available_inverse[[other_clause_idx]] - not_subset_count[[roe_idx]] = sum(is_not_subset_of[[meta_idx_other]][meta_idx, ]) - } + not_subset_count_current = not_subset_count[available_inverse[remaining_other_entries], meta_idx] + # for (roe_idx in seq_along(remaining_other_entries)) { + # # if we had set up is_not_subset_of as a 3-dim array, then the following could just have been a colSums over is_not_subset_of[, meta_idx, ] + # # However, that array would take a lot of memory: N_clauses^2 x N_all_symbols; The current setup has N_clauses^2 x max(N_symbols_per_clause) + # other_clause_idx = remaining_other_entries[[roe_idx]] + # meta_idx_other = available_inverse[[other_clause_idx]] + # not_subset_count[[roe_idx]] = sum(is_not_subset_of[[meta_idx_other]][meta_idx, ]) + # } repeat { # we do HLA by looking for a clause that is a subset of the current clause w/r/t all except one symbol. # We also only consider every clause at most once, since it won't have anything else to add a second time. # No need to check for == 0 here: if it was the case before, then we eliminated the clause already. If it becomes the case during the loop, we check # for it further down. - hla_clause_idx = match(TRUE, not_subset_count == 1L & !was_used) + hla_clause_idx = match(TRUE, not_subset_count_current == 1L & !was_used) if (is.na(hla_clause_idx)) break # no more clauses to consider: all are either used or have no_subset_count > 1 clause_idx_other = remaining_other_entries[[hla_clause_idx]] meta_idx_other = available_inverse[[clause_idx_other]] @@ -491,7 +508,7 @@ simplify_cnf = function(entries, universe) { remaining_nonunit_entries = remaining_other_entries break } - # Now loop over clauses that also use the symbol, checking if they have one less `not_subset_count` because of that + # Now loop over clauses that also use the symbol, checking if they have one less `not_subset_count_current` because of that # Note we do not need to check subsumption w/r/t units any more: All symbols are proper subsets w/r/t units at this point, # so if adding the complement of one symbol to another made it a superset of a unit, the result was a tautology already. for (updating_clause_meta_idx in available_inverse[symbol_registry[[symbol]]]) { @@ -500,8 +517,8 @@ simplify_cnf = function(entries, universe) { all(entries[[available[[updating_clause_meta_idx]]]][[symbol]] %in% range_new)) { is_not_subset_of[[updating_clause_meta_idx]][meta_idx, symbol] = FALSE roe_idx = match(available[[updating_clause_meta_idx]], remaining_other_entries) # I wished I didn't have to do this - not_subset_count[[roe_idx]] = not_subset_count[[roe_idx]] - 1L - if (not_subset_count[[roe_idx]] == 0L) { + not_subset_count_current[[roe_idx]] = not_subset_count_current[[roe_idx]] - 1L + if (not_subset_count_current[[roe_idx]] == 0L) { # hidden subsumption elimination eliminate_clause_update_sr(clause_idx) remaining_nonunit_entries = remaining_other_entries diff --git a/R/CnfFormula_simplify2.R b/R/CnfFormula_simplify2.R index b370e76b5..4fd03867e 100644 --- a/R/CnfFormula_simplify2.R +++ b/R/CnfFormula_simplify2.R @@ -1,6 +1,6 @@ -simplify_cnf = function(entries, universe) { +simplify_cnf_2 = function(entries, universe) { ################################# # Some vocabulary: # - `entries` is a list of `clauses`, which are named lists. diff --git a/attic/experiments.R b/attic/experiments.R index 33d5f8e30..70476c668 100644 --- a/attic/experiments.R +++ b/attic/experiments.R @@ -1091,3 +1091,10 @@ CnfFormula: & (X ∈ {u} | Y ∈ {w, x} | W ∈ {q}) 5, 6, + + if (!is.null(is_not_subset_of) && any(!eliminated & !is_unit)) { + indices = available_inverse[!eliminated & !is_unit] + assert_true(all.equal(not_subset_count[indices, indices, drop = FALSE], + t(sapply(indices, function(i) sapply(indices, function(j) if (is.na(not_subset_count[i, j])) NA_integer_ else sum(is_not_subset_of[[i]][j, ])))) + )) + } From fbc4e54d81c52bbaf9b828b7a80daa823aba32f4 Mon Sep 17 00:00:00 2001 From: mb706 Date: Mon, 23 Sep 2024 01:11:03 +0200 Subject: [PATCH 65/87] lets see if this got us anywhere --- R/CnfFormula_simplify1.R | 160 +++++++++++++++++++++++++++++++++++++-- 1 file changed, 154 insertions(+), 6 deletions(-) diff --git a/R/CnfFormula_simplify1.R b/R/CnfFormula_simplify1.R index e8bef9161..8f57c79f6 100644 --- a/R/CnfFormula_simplify1.R +++ b/R/CnfFormula_simplify1.R @@ -29,7 +29,7 @@ simplify_cnf = function(entries, universe) { # faster intersect, setdiff etc. that rely on x, y being characters with no duplicates char_intersect = function(x, y) x[x %in% y] char_setdiff = function(x, y) x[!x %in% y] - + char_union = function(x, y) c(x, y[!y %in% x]) # construct the CnfFormula return object return_entries = function(entries) { structure( @@ -217,10 +217,10 @@ simplify_cnf = function(entries, universe) { if (identical(ousr, TRUE)) return(TRUE) # forward contradiction signal. We don't care if other_meta_idx was eliminated. if (eliminated[[clause_idx]]) return(NULL) # need to check more directly if things escalated somehow and clause_idx was eliminated indirectly } - # TODO: call on_domain_changed_handle_2nd_order_sse + # call on_domain_changed_handle_2nd_order_sse # it is not a waste w/r/t the 'on_updated_subset_relations' call, since that one only deals with clauses for which the symbol is set to FALSE now, # i.e. precisely the other clauses. - FALSE # no contradiction + on_update_range(meta_idx, symbol) } # eliminate `symbol` from `clause_idx` @@ -288,7 +288,14 @@ simplify_cnf = function(entries, universe) { # the row `meta_idx_other` of `is_not_subset_of[[meta_idx]]` has been updated. # we now check whether we can apply subsumption elimination, or at least self-subsumption elimination, on `meta_idx`. rowsum = not_subset_count[meta_idx, meta_idx_other] - if (rowsum > 1) return(FALSE) # nothing to do + if (rowsum > 2L) return(FALSE) # nothing to do + if (rowsum == 2L) { + hs2oo = handle_sse_2nd_order_twoend(meta_idx, meta_idx_other, NULL) + if (identical(hs2oo, TRUE)) return(TRUE) + clause_other = available[[meta_idx_other]] + if (eliminated[[clause_other]] || is_unit[[clause_other]]) return(NULL) + return(FALSE) + } if (rowsum == 0) { eliminate_clause_update_sr(available[[meta_idx_other]]) return(NULL) @@ -301,8 +308,149 @@ simplify_cnf = function(entries, universe) { # we can therefore intersect that last symbol in the other clause with the range of that symbol in the current clause. # apply_domain_restriction will take care of eliminating the symbol if the range becomes empty. # It could in theory even do subsumption, but we have already taken care of that above. - apply_domain_restriction(available[[meta_idx_other]], symbol_to_restrict, entries[[available[[meta_idx]]]][[symbol_to_restrict]], FALSE) - # TODO: handle == 2 case + adr = apply_domain_restriction(available[[meta_idx_other]], symbol_to_restrict, entries[[available[[meta_idx]]]][[symbol_to_restrict]], FALSE) + if (is.null(adr)) return(NULL) + if (adr) return(TRUE) + clause_idx = available[[meta_idx]] + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) return(FALSE) + hs2oo = handle_sse_2nd_order_oneend(meta_idx, meta_idx_other, symbol_to_restrict) + if (is.null(hs2oo)) return(NULL) + if (hs2oo) return(TRUE) + clause_other = available[[meta_idx_other]] + if (eliminated[[clause_other]] || is_unit[[clause_other]]) return(NULL) + FALSE + } + + # second order self-subsumption elimination + # this is called whenever the range of symbol in meta_idx shrinks, opening up the possibility for 2nd order self-subsumption. + # meta_idx is the clause that will remove symbol range from other clauses. + # returns NULL if meta_idx was eliminated, FALSE if no contradiction, TRUE if contradiction + on_update_range = function(meta_idx, symbol) { + ## assuming the symbol exists in meta_idx + # availability of symbol in the other clause is not necessary here! + # units don't need to be treated separately: + # - since they only work with 2 length-2-clauses that have both the same symbol: the one of the unit, and another one; in the other one they must be disjoint. + # - because of this, they will HS-eliminate the unit. + + inso_symbol_col = match(symbol, colnames(is_not_subset_of[[meta_idx]])) + potential_targets = which(is_not_subset_of[[meta_idx]][, inso_symbol_col] & !eliminated[available] & !is_unit[available] & !is.na(not_subset_count[meta_idx, ])) + + targets_while_oneend = potential_targets[not_subset_count[meta_idx, potential_targets] == 1L] + + for (meta_idx_target in targets_while_oneend) { + hs2oo = handle_sse_2nd_order_oneend(meta_idx, meta_idx_target, symbol) + if (is.null(hs2oo)) return(NULL) # meta_idx eliminated + if (hs2oo) return(TRUE) + } + + targets_while_twoend = potential_targets[not_subset_count[meta_idx, potential_targets] == 2L] + for (meta_idx_target in targets_while_twoend) { + hs2oo = handle_sse_2nd_order_twoend(meta_idx, meta_idx_target, symbol) + if (is.null(hs2oo)) return(NULL) # meta_idx eliminated + if (hs2oo) return(TRUE) + } + FALSE + } + + # meta_idx is not subset of meta_idx_target over 'symbol'. + # check if there are other clauses that are non-subsets of meta_idx_target for two symbols, one of which is 'symbol' as well. + # return NULL if clause_idx is eliminated. + handle_sse_2nd_order_oneend = function(meta_idx, meta_idx_target, symbol) { + # we don't need to check whether symbol is in meta_idx, since then it will automatically not be a non-subset of target + inso_symbol_col = match(symbol, colnames(is_not_subset_of[[meta_idx]])) + clause_idx = available[[meta_idx]] + symbol_clauses = symbol_registry[[symbol]] + symbol_clauses_meta = available_inverse[symbol_clauses] + + clause_idx_target = available[[meta_idx_target]] + # intersect on symbol with some other clause that has not_subset_count == 2, and where the target symbol is present in the garget + if (eliminated[[clause_idx_target]] || is_unit[[clause_idx_target]]) next + twoends = symbol_clauses_meta[not_subset_count[symbol_clauses_meta, meta_idx_target] == 2L] + for (meta_idx_twoend in twoends) { + # in every loop iteration, check our conditions again, since anything can happen when we do sse: + # target exists, is not a unit (these are checked outside the for loop as well as with `ts2o`), and exactly one symbol ("symbol") of meta_idx does not cover it. + if (not_subset_count[meta_idx, meta_idx_target] != 1L || !is_not_subset_of[[meta_idx]][meta_idx_target, inso_symbol_col]) break + clause_idx_twoend = available[[meta_idx_twoend]] + # now check that the meta_idx_twoend is still valid: + # exists, not a unit, it does not cover the target with exactly two symbols, one of which is `symbol` + if (eliminated[[clause_idx_twoend]] || is_unit[[clause_idx_twoend]] || + not_subset_count[meta_idx_twoend, meta_idx_target] != 2L) { + next + } + symbol_target = colnames(is_not_subset_of[[meta_idx_twoend]])[is_not_subset_of[[meta_idx_twoend]][meta_idx_target, ]] + symbol_target = symbol_target[symbol_target != symbol] + if (length(symbol_target) != 1L) next # this can happen if a previous loop changed the clause in some way + if (!symbol_target %in% names(entries[[clause_idx_target]])) next + # `symbol_target` is two symbols here: target and intersect + ts2o = try_sse_2nd_order(meta_idx, meta_idx_twoend, meta_idx_target, symbol, symbol_target) + if (identical(ts2o, TRUE)) return(TRUE) + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) return(NULL) + if (is.null(ts2o)) return(FALSE) # target was eliminated + } + FALSE + } + + handle_sse_2nd_order_twoend = function(meta_idx, meta_idx_target, symbol) { + clause_idx = available[[meta_idx]] + + clause_idx_target = available[[meta_idx_target]] + # check that meta_idx_target is still valid: not eliminated, not a unit, not_subset_count 2 w/r/t the target, one of which is still the symbol itself. + if (eliminated[[clause_idx_target]] || is_unit[[clause_idx_target]] || not_subset_count[meta_idx, meta_idx_target] != 2) next + inso_symbols_cols = which(is_not_subset_of[[meta_idx]][meta_idx_target, ]) + symbols_twoend = colnames(is_not_subset_of[[meta_idx]])[inso_symbols_cols] + if (!is.null(symbol) && !symbol %in% symbols_twoend) next + for (symbol_inner_idx in 1:2) { + symbol_inner = symbols_twoend[[symbol_inner_idx]] # the intersection symbol + symbol_other = symbols_twoend[[3 - symbol_inner_idx]] + # symbol_other must be present in the target clause, otherwise we can skip. + if (!symbol_other %in% names(entries[[clause_idx_target]])) next + symbol_inner_clauses_meta = available_inverse[symbol_registry[[symbol_inner]]] + # 'oneends' may either have 1 or 2 non-subset symbols, with both symbols equal in the latter case. + # We do this in both inner loops, since we switch on which one of them is the target. + oneends = symbol_inner_clauses_meta[not_subset_count[symbol_inner_clauses_meta, meta_idx_target] <= 2L] + for (meta_idx_oneend in oneends) { + # check if the twoend-bit broke + if (not_subset_count[meta_idx, meta_idx_target] != 2 || !all(is_not_subset_of[[meta_idx]][meta_idx_target, inso_symbols_cols])) break + + # check if theoneend-bit broke + clause_idx_oneend = available[[meta_idx_oneend]] + if (eliminated[[clause_idx_oneend]] || is_unit[[clause_idx_oneend]]) next + # so the 'oneend' thing may also overlap with 'twoend' on the other symbol. + # The trouble is that we cannot rely on both symbols being in is_not_subset_of[[meta_idx_oneend]]. + # We therefore get the columns, with '0' if one of the symbols is not there, and then check whether the two columns are the only + # two that are TRUE (where the sum may be either 1 or 2). + symbols_twoend_idx = match(symbols_twoend, colnames(is_not_subset_of[[meta_idx_oneend]]), nomatch = 0L) + if (not_subset_count[meta_idx_oneend, meta_idx_target] != sum(is_not_subset_of[[meta_idx_oneend]][meta_idx_target, symbols_twoend_idx])) { + next + } + if (!symbol_other %in% names(entries[[clause_idx_target]])) next + ts2o = try_sse_2nd_order(meta_idx_oneend, meta_idx, meta_idx_target, symbol_inner, symbol_other) + if (identical(ts2o, TRUE)) return(TRUE) + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) return(NULL) + if (is.null(ts2o)) return(FALSE) # target was eliminated + } + } + FALSE + } + + try_sse_2nd_order = function(meta_idx_oneend, meta_idx_twoends, meta_idx_target, symbol_intersect, symbol_target) { + ## assuming that symbol_target exists in meta_idx_target + ## assuming that meta_idx_oneend and meta_idx_twoends both have symbol_intersect, and that at least meta_idx_twoends has symbol_target + if (!all(is_not_subset_of[[meta_idx_target]][c(meta_idx_oneend, meta_idx_twoends), symbol_target])) return(FALSE) + idx_oneend = available[[meta_idx_oneend]] + idx_twoends = available[[meta_idx_twoends]] + idx_target = available[[meta_idx_target]] + # if (any(eliminated[c(idx_oneend, idx_twoends, idx_target)]) || any(is_unit[c(idx_oneend, idx_twoends, idx_target)])) return(FALSE) + clause_oneend = entries[[idx_oneend]] + clause_twoends = entries[[idx_twoends]] + + # only proceed if clause_oneend and clause_twoends are disjoint outside of clause_target, with respect to symbol_intersect + clause_oneend_symbol_intersect = clause_oneend[[symbol_intersect]] + if (any(clause_oneend_symbol_intersect %in% clause_twoends[[symbol_intersect]] & + !clause_oneend_symbol_intersect %in% entries[[idx_target]][[symbol_intersect]])) { + return(FALSE) + } + apply_domain_restriction(idx_target, symbol_target, char_union(clause_oneend[[symbol_target]], clause_twoends[[symbol_target]]), FALSE) } # mark a clause as eliminated and update symbol registry From 79c66fcb08b195ff7e7024538ab1e13dbebc56ef Mon Sep 17 00:00:00 2001 From: mb706 Date: Mon, 23 Sep 2024 01:18:52 +0200 Subject: [PATCH 66/87] difficult to believe that there are no problems --- R/CnfFormula_simplify1.R | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/R/CnfFormula_simplify1.R b/R/CnfFormula_simplify1.R index 8f57c79f6..1aff5786f 100644 --- a/R/CnfFormula_simplify1.R +++ b/R/CnfFormula_simplify1.R @@ -364,9 +364,9 @@ simplify_cnf = function(entries, universe) { clause_idx_target = available[[meta_idx_target]] # intersect on symbol with some other clause that has not_subset_count == 2, and where the target symbol is present in the garget - if (eliminated[[clause_idx_target]] || is_unit[[clause_idx_target]]) next + if (eliminated[[clause_idx_target]] || is_unit[[clause_idx_target]]) return(FALSE) twoends = symbol_clauses_meta[not_subset_count[symbol_clauses_meta, meta_idx_target] == 2L] - for (meta_idx_twoend in twoends) { + for (meta_idx_twoend in twoends[!is.na(twoends)]) { # twoends is NA for clauses that have not been processed yet # in every loop iteration, check our conditions again, since anything can happen when we do sse: # target exists, is not a unit (these are checked outside the for loop as well as with `ts2o`), and exactly one symbol ("symbol") of meta_idx does not cover it. if (not_subset_count[meta_idx, meta_idx_target] != 1L || !is_not_subset_of[[meta_idx]][meta_idx_target, inso_symbol_col]) break @@ -395,10 +395,10 @@ simplify_cnf = function(entries, universe) { clause_idx_target = available[[meta_idx_target]] # check that meta_idx_target is still valid: not eliminated, not a unit, not_subset_count 2 w/r/t the target, one of which is still the symbol itself. - if (eliminated[[clause_idx_target]] || is_unit[[clause_idx_target]] || not_subset_count[meta_idx, meta_idx_target] != 2) next + if (eliminated[[clause_idx_target]] || is_unit[[clause_idx_target]] || not_subset_count[meta_idx, meta_idx_target] != 2) return(FALSE) inso_symbols_cols = which(is_not_subset_of[[meta_idx]][meta_idx_target, ]) symbols_twoend = colnames(is_not_subset_of[[meta_idx]])[inso_symbols_cols] - if (!is.null(symbol) && !symbol %in% symbols_twoend) next + if (!is.null(symbol) && !symbol %in% symbols_twoend) return(FALSE) for (symbol_inner_idx in 1:2) { symbol_inner = symbols_twoend[[symbol_inner_idx]] # the intersection symbol symbol_other = symbols_twoend[[3 - symbol_inner_idx]] @@ -408,7 +408,7 @@ simplify_cnf = function(entries, universe) { # 'oneends' may either have 1 or 2 non-subset symbols, with both symbols equal in the latter case. # We do this in both inner loops, since we switch on which one of them is the target. oneends = symbol_inner_clauses_meta[not_subset_count[symbol_inner_clauses_meta, meta_idx_target] <= 2L] - for (meta_idx_oneend in oneends) { + for (meta_idx_oneend in oneends[!is.na(oneends)]) { # oneends is NA for clauses that have not been processed yet # check if the twoend-bit broke if (not_subset_count[meta_idx, meta_idx_target] != 2 || !all(is_not_subset_of[[meta_idx]][meta_idx_target, inso_symbols_cols])) break From d1d9b7f2b726518dee5ef74ca957c069af16cb36 Mon Sep 17 00:00:00 2001 From: mb706 Date: Mon, 23 Sep 2024 01:49:20 +0200 Subject: [PATCH 67/87] more tests --- tests/testthat/test_CnfFormula.R | 142 +++++++++++++++++++++++++++---- 1 file changed, 126 insertions(+), 16 deletions(-) diff --git a/tests/testthat/test_CnfFormula.R b/tests/testthat/test_CnfFormula.R index 26482332f..76a397390 100644 --- a/tests/testthat/test_CnfFormula.R +++ b/tests/testthat/test_CnfFormula.R @@ -571,6 +571,22 @@ test_that("CnfFormula performs all simplifications in a complex formula", { }) +formula_to_expression = function(formula) { + if (is.logical(formula)) return(c(formula)) + clause_exprs = lapply(as.CnfFormula(formula), function(clause) { + atom_exprs = lapply(clause, function(atom) { + substitute(symbol %among% values, list(symbol = as.name(atom$symbol), values = atom$values)) + }) + Reduce(function(x, y) substitute(x | y, list(x = x, y = y)), atom_exprs) + }) + Reduce(function(x, y) substitute(x & y, list(x = x, y = y)), clause_exprs) +} + +evaluate_expression = function(expression, assignment) { + substituted = do.call(substitute, list(expression, c(list("%among%" = quote(`%in%`)), assignment))) + eval(substituted, envir = baseenv()) +} + test_that("Brute-force test", { skip_on_cran() @@ -604,22 +620,6 @@ test_that("Brute-force test", { substitute(op(left_expr, right_expr), list(op = op, left_expr = left_expr, right_expr = right_expr)) } - formula_to_expression = function(formula) { - if (is.logical(formula)) return(c(formula)) - clause_exprs = lapply(as.CnfFormula(formula), function(clause) { - atom_exprs = lapply(clause, function(atom) { - substitute(symbol %among% values, list(symbol = as.name(atom$symbol), values = atom$values)) - }) - Reduce(function(x, y) substitute(x | y, list(x = x, y = y)), atom_exprs) - }) - Reduce(function(x, y) substitute(x & y, list(x = x, y = y)), clause_exprs) - } - - evaluate_expression = function(expression, assignment) { - substituted = do.call(substitute, list(expression, c(list("%among%" = quote(`%in%`)), assignment))) - eval(substituted, envir = baseenv()) - } - expression_weight = function(expression) { if (is.logical(expression)) return(0) sum(all.names(expression) %in% c("|", "&")) + 1 @@ -691,3 +691,113 @@ test_that("Brute-force test", { }) + +test_that("Constructed test cases", { + + u = CnfUniverse() + A = CnfSymbol(u, "A", c("a1", "a2", "a3", "a4")) + B = CnfSymbol(u, "B", c("b1", "b2", "b3", "b4")) + C = CnfSymbol(u, "C", c("c1", "c2", "c3", "c4")) + D = CnfSymbol(u, "D", c("d1", "d2", "d3", "d4")) + + varnames = names(u) + assignments = expand.grid(lapply(varnames, function(var) u[[var]]), stringsAsFactors = FALSE) + colnames(assignments) = varnames + +# greedy self-subsumption eliminatoin fails for the following: + original = quote((A %among% "a1" | B %among% c("b1", "b2")) & (A %among% "a1" | B %among% "b2" | C %among% "c1") & (A %among% "a2" | C %among% "c2")) + + simplified = CnfFormula(list( + CnfClause(list(CnfAtom(A, c("a1")), CnfAtom(B, c("b1", "b2")))), + CnfClause(list(CnfAtom(A, c("a1")), CnfAtom(B, c("b2")), CnfAtom(C, c("c1")))), + CnfClause(list(CnfAtom(A, c("a2")), CnfAtom(C, c("c2")))) + )) + + expect_equal(evaluate_expression(formula_to_expression(simplified), assignments), + evaluate_expression(original, assignments)) + + +## exactly one of the clauses in the following is eliminated +# - 1 (A %among% "a1" | B %among% "b1" | D %among% "d1") & +# 2 (A %among% "a1" | C %among% "c1" | D %among% "d1") & +# 3 (A %among% "a1" | B %among% "b1" | C %among% "c2") & +# 4 (B %among% "b2" | C %among% "c1" | D %among% "d1") + + original = quote( + (A %among% "a1" | B %among% "b1" | D %among% "d1") & + (A %among% "a1" | C %among% "c1" | D %among% "d1") & + (A %among% "a1" | B %among% "b1" | C %among% "c2") & + (B %among% "b2" | C %among% "c1" | D %among% "d1") + ) + + simplified = CnfFormula(list( + CnfClause(list(CnfAtom(A, c("a1")), CnfAtom(B, c("b1")), CnfAtom(D, c("d1")))), + CnfClause(list(CnfAtom(A, c("a1")), CnfAtom(C, c("c1")), CnfAtom(D, c("d1")))), + CnfClause(list(CnfAtom(A, c("a1")), CnfAtom(B, c("b1")), CnfAtom(C, c("c2")))), + CnfClause(list(CnfAtom(B, c("b2")), CnfAtom(C, c("c1")), CnfAtom(D, c("d1")))) + )) + + expect_equal(length(as.list(simplified)), 3) + + expect_equal(evaluate_expression(formula_to_expression(simplified), assignments), + evaluate_expression(original, assignments)) + + +# 1 A %among% c("a1", "a2") | B %among% "b1" | C %among% c("c1", "c2") +# 2 B %among% c("b1", "b2") | C %among% c("c1", "c3") +# 3 A %among% c("a1", "a2") | B %among% c("b1", "b3") +# 4 A %among% "a2" | B %among% "b3" | D %among% "d1" +# 5 A %among% "a1" | B %among% "b3" | D %among% c("d2", "d3") +# - clause 3 adds 'b2' to clause 1; clause 2 can then restrict clause 1 to 'c1' +# - in other words: clauses 2 + 3 combine on symbol B to form A %among% c("a1", "a2") | C %among% c("c1", "c3") +# with respect to clause 1 (which conditions on B %among% "b1") +# - however, clauses 4 and 5 eliminate clause 3 through hidden subsumption elimination +# - at least B %among% "b1" can be removed from 1 by combining 4 and 5 over D., even if 3 is not present. + + original = quote( + (A %among% c("a1", "a2") | B %among% "b1" | C %among% c("c1", "c2")) & + (B %among% c("b1", "b2") | C %among% c("c1", "c3")) & + (A %among% c("a1", "a2") | B %among% c("b1", "b3")) & + (A %among% "a2" | B %among% "b3" | D %among% "d1") & + (A %among% "a1" | B %among% "b3" | D %among% c("d2", "d3")) + ) + + simplified = CnfFormula(list( + CnfClause(list(CnfAtom(A, c("a1", "a2")), CnfAtom(B, c("b1")), CnfAtom(C, c("c1", "c2")))), + CnfClause(list(CnfAtom(B, c("b1", "b2")), CnfAtom(C, c("c1", "c3")))), + CnfClause(list(CnfAtom(A, c("a1", "a2")), CnfAtom(B, c("b1", "b3")))), + CnfClause(list(CnfAtom(A, c("a2")), CnfAtom(B, c("b3")), CnfAtom(D, c("d1")))), + CnfClause(list(CnfAtom(A, c("a1")), CnfAtom(B, c("b3")), CnfAtom(D, c("d2", "d3")))) + )) + + simplified2 = CnfFormula(list( + CnfClause(list(CnfAtom(A, c("a1", "a2")), CnfAtom(B, c("b1")), CnfAtom(C, c("c1", "c2")))), + CnfClause(list(CnfAtom(B, c("b1", "b2")), CnfAtom(C, c("c1", "c3")))), + CnfClause(list(CnfAtom(A, c("a2")), CnfAtom(B, c("b3")), CnfAtom(D, c("d1")))), + CnfClause(list(CnfAtom(A, c("a1")), CnfAtom(B, c("b3")), CnfAtom(D, c("d2", "d3")))) + )) + + simplified3 = CnfFormula(list( + CnfClause(list(CnfAtom(A, c("a1", "a2")), CnfAtom(C, c("c1", "c2")))), + CnfClause(list(CnfAtom(B, c("b1", "b2")), CnfAtom(C, c("c1", "c3")))), + CnfClause(list(CnfAtom(A, c("a1", "a2")), CnfAtom(B, c("b1", "b3")))), + CnfClause(list(CnfAtom(A, c("a2")), CnfAtom(B, c("b3")), CnfAtom(D, c("d1")))), + CnfClause(list(CnfAtom(A, c("a1")), CnfAtom(B, c("b3")), CnfAtom(D, c("d2", "d3")))) + )) + + expect_equal(evaluate_expression(formula_to_expression(simplified), assignments), + evaluate_expression(original, assignments)) + + expect_equal(evaluate_expression(formula_to_expression(simplified2), assignments), + evaluate_expression(original, assignments)) + + expect_equal(evaluate_expression(formula_to_expression(simplified3), assignments), + evaluate_expression(original, assignments)) + + # check that 'B' was treated the same in all cases, even if C is still unreliable: + # clause 2 is always unchanged with 'b1', 'b2'; clauses 4 and 5 contribute one 'b3' each. + expect_set_equal(unlist(lapply(as.list(simplified), function(x) unclass(x)$B)), c("b1", "b2", "b3", "b3")) + expect_set_equal(unlist(lapply(as.list(simplified2), function(x) unclass(x)$B)), c("b1", "b2", "b3", "b3")) + expect_set_equal(unlist(lapply(as.list(simplified3), function(x) unclass(x)$B)), c("b1", "b2", "b3", "b3")) + +}) From a8a1aa1ab616d1844f414d4e578f7870dfb19d7e Mon Sep 17 00:00:00 2001 From: mb706 Date: Mon, 23 Sep 2024 02:24:45 +0200 Subject: [PATCH 68/87] experiment files --- attic/expression_evaluation_general.R | 151 ++++++++++++++++++++++++++ 1 file changed, 151 insertions(+) create mode 100644 attic/expression_evaluation_general.R diff --git a/attic/expression_evaluation_general.R b/attic/expression_evaluation_general.R new file mode 100644 index 000000000..b660142d8 --- /dev/null +++ b/attic/expression_evaluation_general.R @@ -0,0 +1,151 @@ + +# arguments: 1 - seed, +# 2: varcount: 4 or 5 +# 3 - value per var count: 3 or 4 +# 4: maxdepth: 12 or 13; last 2 are special +# 5: with_subexps: TRUE or FALSE + +# Get 'ss' from command line arguments +args <- commandArgs(trailingOnly = TRUE) +checkmate::assert_integer(ss <- as.integer(args[1]), lower = 1, len = 1, any.missing = FALSE) +checkmate::assert_integer(varcount <- as.integer(args[2]), lower = 3, upper = 7, len = 1, any.missing = FALSE) +checkmate::assert_integer(vals_per_count <- as.integer(args[3]), lower = 2, upper = 6, len = 1, any.missing = FALSE) +checkmate::assert_integer(maxdepth <- as.integer(args[4]), lower = 3, upper = 20, len = 1, any.missing = FALSE) +checkmate::assert_logical(with_subexps <- as.logical(args[5]), len = 1) + +library("mlr3pipelines") +library("testthat") +library("data.table") +options(width = 10000) + +u = CnfUniverse() + +for (varidx in seq_len(varcount)) { + assign(sprintf("V%i", varidx), CnfSymbol(u, sprintf("V%i", varidx), paste0("v", varidx, "_", seq_len(vals_per_count)))) +} + +all_vars = lapply(sprintf("V%i", seq_len(varcount)), as.name) + +random_atom_expression = function() { + symbol = sample(all_vars, 1)[[1]] + values = sample(u[[deparse(symbol)]], sample(vals_per_count - 1, 1)) + substitute(symbol %among% values, list(symbol = symbol, values = values)) +} + +random_cnf_expression = function(depth, do_cnf = FALSE, ddepth = 0) { + if (depth <= 1) { + # base case: return a random symbol expression call + return(random_atom_expression()) + } + # recursively build a random tree of expressions + if (do_cnf) { + op = if (depth <= ddepth) quote(`|`) else quote(`&`) + } else { + op = sample(alist(`&`, `|`), 1)[[1]] # randomly choose between AND and OR + } + left_expr = random_cnf_expression(depth - 1, do_cnf, ddepth) + right_expr = random_cnf_expression(depth - 1, do_cnf, ddepth) + + # create a call object for the expression: (left_expr op right_expr) + substitute(op(left_expr, right_expr), list(op = op, left_expr = left_expr, right_expr = right_expr)) +} + +formula_to_expression = function(formula) { + if (is.logical(formula)) return(c(formula)) + clause_exprs = lapply(as.CnfFormula(formula), function(clause) { + atom_exprs = lapply(clause, function(atom) { + substitute(symbol %among% values, list(symbol = as.name(atom$symbol), values = atom$values)) + }) + Reduce(function(x, y) substitute(x | y, list(x = x, y = y)), atom_exprs) + }) + Reduce(function(x, y) substitute(x & y, list(x = x, y = y)), clause_exprs) +} + +evaluate_expression = function(expression, assignment) { + substituted = do.call(substitute, list(expression, c(list("%among%" = quote(`%in%`)), assignment))) + eval(substituted, envir = baseenv()) +} + +expression_weight = function(expression) { + if (is.logical(expression)) return(0) + sum(all.names(expression) %in% c("|", "&")) + 1 +} + +varnames = names(u) +assignments = expand.grid(lapply(varnames, function(var) u[[var]]), stringsAsFactors = FALSE) +colnames(assignments) = varnames + +stats = list(depth = integer(0), expweight = numeric(0), simpweight = numeric(0), was_tautology = logical(0), was_contradiction = logical(0)) +set.seed(ss) +for (depth_to_check in 2:maxdepth) { + for (repetition in seq_len(2000)) { + if (!with_subexps) { + if (depth_to_check == (maxdepth - 1)) { + expression = random_cnf_expression(10, TRUE, 4) + } else if (depth_to_check == maxdepth) { + expression = random_cnf_expression(5, TRUE, 2) + } else { + expression = random_cnf_expression(depth_to_check) + } + cat(sprintf("%s\n", deparse1(expression))) + simplified = formula_to_expression(eval(expression)) + } else { + subexps = replicate(if (depth_to_check == maxdepth) 10 else 4, { + repeat { + if (depth_to_check == maxdepth) { + expression = random_cnf_expression(10, TRUE, 4) + } else { + expression = random_cnf_expression(depth_to_check) + } + cat(sprintf("%s\n", deparse1(expression))) + result = eval(expression) + if (!is.logical(result)) break + } + result + }, simplify = FALSE) + expression = Reduce(function(x, y) substitute(x & y, list(x = x, y = y)), lapply(subexps, formula_to_expression)) + cat(sprintf("%s\n\n", deparse1(expression))) + simplified = formula_to_expression(CnfFormula(subexps)) + } + + stats$depth[[length(stats$depth) + 1]] = depth_to_check + stats$expweight[[length(stats$expweight) + 1]] = expression_weight(expression) + stats$simpweight[[length(stats$simpweight) + 1]] = expression_weight(simplified) + + truevals = evaluate_expression(expression, assignments) + simpvals = evaluate_expression(simplified, assignments) + + stats$was_tautology[[length(stats$was_tautology) + 1]] = all(truevals) + stats$was_contradiction[[length(stats$was_contradiction) + 1]] = all(!truevals) + + if (!all(truevals == simpvals)) { + trueval = truevals[[which(!truevals == simpvals)[1]]] + simpval = simpvals[[which(!truevals == simpvals)[1]]] + assignment = assignments[which(!truevals == simpvals)[1], , drop = FALSE] + } else { + # alibi + trueval = simpval = TRUE + assignment = NULL + } + expect_equal(trueval, simpval, + info = sprintf("Expression: %s\nAssignment:\n%s\nSimplified to: %s", + deparse1(expression), + paste(capture.output(print(assignment)), collapse = "\n"), + deparse1(simplified) + )) + } +} +dti <- as.data.table(stats) + +saveRDS(dti, sprintf("expression_experiments_3_%05i.rds", ss)) + +dti[, .( + ew = mean(expweight), sw = mean(simpweight), + etriv = mean(expweight == 0), + striv = mean(simpweight == 0), + could_simplify = mean(expweight > simpweight), + was_tautology = mean(was_tautology), + was_contradiction = mean(was_contradiction), + tautologies_not_recognized = mean(was_tautology & simpweight > 0), + contradictions_not_recognized = mean(was_contradiction & simpweight > 0) + ), by = "depth"] From 84b506e743c344ce11b66c3ed238986d49a63427 Mon Sep 17 00:00:00 2001 From: mb706 Date: Mon, 23 Sep 2024 02:35:05 +0200 Subject: [PATCH 69/87] document --- DESCRIPTION | 1 + 1 file changed, 1 insertion(+) diff --git a/DESCRIPTION b/DESCRIPTION index 79e005d63..42d096484 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -102,6 +102,7 @@ Collate: 'CnfClause.R' 'CnfFormula.R' 'CnfFormula_simplify.R' + 'CnfFormula_simplify1.R' 'CnfFormula_simplify2.R' 'CnfSymbol.R' 'CnfUniverse.R' From 999716cdab4f867ff13ec34c5d98d7d3781c85e5 Mon Sep 17 00:00:00 2001 From: mb706 Date: Mon, 23 Sep 2024 03:08:25 +0200 Subject: [PATCH 70/87] bugfix --- R/CnfFormula_simplify1.R | 3 +-- attic/mvsat.mv | 3 +++ 2 files changed, 4 insertions(+), 2 deletions(-) diff --git a/R/CnfFormula_simplify1.R b/R/CnfFormula_simplify1.R index 1aff5786f..6f5da51cc 100644 --- a/R/CnfFormula_simplify1.R +++ b/R/CnfFormula_simplify1.R @@ -314,8 +314,7 @@ simplify_cnf = function(entries, universe) { clause_idx = available[[meta_idx]] if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) return(FALSE) hs2oo = handle_sse_2nd_order_oneend(meta_idx, meta_idx_other, symbol_to_restrict) - if (is.null(hs2oo)) return(NULL) - if (hs2oo) return(TRUE) + if (identical(hs2oo, TRUE)) return(TRUE) clause_other = available[[meta_idx_other]] if (eliminated[[clause_other]] || is_unit[[clause_other]]) return(NULL) FALSE diff --git a/attic/mvsat.mv b/attic/mvsat.mv index aa3faaa96..6f405468f 100644 --- a/attic/mvsat.mv +++ b/attic/mvsat.mv @@ -210,3 +210,6 @@ # Int he old implementation, this is solved by the fact that we do HLA for one clause at a time, either # eliminating it or not. +# Now that 2nd order sse is implemented, one more possible obvious optimizatoin would be to keep original larger versions of clauses around +# and use these for self-subsumption elimination. +# problem: this would make unit handling weird, since we get new units that can now still be self-subsumed. From f2ba50603744e36260c56c381258aa7f013b9e5e Mon Sep 17 00:00:00 2001 From: mb706 Date: Mon, 23 Sep 2024 03:35:45 +0200 Subject: [PATCH 71/87] bugfix ii --- R/CnfFormula_simplify1.R | 1 + 1 file changed, 1 insertion(+) diff --git a/R/CnfFormula_simplify1.R b/R/CnfFormula_simplify1.R index 6f5da51cc..357a448d9 100644 --- a/R/CnfFormula_simplify1.R +++ b/R/CnfFormula_simplify1.R @@ -210,6 +210,7 @@ simplify_cnf = function(entries, universe) { # we are now a subset (and most likely were not before) # ("most likely" because it could probably happen that we re-enter this part through some cascading elimination / propagation) + if (!is_not_subset_of[[meta_idx]][other_meta_idx, is_not_subset_of_col]) next is_not_subset_of[[meta_idx]][other_meta_idx, is_not_subset_of_col] <<- FALSE not_subset_count[meta_idx, other_meta_idx] <<- (rowsum = not_subset_count[meta_idx, other_meta_idx] - 1L) if (rowsum > 2L) next From e428a9423b313019e4d10dd05c26aa95a85dbd5b Mon Sep 17 00:00:00 2001 From: mb706 Date: Mon, 23 Sep 2024 04:17:54 +0200 Subject: [PATCH 72/87] bugfix iii --- R/CnfFormula_simplify1.R | 2 +- attic/experiments.R | 35 +++++++++++++++++++++++++++++++++++ attic/mvsat.mv | 1 + 3 files changed, 37 insertions(+), 1 deletion(-) diff --git a/R/CnfFormula_simplify1.R b/R/CnfFormula_simplify1.R index 357a448d9..d2c6c25bb 100644 --- a/R/CnfFormula_simplify1.R +++ b/R/CnfFormula_simplify1.R @@ -278,7 +278,7 @@ simplify_cnf = function(entries, universe) { ousr = on_updated_subset_relations(meta_idx, meta_idx_other) if (identical(ousr, TRUE)) return(TRUE) # on_updated_subset_relations could cascade down to eliminating meta_idx (i.e. clause_idx) - if (eliminated[[clause_idx]]) return(NULL) + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) return(NULL) } FALSE } diff --git a/attic/experiments.R b/attic/experiments.R index 70476c668..5c3af42ec 100644 --- a/attic/experiments.R +++ b/attic/experiments.R @@ -1098,3 +1098,38 @@ CnfFormula: t(sapply(indices, function(i) sapply(indices, function(j) if (is.na(not_subset_count[i, j])) NA_integer_ else sum(is_not_subset_of[[i]][j, ])))) )) } + + +((V1 %among% c("v1_1", "v1_4", "v1_5") | V4 %among% c("v4_1", "v4_3", "v4_5")) & (V2 %among% c("v2_4", "v2_3", "v2_2") & V1 %among% c("v1_2", "v1_1", "v1_5", "v1_3")) & +((V1 %among% c("v1_1", "v1_4", "v1_3") | V2 %among% c("v2_5", "v2_1")) & (V1 %among% c("v1_2", "v1_5", "v1_4") & V1 %among% c("v1_4", "v1_5", "v1_1", "v1_2"))) & +((V2 %among% "v2_4" | V4 %among% c("v4_4", "v4_2", "v4_3", "v4_5") | V1 %among% c("v1_4", "v1_2", "v1_3", "v1_1") & V4 %among% "v4_2") & (V3 %among% c("v3_5", "v3_4", "v3_1" ) | +V2 %among% c("v2_1", "v2_3") | V1 %among% c("v1_5", "v1_1") & V1 %among% c("v1_4", "v1_2"))) & (V2 %among% c("v2_5", "v2_2") & V3 %among% "v3_4" & (V2 %among% c("v2_1", "v2_5") & +V4 %among% c("v4_5", "v4_2", "v4_4", "v4_3")) & (V3 %among% "v3_5" & V2 %among% c("v2_5", "v2_2") | V3 %among% c("v3_1", "v3_3", "v3_5") & +V3 %among% c("v3_5", "v3_2", "v3_3", "v3_4")) & (V3 %among% c("v3_1", "v3_2", "v3_3") & V4 %among% c("v4_1", "v4_2") & (V1 %among% c("v1_5", "v1_1", "v1_2") | +V2 %among% "v2_4") | (V4 %among% "v4_2" & V3 %among% c("v3_3", "v3_2") | V2 %among% c("v2_5", "v2_3", "v2_4") & V1 %among% c("v1_2", "v1_3", "v1_5")))) | +(((V4 %among% c("v4_1", "v4_2", "v4_3", "v4_5") | V1 %among% c("v1_5", "v1_2", "v1_1", "v1_4")) & (V3 %among% c("v3_5", "v3_4") | V3 %among% c("v3_5", "v3_4", "v3_1")) | +(V4 %among% "v4_5" & V3 %among% c("v3_3", "v3_5", "v3_1", "v3_2") | (V1 %among% c("v1_4", "v1_2", "v1_3", "v1_5") | V3 %among% "v3_3"))) & ((V2 %among% c("v2_5", "v2_1") | +V1 %among% "v1_2") & (V2 %among% c("v2_2", "v2_3") & V4 %among% c("v4_5", "v4_3")) & (V4 %among% c("v4_3", "v4_5", "v4_2") & V1 %among% c("v1_3", "v1_5", "v1_1") & +(V1 %among% c("v1_5", "v1_3", "v1_1", "v1_4") | V3 %among% c("v3_4", "v3_3", "v3_1", "v3_5")))) | (V4 %among% c("v4_1", "v4_5", "v4_3") & V1 %among% c("v1_2", "v1_1", "v1_5") & +(V3 %among% c("v3_3", "v3_2", "v3_4", "v3_5") & V4 %among% c("v4_3", "v4_2", "v4_5", "v4_1")) | V4 %among% c("v4_1", "v4_4", "v4_2") & V1 %among% c("v1_3", "v1_4", "v1_1") & +(V4 %among% c("v4_4", "v4_3", "v4_2") & V3 %among% c("v3_2", "v3_3", "v3_1"))) & ((V1 %among% c("v1_5", "v1_4", "v1_1") | V4 %among% "v4_4") & (V2 %among% c("v2_3", "v2_2") & +V2 %among% "v2_2") & (V3 %among% c("v3_1", "v3_5", "v3_3", "v3_4") & V1 %among% c("v1_5", "v1_3", "v1_2", "v1_4") | V2 %among% "v2_1" & V3 %among% c("v3_1", "v3_4", "v3_2"))))) & +((V3 %among% c("v3_5", "v3_4", "v3_2", "v3_1") | V1 %among% c("v1_4", "v1_5", "v1_2")) & (V3 %among% c("v3_2", "v3_5") | V3 %among% c("v3_4", "v3_3", "v3_5", "v3_2")) & +(V1 %among% c("v1_2", "v1_3", "v1_1", "v1_5") | V4 %among% c("v4_1", "v4_3") | V2 %among% "v2_2" & V2 %among% c("v2_3", "v2_4", "v2_5", "v2_2")) & +((V3 %among% c("v3_5", "v3_1", "v3_2") | V3 %among% "v3_4") & (V3 %among% c("v3_5", "v3_1") | V1 %among% c("v1_4", "v1_1", "v1_2", "v1_3")) & +(V4 %among% c("v4_2", "v4_1", "v4_4") & +V4 %among% c("v4_5", "v4_4", "v4_1") | V1 %among% c("v1_2", "v1_5", "v1_4", "v1_1") & V3 %among% c("v3_1", "v3_5", "v3_2", "v3_3"))) & (V4 %among% "v4_4" & +V2 %among% c("v2_5", "v2_1", "v2_3") & (V3 %among% c("v3_3", "v3_1") & V4 %among% "v4_5") & (V4 %among% "v4_3" | V4 %among% c("v4_2", "v4_1", "v4_4") | +(V1 %among% c("v1_4", "v1_2", "v1_3") | +V3 %among% c("v3_4", "v3_1"))) & ((V3 %among% c("v3_4", "v3_1") & V4 %among% c("v4_5", "v4_4", "v4_1", "v4_3") | V3 %among% c("v3_5", "v3_1") & +V2 %among% c("v2_4", "v2_5", "v2_1")) & +((V2 %among% c("v2_4", "v2_3") | V3 %among% c("v3_5", "v3_2")) & (V2 %among% c("v2_4", "v2_1", "v2_3") & V1 %among% c("v1_4", "v1_3", "v1_5", "v1_1" ))))) | +((V2 %among% c("v2_5", "v2_4", "v2_2", "v2_3") & V3 %among% c("v3_1", "v3_5", "v3_2", "v3_4") & (V2 %among% c("v2_1", "v2_4", "v2_5") | V3 %among% c("v3_4", "v3_5", "v3_2")) | +(V2 %among% c("v2_4", "v2_1") | V1 %among% c("v1_5", "v1_4", "v1_1") | V3 %among% c("v3_3", "v3_4", "v3_2") & V4 %among% c("v4_5", "v4_2", "v4_4"))) & +(V2 %among% c("v2_2", "v2_4") & V1 %among% c("v1_1", "v1_2") | V3 %among% "v3_2" & V3 %among% c("v3_1", "v3_2", "v3_4") | V1 %among% c("v1_5", "v1_4", "v1_1", "v1_2") & +V4 %among% c("v4_3", "v4_2") & (V1 %among% "v1_1" & V1 %among% c("v1_5", "v1_1", "v1_4", "v1_3"))) | (V2 %among% c("v2_1", "v2_4") & V2 %among% "v2_3" | +V2 %among% c("v2_5", "v2_2", "v2_3") & V2 %among% c("v2_5", "v2_4", "v2_3", "v2_2") | (V4 %among% "v4_4" | V4 %among% c("v4_3", "v4_1")) & +(V2 %among% c("v2_4", "v2_2", "v2_5") & +V2 %among% c("v2_2", "v2_1"))) & (V1 %among% c("v1_5", "v1_3") & V4 %among% c("v4_3", "v4_5", "v4_4") & (V1 %among% c("v1_4", "v1_5", "v1_2", "v1_3") & +V4 %among% c("v4_3", "v4_2", "v4_1")) | +V3 %among% c("v3_2", "v3_3", "v3_1") & V3 %among% c("v3_1", "v3_5", "v3_2") & (V4 %among% "v4_4" & V2 %among% c("v2_1", "v2_5", "v2_3", "v2_2"))))) diff --git a/attic/mvsat.mv b/attic/mvsat.mv index 6f405468f..cf17b62f9 100644 --- a/attic/mvsat.mv +++ b/attic/mvsat.mv @@ -213,3 +213,4 @@ # Now that 2nd order sse is implemented, one more possible obvious optimizatoin would be to keep original larger versions of clauses around # and use these for self-subsumption elimination. # problem: this would make unit handling weird, since we get new units that can now still be self-subsumed. + From 7583cab4656a3eb38bda2e076274877ed455e326 Mon Sep 17 00:00:00 2001 From: mb706 Date: Mon, 23 Sep 2024 05:34:33 +0200 Subject: [PATCH 73/87] bugfix --- R/CnfFormula_simplify1.R | 6 +- attic/experiments.R | 121 +++++++++++++++++++++++++++++++++++++++ 2 files changed, 125 insertions(+), 2 deletions(-) diff --git a/R/CnfFormula_simplify1.R b/R/CnfFormula_simplify1.R index d2c6c25bb..19fe2ad3c 100644 --- a/R/CnfFormula_simplify1.R +++ b/R/CnfFormula_simplify1.R @@ -586,6 +586,7 @@ simplify_cnf = function(entries, universe) { } # prefer to eliminate the outer loopo clause first, since we have already # done more work for the inner loop clause (which comes earlier in 'entries') + not_subset_count[meta_idx_outer, meta_idx_inner] = sum(is_not_subset_of[[meta_idx_outer]][meta_idx_inner, ]) rowsum = sum(is_not_subset_of[[meta_idx_inner]][meta_idx_outer, ]) not_subset_count[meta_idx_inner, meta_idx_outer] = rowsum if (rowsum <= 2) { @@ -594,8 +595,8 @@ simplify_cnf = function(entries, universe) { if (ousr) return(return_entries(FALSE)) if (eliminated[[clause_idx_inner]] || is_unit[[clause_idx_inner]]) next # yes this can happen. } - rowsum = sum(is_not_subset_of[[meta_idx_outer]][meta_idx_inner, ]) - not_subset_count[meta_idx_outer, meta_idx_inner] = rowsum + # need to get rowsum back again, since the call above could have changed something! + rowsum = not_subset_count[meta_idx_outer, meta_idx_inner] if (rowsum <= 2) { ousr = on_updated_subset_relations(meta_idx_outer, meta_idx_inner) if (identical(ousr, TRUE)) return(return_entries(FALSE)) @@ -604,6 +605,7 @@ simplify_cnf = function(entries, universe) { } } } + # Now for the big one: Asymmetric Hidden Literal Addition (Marijn et al.) # First, we do non-units, then we do units separately. diff --git a/attic/experiments.R b/attic/experiments.R index 5c3af42ec..a3c592e2c 100644 --- a/attic/experiments.R +++ b/attic/experiments.R @@ -1133,3 +1133,124 @@ V2 %among% c("v2_5", "v2_2", "v2_3") & V2 %among% c("v2_5", "v2_4", "v2_3", "v2_ V2 %among% c("v2_2", "v2_1"))) & (V1 %among% c("v1_5", "v1_3") & V4 %among% c("v4_3", "v4_5", "v4_4") & (V1 %among% c("v1_4", "v1_5", "v1_2", "v1_3") & V4 %among% c("v4_3", "v4_2", "v4_1")) | V3 %among% c("v3_2", "v3_3", "v3_1") & V3 %among% c("v3_1", "v3_5", "v3_2") & (V4 %among% "v4_4" & V2 %among% c("v2_1", "v2_5", "v2_3", "v2_2"))))) + + +quote((V3 %among% c("v3_3", "v3_1") & V2 %among% c("v2_1", "v2_5", "v2_4") & (V1 %among% c("v1_1", "v1_4", "v1_2", "v1_5") & V3 %among% "v3_3") | +(V3 %among% c("v3_2", "v3_1", "v3_3") & V2 %among% c("v2_5", "v2_4") | V1 %among% c("v1_2", "v1_1", "v1_5", "v1_3") & V4 %among% c("v4_4", "v4_2", "v4_1"))) & +(V4 %among% c("v4_2", "v4_3", "v4_1", "v4_5") & V4 %among% c("v4_1", "v4_4", "v4_5") | (V2 %among% c("v2_3", "v2_2", "v2_5", "v2_4") | V3 %among% "v3_1") | +V4 %among% c("v4_3", "v4_4", "v4_5") & V4 %among% c("v4_1", "v4_5", "v4_4") & (V1 %among% c("v1_3", "v1_1", "v1_5") | V3 %among% "v3_2")) & +((V3 %among% c("v3_2", "v3_3") & V2 %among% "v2_5" | (V1 %among% "v1_3" | V4 %among% c("v4_3", "v4_2", "v4_4", "v4_1")) | V2 %among% c("v2_5", "v2_4") & +V4 %among% c("v4_5", "v4_2") & (V2 %among% c("v2_5", "v2_4", "v2_3") | V4 %among% c("v4_1", "v4_5", "v4_4"))) & (V1 %among% "v1_2" & V2 %among% "v2_2" | +(V2 %among% c("v2_3", "v2_4") | V2 %among% c("v2_3", "v2_4", "v2_1", "v2_2")) | +(V3 %among% c("v3_1", "v3_5", "v3_2", "v3_4") & V4 %among% c("v4_1", "v4_4") | V3 %among% "v3_4" & V4 %among% c("v4_5", "v4_4")))) +) |> eval() |> formula_to_expression() |> evaluate_expression(assignments) -> a1 + +quote((V3 %among% c("v3_3", "v3_1") & V2 %among% c("v2_1", "v2_5", "v2_4") & (V1 %among% c("v1_1", "v1_4", "v1_2", "v1_5") & V3 %among% "v3_3") | +(V3 %among% c("v3_2", "v3_1", "v3_3") & V2 %among% c("v2_5", "v2_4") | V1 %among% c("v1_2", "v1_1", "v1_5", "v1_3") & V4 %among% c("v4_4", "v4_2", "v4_1"))) & +(V4 %among% c("v4_2", "v4_3", "v4_1", "v4_5") & V4 %among% c("v4_1", "v4_4", "v4_5") | (V2 %among% c("v2_3", "v2_2", "v2_5", "v2_4") | V3 %among% "v3_1") | +V4 %among% c("v4_3", "v4_4", "v4_5") & V4 %among% c("v4_1", "v4_5", "v4_4") & (V1 %among% c("v1_3", "v1_1", "v1_5") | V3 %among% "v3_2")) & +((V3 %among% c("v3_2", "v3_3") & V2 %among% "v2_5" | (V1 %among% "v1_3" | V4 %among% c("v4_3", "v4_2", "v4_4", "v4_1")) | V2 %among% c("v2_5", "v2_4") & +V4 %among% c("v4_5", "v4_2") & (V2 %among% c("v2_5", "v2_4", "v2_3") | V4 %among% c("v4_1", "v4_5", "v4_4"))) & (V1 %among% "v1_2" & V2 %among% "v2_2" | +(V2 %among% c("v2_3", "v2_4") | V2 %among% c("v2_3", "v2_4", "v2_1", "v2_2")) | +(V3 %among% c("v3_1", "v3_5", "v3_2", "v3_4") & V4 %among% c("v4_1", "v4_4") | V3 %among% "v3_4" & V4 %among% c("v4_5", "v4_4")))) +) |> evaluate_expression(assignments) -> a2 + +which(a1 != a2) + + + +quote( + +(((V2 %among% "v2_2" | V1 %among% "v1_2") & (V1 %among% c("v1_1", "v1_3") & V4 %among% c("v4_3", "v4_1")) | (V3 %among% c("v3_2", "v3_3") & +V3 %among% c("v3_3", "v3_1") | V1 %among% "v1_1" & V3 %among% "v3_2") | (V3 %among% "v3_3" | V3 %among% c("v3_3", "v3_2") | +V1 %among% c("v1_1", "v1_3") & V1 %among% "v1_2" | (V1 %among% c("v1_1", "v1_3") | V1 %among% "v1_1" | (V2 %among% c("v2_2", "v2_1") | + V4 %among% "v4_2")))) & (((V2 %among% c("v2_2", "v2_1") | V4 %among% c("v4_3", "v4_1")) & (V2 %among% c("v2_2", "v2_3") & V4 %among% c("v4_1", "v4_2")) | + (V1 %among% c("v1_3", "v1_1") | V4 %among% c("v4_1", "v4_2")) & (V1 %among% "v1_3" & V2 %among% "v2_3")) & (V2 %among% "v2_3" & V4 %among% "v4_2" | (V3 %among% "v3_3" | + V3 %among% c("v3_2", "v3_3")) | (V2 %among% "v2_2" | V1 %among% "v1_2" | V2 %among% "v2_2" & V4 %among% c("v4_3", "v4_2")))) | ((V3 %among% "v3_2" | V3 %among% c("v3_2", "v3_1")) & + (V2 %among% "v2_1" | V2 %among% c("v2_2", "v2_3")) | V1 %among% "v1_1" & V1 %among% "v1_1" & (V2 %among% "v2_2" | V3 %among% "v3_3")) & + ((V4 %among% c("v4_2", "v4_3") & V3 %among% "v3_1" | (V2 %among% c("v2_3", "v2_2") | V2 %among% c("v2_3", "v2_2"))) & (V1 %among% "v1_2" & + V2 %among% "v2_2" & (V2 %among% "v2_3" & V1 %among% "v1_3"))) & ((V2 %among% "v2_1" | V2 %among% c("v2_1", "v2_2") | V2 %among% "v2_2" & + V2 %among% c("v2_2", "v2_3") | (V1 %among% c("v1_1", "v1_2") | V2 %among% c("v2_3", "v2_2")) & (V3 %among% c("v3_1", "v3_3") & V4 %among% c("v4_1", "v4_3"))) & + (V3 %among% "v3_3" & V3 %among% c("v3_2", "v3_1") | V4 %among% "v4_2" & V2 %among% "v2_2" | V3 %among% c("v3_1", "v3_3") & V4 %among% c("v4_2", "v4_1") & + (V3 %among% "v3_2" & V4 %among% "v4_1")))) & + + ((V2 %among% c("v2_1", "v2_2") & V2 %among% "v2_2" & (V2 %among% c("v2_3", "v2_1") | V3 %among% c("v3_2", "v3_3")) | + (V1 %among% "v1_1" | V1 %among% c("v1_2", "v1_1") | (V2 %among% "v2_2" | V2 %among% c("v2_2", "v2_3"))) | (V2 %among% "v2_3" & V2 %among% c("v2_1", "v2_3") & + (V4 %among% "v4_2" | V3 %among% c("v3_2", "v3_1")) | V2 %among% "v2_1" & V4 %among% "v4_3" & (V3 %among% "v3_2" | V2 %among% c("v2_2", "v2_3")))) & + (((V1 %among% c("v1_1", "v1_3") | V1 %among% "v1_3") & (V4 %among% c("v4_3", "v4_2") | V1 %among% c("v1_1", "v1_2")) | V3 %among% "v3_1" & V2 %among% c("v2_1", "v2_3") & + (V4 %among% c("v4_3", "v4_2") & V3 %among% c("v3_2", "v3_1"))) & ((V1 %among% c("v1_3", "v1_1") | V1 %among% c("v1_3", "v1_2")) & (V2 %among% c("v2_3", "v2_2") & V1 %among% "v1_2") | + V4 %among% c("v4_3", "v4_1") & V3 %among% "v3_2" & (V3 %among% c("v3_2", "v3_1") | V2 %among% "v2_3"))) & (((V1 %among% "v1_2" | V4 %among% "v4_3") & (V1 %among% c("v1_1", "v1_2") | + V2 %among% "v2_3") | V3 %among% "v3_2" & V1 %among% c("v1_2", "v1_3") & (V3 %among% c("v3_3", "v3_1") | V2 %among% c("v2_3", "v2_2"))) & (V1 %among% c("v1_1", "v1_2") & + V2 %among% c("v2_2", "v2_1") | (V3 %among% "v3_2" | V2 %among% "v2_3") | V2 %among% c("v2_2", "v2_3") & V1 %among% c("v1_3", "v1_1") & (V2 %among% "v2_2" | V2 %among% c("v2_1", "v2_2"))) | + (V2 %among% "v2_1" & V2 %among% "v2_3" | V4 %among% "v4_1" & V2 %among% "v2_1" | V1 %among% c("v1_1", "v1_3") & V1 %among% c("v1_1", "v1_2") & (V4 %among% c("v4_1", "v4_2") & V2 %among% "v2_2")) & + (V1 %among% "v1_1" & V1 %among% c("v1_3", "v1_2") | V3 %among% c("v3_2", "v3_1") & V3 %among% "v3_2" | (V2 %among% c("v2_1", "v2_2") | V4 %among% "v4_1" | V2 %among% "v2_3" & V3 %among% "v3_2")))) +) -> bigex + +evaluate_expression(bigex, ass) +evaluate_expression(formula_to_expression(eval(bigex)), ass) + + +# |> eval() |> formula_to_expression() |> evaluate_expression(assignments) -> a1 + +which(a1 != a2) + +ass <- assignments[which(a1 != a2), ] + + + +eval(bigex) |> as.list() |> lapply(as.CnfFormula) |> lapply(formula_to_expression) |> sapply(evaluate_expression, assignment = ass) -> clauses + + +which(!clauses) + + +e1 <- (((V2 %among% "v2_2" | V1 %among% "v1_2") & (V1 %among% c("v1_1", "v1_3") & V4 %among% c("v4_3", "v4_1")) | (V3 %among% c("v3_2", "v3_3") & +V3 %among% c("v3_3", "v3_1") | V1 %among% "v1_1" & V3 %among% "v3_2") | (V3 %among% "v3_3" | V3 %among% c("v3_3", "v3_2") | +V1 %among% c("v1_1", "v1_3") & V1 %among% "v1_2" | (V1 %among% c("v1_1", "v1_3") | V1 %among% "v1_1" | (V2 %among% c("v2_2", "v2_1") | + V4 %among% "v4_2")))) & (((V2 %among% c("v2_2", "v2_1") | V4 %among% c("v4_3", "v4_1")) & (V2 %among% c("v2_2", "v2_3") & V4 %among% c("v4_1", "v4_2")) | + (V1 %among% c("v1_3", "v1_1") | V4 %among% c("v4_1", "v4_2")) & (V1 %among% "v1_3" & V2 %among% "v2_3")) & (V2 %among% "v2_3" & V4 %among% "v4_2" | (V3 %among% "v3_3" | + V3 %among% c("v3_2", "v3_3")) | (V2 %among% "v2_2" | V1 %among% "v1_2" | V2 %among% "v2_2" & V4 %among% c("v4_3", "v4_2")))) | ((V3 %among% "v3_2" | V3 %among% c("v3_2", "v3_1")) & + (V2 %among% "v2_1" | V2 %among% c("v2_2", "v2_3")) | V1 %among% "v1_1" & V1 %among% "v1_1" & (V2 %among% "v2_2" | V3 %among% "v3_3")) & + ((V4 %among% c("v4_2", "v4_3") & V3 %among% "v3_1" | (V2 %among% c("v2_3", "v2_2") | V2 %among% c("v2_3", "v2_2"))) & (V1 %among% "v1_2" & + V2 %among% "v2_2" & (V2 %among% "v2_3" & V1 %among% "v1_3"))) & ((V2 %among% "v2_1" | V2 %among% c("v2_1", "v2_2") | V2 %among% "v2_2" & + V2 %among% c("v2_2", "v2_3") | (V1 %among% c("v1_1", "v1_2") | V2 %among% c("v2_3", "v2_2")) & (V3 %among% c("v3_1", "v3_3") & V4 %among% c("v4_1", "v4_3"))) & + (V3 %among% "v3_3" & V3 %among% c("v3_2", "v3_1") | V4 %among% "v4_2" & V2 %among% "v2_2" | V3 %among% c("v3_1", "v3_3") & V4 %among% c("v4_2", "v4_1") & + (V3 %among% "v3_2" & V4 %among% "v4_1")))) + +e2 <- ((V2 %among% c("v2_1", "v2_2") & V2 %among% "v2_2" & (V2 %among% c("v2_3", "v2_1") | V3 %among% c("v3_2", "v3_3")) | + (V1 %among% "v1_1" | V1 %among% c("v1_2", "v1_1") | (V2 %among% "v2_2" | V2 %among% c("v2_2", "v2_3"))) | (V2 %among% "v2_3" & V2 %among% c("v2_1", "v2_3") & + (V4 %among% "v4_2" | V3 %among% c("v3_2", "v3_1")) | V2 %among% "v2_1" & V4 %among% "v4_3" & (V3 %among% "v3_2" | V2 %among% c("v2_2", "v2_3")))) & + (((V1 %among% c("v1_1", "v1_3") | V1 %among% "v1_3") & (V4 %among% c("v4_3", "v4_2") | V1 %among% c("v1_1", "v1_2")) | V3 %among% "v3_1" & V2 %among% c("v2_1", "v2_3") & + (V4 %among% c("v4_3", "v4_2") & V3 %among% c("v3_2", "v3_1"))) & ((V1 %among% c("v1_3", "v1_1") | V1 %among% c("v1_3", "v1_2")) & (V2 %among% c("v2_3", "v2_2") & V1 %among% "v1_2") | + V4 %among% c("v4_3", "v4_1") & V3 %among% "v3_2" & (V3 %among% c("v3_2", "v3_1") | V2 %among% "v2_3"))) & (((V1 %among% "v1_2" | V4 %among% "v4_3") & (V1 %among% c("v1_1", "v1_2") | + V2 %among% "v2_3") | V3 %among% "v3_2" & V1 %among% c("v1_2", "v1_3") & (V3 %among% c("v3_3", "v3_1") | V2 %among% c("v2_3", "v2_2"))) & (V1 %among% c("v1_1", "v1_2") & + V2 %among% c("v2_2", "v2_1") | (V3 %among% "v3_2" | V2 %among% "v2_3") | V2 %among% c("v2_2", "v2_3") & V1 %among% c("v1_3", "v1_1") & (V2 %among% "v2_2" | V2 %among% c("v2_1", "v2_2"))) | + (V2 %among% "v2_1" & V2 %among% "v2_3" | V4 %among% "v4_1" & V2 %among% "v2_1" | V1 %among% c("v1_1", "v1_3") & V1 %among% c("v1_1", "v1_2") & (V4 %among% c("v4_1", "v4_2") & V2 %among% "v2_2")) & + (V1 %among% "v1_1" & V1 %among% c("v1_3", "v1_2") | V3 %among% c("v3_2", "v3_1") & V3 %among% "v3_2" | (V2 %among% c("v2_1", "v2_2") | V4 %among% "v4_1" | V2 %among% "v2_3" & V3 %among% "v3_2")))) + +evaluate_expression(formula_to_expression(e1), ass) +evaluate_expression(formula_to_expression(e2), ass) +evaluate_expression(formula_to_expression(e1 & e2), ass) + +e1 +e2 +eval(e1 & e2) |> as.list() |> lapply(as.CnfFormula) |> lapply(formula_to_expression) |> sapply(evaluate_expression, assignment = ass) -> clauses + +e1&e2 + +entries[!eliminated] |> lapply(function(x) structure(list(x), universe = universe, class = "CnfFormula")) |> lapply(formula_to_expression) |> sapply(evaluate_expression, assignment = ass) -> cl +entries[!eliminated][!cl] |> lapply(structure, class = "CnfClause") + +meta_idx_inner +c +lapply(seq_along(eliminated), function(x) if (eliminated[[x]]) FALSE else structure(entries[[x]], class = "CnfClause")) + +entries[!eliminated] |> lapply(structure, class = "CnfClause") +which(eliminated) + +which(!clauses) + +e1&e2 +e1 +e2 + From a2bf0563b553c7069a97e57a08085d0e2e415328 Mon Sep 17 00:00:00 2001 From: mb706 Date: Mon, 23 Sep 2024 06:30:01 +0200 Subject: [PATCH 74/87] bug --- R/CnfFormula_simplify1.R | 3 +- attic/experiments.R | 81 ++++++++++++++++++++++++++++++++++++++++ 2 files changed, 82 insertions(+), 2 deletions(-) diff --git a/R/CnfFormula_simplify1.R b/R/CnfFormula_simplify1.R index 19fe2ad3c..dc400f1d5 100644 --- a/R/CnfFormula_simplify1.R +++ b/R/CnfFormula_simplify1.R @@ -216,7 +216,7 @@ simplify_cnf = function(entries, universe) { if (rowsum > 2L) next ousr = on_updated_subset_relations(meta_idx, other_meta_idx) if (identical(ousr, TRUE)) return(TRUE) # forward contradiction signal. We don't care if other_meta_idx was eliminated. - if (eliminated[[clause_idx]]) return(NULL) # need to check more directly if things escalated somehow and clause_idx was eliminated indirectly + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) return(NULL) # need to check more directly if things escalated somehow and clause_idx was eliminated indirectly } # call on_domain_changed_handle_2nd_order_sse # it is not a waste w/r/t the 'on_updated_subset_relations' call, since that one only deals with clauses for which the symbol is set to FALSE now, @@ -342,7 +342,6 @@ simplify_cnf = function(entries, universe) { if (is.null(hs2oo)) return(NULL) # meta_idx eliminated if (hs2oo) return(TRUE) } - targets_while_twoend = potential_targets[not_subset_count[meta_idx, potential_targets] == 2L] for (meta_idx_target in targets_while_twoend) { hs2oo = handle_sse_2nd_order_twoend(meta_idx, meta_idx_target, symbol) diff --git a/attic/experiments.R b/attic/experiments.R index a3c592e2c..25ef2923e 100644 --- a/attic/experiments.R +++ b/attic/experiments.R @@ -1254,3 +1254,84 @@ e1&e2 e1 e2 + + + (V3 %among% c("v3_3", "v3_4") | V1 %among% "v1_2" | (V1 %among% "v1_1" | V1 %among% c("v1_1", "v1_5", "v1_4"))) & ((V1 + %among% "v1_3" | V4 %among% "v4_3") & (V1 %among% c("v1_5", "v1_3", "v1_4", "v1_1") | V4 %among% "v4_3")) & (V3 %among% + c("v3_3", "v3_4", "v3_1", "v3_2") | V3 %among% "v3_5" | (V1 %among% c("v1_1", "v1_2", "v1_4", "v1_3") | V4 %among% + c("v4_3", "v4_1")) | (V4 %among% c("v4_2", "v4_3", "v4_1", "v4_4") | V3 %among% c("v3_4", "v3_2", "v3_1", "v3_5")) & + (V2 %among% c("v2_2", "v2_1", "v2_3", "v2_4") | V3 %among% c("v3_2", "v3_5", "v3_3"))) & (V4 %among% "v4_2" | V2 + %among% c("v2_1", "v2_3", "v2_2", "v2_5") | V2 %among% c("v2_3", "v2_5") & V2 %among% c("v2_2", "v2_5") | (V1 %among% + c("v1_1", "v1_5", "v1_3", "v1_4") & V1 %among% c("v1_5", "v1_3", "v1_1", "v1_4") | V2 %among% "v2_2" & V1 %among% + c("v1_3", "v1_2")) | (V2 %among% c("v2_5", "v2_2", "v2_1") | V1 %among% c("v1_3", "v1_1") | V1 %among% c("v1_5", + "v1_3") & V4 %among% c("v4_1", "v4_4") | (V2 %among% c("v2_2", "v2_1") | V2 %among% "v2_3") & (V2 %among% c("v2_1", + "v2_3", "v2_5", "v2_4") & V4 %among% "v4_5"))) & ((V4 %among% c("v4_4", "v4_1") & V4 %among% c("v4_1", "v4_3", "v4_5") + | (V2 %among% c("v2_3", "v2_2") | V4 %among% c("v4_2", "v4_4", "v4_5", "v4_3"))) & (V4 %among% c("v4_5", "v4_1") | V1 + %among% c("v1_5", "v1_2") | V1 %among% "v1_4" & V1 %among% "v1_5") | (V4 %among% c("v4_1", "v4_3") & V3 %among% "v3_2" + | V1 %among% c("v1_4", "v1_1", "v1_5", "v1_2") & V1 %among% c("v1_5", "v1_1") | (V2 %among% c("v2_2", "v2_4") | V3 + %among% c("v3_4", "v3_1", "v3_3", "v3_5")) & (V2 %among% c("v2_3", "v2_5") | V1 %among% c("v1_2", "v1_1", "v1_5", + "v1_3"))) | (V1 %among% c("v1_4", "v1_2") & V1 %among% c("v1_5", "v1_1") | (V3 %among% c("v3_2", "v3_1", "v3_4", + "v3_5") | V1 %among% c("v1_3", "v1_5", "v1_4", "v1_2"))) & (V4 %among% c("v4_5", "v4_1") & V1 %among% c("v1_4", "v1_3") + | V4 %among% c("v4_4", "v4_2") & V4 %among% c("v4_4", "v4_1", "v4_5")) & ((V2 %among% c("v2_3", "v2_4") | V2 %among% + c("v2_5", "v2_4", "v2_1" )) & (V4 %among% c("v4_5", "v4_2", "v4_4") | V4 %among% "v4_5") & (V1 %among% "v1_4" | V4 + %among% c("v4_4", "v4_3") | V4 %among% c("v4_3", "v4_1") & V3 %among% c("v3_3", "v3_5", "v3_1")))) & (V4 %among% + c("v4_2", "v4_4", "v4_1", "v4_3") & V3 %among% "v3_3" & (V1 %among% c("v1_1", "v1_4", "v1_2", "v1_5") & V2 %among% + c("v2_5", "v2_3")) & (V1 %among% c("v1_1", "v1_3", "v1_4", "v1_2") | V1 %among% "v1_5" | V3 %among% c("v3_5", "v3_4") & + V1 %among% c("v1_4", "v1_1")) & (V1 %among% c("v1_1", "v1_5", "v1_3", "v1_4") | V2 %among% c("v2_4", "v2_3") | (V2 + %among% c("v2_1", "v2_5") | V2 %among% c("v2_5", "v2_4", "v2_3", "v2_2")) | V4 %among% c("v4_5", "v4_2") & V3 %among% + "v3_1" & (V1 %among% c("v1_3", "v1_5") & V1 %among% c("v1_2", "v1_1", "v1_3", "v1_4"))) | (V3 %among% c("v3_1", "v3_4") + | V2 %among% "v2_5" | V4 %among% c("v4_4", "v4_1", "v4_3") & V2 %among% c("v2_2", "v2_5") | (V1 %among% "v1_4" | V4 + %among% c("v4_5", "v4_2")) & (V2 %among% "v2_3" & V2 %among% "v2_5") | ((V3 %among% "v3_3" | V4 %among% c("v4_2", + "v4_3")) & (V3 %among% c("v3_1", "v3_2", "v3_4") | V4 %among% c("v4_3", "v4_1", "v4_4", "v4_5")) | (V4 %among% "v4_1" | + V4 %among% c("v4_4", "v4_3", "v4_5")) & (V1 %among% c("v1_4", "v1_2", "v1_3") & V1 %among% c("v1_1", "v1_3")))) | ((V2 + %among% "v2_2" | V1 %among% "v1_1") & (V2 %among% "v2_5" & V3 %among% "v3_5") & (V1 %among% c("v1_5", "v1_3", "v1_4") | + V1 %among% c("v1_1", "v1_3", "v1_4") | (V1 %among% c("v1_3", "v1_5", "v1_4") | V1 %among% c("v1_4", "v1_1"))) | (V1 + %among% "v1_1" & V4 %among% c("v4_1", "v4_4", "v4_2") | V1 %among% c("v1_3", "v1_5") & V3 %among% c("v3_1", "v3_3", + "v3_5")) & (V1 %among% "v1_5" & V1 %among% c("v1_1", "v1_4") & (V3 %among% "v3_4" | V1 %among% c("v1_5", "v1_2", + "v1_1"))) | (V3 %among% c("v3_1", "v3_5", "v3_4", "v3_3") | V1 %among% c("v1_2", "v1_5", "v1_3") | (V4 %among% + c("v4_2", "v4_5", "v4_3", "v4_1") | V2 %among% c("v2_5", "v2_2", "v2_3", "v2_1")) | V3 %among% c("v3_2", "v3_1") & V1 + %among% c("v1_3", "v1_1", "v1_2", "v1_4") & (V2 %among% "v2_3" & V2 %among% c("v2_4", "v2_5"))) & ((V1 %among% "v1_4" & + V4 %among% c("v4_1", "v4_3") | (V1 %among% c("v1_1", "v1_4") | V4 %among% "v4_5")) & (V2 %among% c("v2_2", "v2_4", + "v2_5", "v2_3") & V4 %among% "v4_5" & (V4 %among% c("v4_2", "v4_4", "v4_3", "v4_1") & V2 %among% c("v2_1", "v2_5", + "v2_4", "v2_3")))))) & (((V4 %among% c("v4_4", "v4_3") & V2 %among% c("v2_5", "v2_2") | V1 %among% c("v1_3", "v1_4", + "v1_5") & V4 %among% c("v4_4", "v4_1", "v4_2", "v4_5")) & (V3 %among% c("v3_1", "v3_3", "v3_4", "v3_2") | V3 %among% + "v3_2" | (V1 %among% c("v1_3", "v1_5", "v1_4", "v1_2") | V1 %among% c("v1_4", "v1_2", "v1_3", "v1_1"))) | V1 %among% + c("v1_5", "v1_2", "v1_4") & V2 %among% "v2_1" & (V3 %among% c("v3_4", "v3_5", "v3_1") | V3 %among% c("v3_2", "v3_1", + "v3_4")) & (V4 %among% c("v4_1", "v4_3", "v4_2") & V2 %among% c("v2_4", "v2_1", "v2_3") | V2 %among% c("v2_3", "v2_2") + & V1 %among% c("v1_2", "v1_3", "v1_4", "v1_5"))) & (((V3 %among% "v3_1" | V1 %among% c("v1_2", "v1_5", "v1_1", "v1_3")) + & (V2 %among% c("v2_2", "v2_5", "v2_4", "v2_1") & V2 %among% c("v2_5", "v2_2", "v2_4")) | (V3 %among% c("v3_3", "v3_4", + "v3_1", "v3_2") & V2 %among% "v2_2" | (V3 %among% c("v3_3", "v3_1", "v3_4") | V4 %among% c("v4_5", "v4_1")))) & ((V3 + %among% c("v3_2", "v3_3", "v3_4", "v3_5") & V4 %among% c("v4_4", "v4_2") | V1 %among% c("v1_3", "v1_2", "v1_4", "v1_1") + & V2 %among% c("v2_2", "v2_3")) & (V3 %among% c("v3_1", "v3_3", "v3_2") | V3 %among% c("v3_3", "v3_1", "v3_5", "v3_4") + | V4 %among% c("v4_3", "v4_5", "v4_2", "v4_4") & V3 %among% c("v3_5", "v3_1")))) & ((V1 %among% c("v1_1", "v1_2", + "v1_4", "v1_5") & V4 %among% c("v4_4", "v4_5", "v4_1") | V3 %among% c("v3_4", "v3_2") & V1 %among% c("v1_3", "v1_2") | + V3 %among% c("v3_1", "v3_5") & V1 %among% c("v1_1", "v1_3") & (V4 %among% "v4_1" & V3 %among% c("v3_3", "v3_5", "v3_2", + "v3_4")) | (V4 %among% c("v4_1", "v4_3") | V4 %among% c("v4_1", "v4_3", "v4_2")) & (V3 %among% c("v3_1", "v3_4", + "v3_2") & V2 %among% c("v2_1", "v2_2", "v2_5", "v2_4")) & (V3 %among% c("v3_3", "v3_1", "v3_4", "v3_5") & V3 %among% + c("v3_3", "v3_5", "v3_4", "v3_1") | V2 %among% c("v2_4", "v2_2", "v2_5", "v2_3") & V2 %among% c("v2_4", "v2_1", + "v2_2"))) & (V4 %among% c("v4_2", "v4_1") & V1 %among% c("v1_4", "v1_2") & (V3 %among% c("v3_2", "v3_5") | V4 %among% + "v4_5") & (V3 %among% c("v3_2", "v3_1", "v3_4") & V2 %among% c("v2_2", "v2_5", "v2_1") | (V2 %among% c("v2_2", "v2_3") + | V3 %among% c("v3_5", "v3_1", "v3_2", "v3_4"))) | (V2 %among% c("v2_4", "v2_1") | V3 %among% c("v3_3", "v3_5", "v3_1", + "v3_4")) & (V1 %among% c("v1_2", "v1_3", "v1_5") & V2 %among% "v2_5") & (V1 %among% c("v1_2", "v1_5") | V2 %among% + c("v2_3", "v2_1", "v2_4", "v2_5") | (V4 %among% "v4_1" | V2 %among% "v2_2")))) | ((V1 %among% c("v1_1", "v1_4", "v1_5") + | V1 %among% "v1_5") & (V1 %among% c("v1_3", "v1_5") | V2 %among% c("v2_4", "v2_1")) & (V2 %among% c("v2_4", "v2_2", + "v2_1", "v2_5") & V1 %among% "v1_2" | (V1 %among% "v1_4" | V2 %among% c("v2_2", "v2_1", "v2_5", "v2_3"))) & (V1 %among% + c("v1_2", "v1_4", "v1_5") & V3 %among% c("v3_5", "v3_3") | V2 %among% "v2_3" & V1 %among% c("v1_5", "v1_3", "v1_4") | + (V4 %among% "v4_4" | V1 %among% "v1_4") & (V4 %among% "v4_3" & V3 %among% c("v3_2", "v3_4", "v3_1", "v3_5"))) | V4 + %among% c("v4_2", "v4_3", "v4_1") & V3 %among% c("v3_3", "v3_5", "v3_1", "v3_2") & (V2 %among% c("v2_4", "v2_1", + "v2_5") & V3 %among% c("v3_3", "v3_4", "v3_2", "v3_5")) & (V2 %among% c("v2_3", "v2_2") & V1 %among% c("v1_1", "v1_3") + | V1 %among% "v1_4" & V1 %among% c("v1_4", "v1_1")) & ((V2 %among% c("v2_5", "v2_3") & V4 %among% c("v4_5", "v4_4", + "v4_2") | V1 %among% "v1_1" & V1 %among% c("v1_3", "v1_5")) & (V4 %among% c("v4_4", "v4_2", "v4_5") & V2 %among% "v2_2" + & (V2 %among% c("v2_4", "v2_3", "v2_5") | V4 %among% c("v4_1", "v4_4"))))) & ((V1 %among% c("v1_3", "v1_2", "v1_1") | + V2 %among% c("v2_3", "v2_1") | (V2 %among% c("v2_4", "v2_5", "v2_1") | V2 %among% c("v2_5", "v2_3", "v2_2", "v2_1")) | + V1 %among% c("v1_3", "v1_1", "v1_2") & V3 %among% c("v3_2", "v3_3", "v3_1") & (V1 %among% c("v1_3", "v1_5", "v1_4", + "v1_1") & V2 %among% c("v2_3", "v2_2"))) & ((V1 %among% c("v1_5", "v1_3", "v1_4", "v1_2") & V3 %among% c("v3_2", + "v3_5", "v3_3", "v3_1") | V3 %among% c("v3_4", "v3_3", "v3_2", "v3_1") & V4 %among% c("v4_4", "v4_3", "v4_2")) & (V1 + %among% c("v1_4", "v1_2") | V4 %among% c("v4_2", "v4_1", "v4_3", "v4_5") | (V1 %among% "v1_5" | V3 %among% c("v3_4", + "v3_1")))) & (((V1 %among% c("v1_4", "v1_3") | V1 %among% "v1_3") & (V4 %among% c("v4_5", "v4_1", "v4_2") & V1 %among% + c("v1_2", "v1_1", "v1_4")) | V1 %among% c("v1_1", "v1_2") & V4 %among% "v4_5" & (V1 %among% c("v1_3", "v1_5", "v1_1", + "v1_4") | V1 %among% c("v1_1", "v1_2", "v1_5"))) & ((V4 %among% c("v4_2", "v4_4", "v4_1") | V2 %among% c("v2_2", + "v2_4")) & (V1 %among% c("v1_3", "v1_2", "v1_5") | V1 %among% c("v1_2", "v1_1", "v1_5")) & (V3 %among% c("v3_2", + "v3_3", "v3_4", "v3_5") & V4 %among% c("v4_4", "v4_5", "v4_3", "v4_2") | V2 %among% c("v2_4", "v2_5", "v2_2", "v2_3") & + V4 %among% c("v4_1", "v4_5", "v4_3")))))) + From bec9834edf11fcc1f274cd84a9ce1c53c23ef336 Mon Sep 17 00:00:00 2001 From: mb706 Date: Mon, 23 Sep 2024 06:40:51 +0200 Subject: [PATCH 75/87] some final thoughts --- attic/mvsat.mv | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/attic/mvsat.mv b/attic/mvsat.mv index cf17b62f9..613cdc850 100644 --- a/attic/mvsat.mv +++ b/attic/mvsat.mv @@ -212,5 +212,6 @@ # Now that 2nd order sse is implemented, one more possible obvious optimizatoin would be to keep original larger versions of clauses around # and use these for self-subsumption elimination. -# problem: this would make unit handling weird, since we get new units that can now still be self-subsumed. - +# - problem: this would make unit handling weird, since we get new units that can now still be self-subsumed. +# - wehn we have that, we can also make sure 2nd order things only run after the initial 1st order things have all run, since we can then expect +# fewer range changes and hende fewer updates; that probably gives a lot of performance benefit. From 4f132e576f5e4d24a92f4827790669ee8417c690 Mon Sep 17 00:00:00 2001 From: mb706 Date: Mon, 23 Sep 2024 21:49:54 +0200 Subject: [PATCH 76/87] first pass: keep extended clauses --- R/CnfFormula_simplify1.R | 146 ++++++++++++++++++----------- attic/CnfFormula_simplify_greedy.R | 1 + 2 files changed, 90 insertions(+), 57 deletions(-) diff --git a/R/CnfFormula_simplify1.R b/R/CnfFormula_simplify1.R index dc400f1d5..f7e69b708 100644 --- a/R/CnfFormula_simplify1.R +++ b/R/CnfFormula_simplify1.R @@ -58,6 +58,7 @@ simplify_cnf = function(entries, universe) { # maps symbol name -> the index of all non-unit clauses that refer to it symbol_registry = new.env(parent = emptyenv()) + symbol_registry_ext = NULL # registry for "extended" clauses (i.e. clauses where no self-subsumption elimination was applied) is_not_subset_of = NULL # see further down @@ -104,27 +105,13 @@ simplify_cnf = function(entries, universe) { eliminated[[unit_idx]] <<- TRUE } # The symbol registry is empty at the start; the following happens when new units are added later - use_inso = FALSE - if (!is.null(is_not_subset_of)) { - # if we have the is_not_subset_of matrix, we can use it to skip some checks - unit_idx_meta = available_inverse[[unit_idx]] - use_inso = unit_idx_meta <= meta_idx_outer # .. but only if we have built the matrix up to the current index - if (use_inso) { - # if the unit is a subset of the other clause, we will never skip. - inso_column = is_not_subset_of[[unit_idx_meta]][, nu] - } - } + for (s_clause_idx in symbol_registry[[nu]]) { # could have been eliminated by subsumption elimination during unit propagation of another clause # (we are not afraid of is_unit here, since we are the unit for the symbol here -- everything else that has the # symbol gets eliminated) if (eliminated[[s_clause_idx]]) next - if (use_inso) { - # if we already know that s_clause_idx[[nu]] is a subset of unit_idx, we can skip this - # exception: unit_idx is *also* a subset, implying equality, in which case we will do subsumption elimination. - s_clause_idx_meta = available_inverse[[s_clause_idx]] - if (s_clause_idx_meta <= meta_idx_outer && inso_column[[s_clause_idx_meta]] && !is_not_subset_of[[s_clause_idx_meta]][unit_idx_meta, nu]) next - } + adr = apply_domain_restriction(s_clause_idx, nu, unit_domains[[nu]], TRUE) if (identical(adr, TRUE)) return(TRUE) # forward contradiction signal } @@ -144,8 +131,10 @@ simplify_cnf = function(entries, universe) { clause_symbol_length_before = length(clause[[symbol_idx]]) clause[[symbol_idx]] = char_intersect(clause[[symbol_idx]], restringent) if (length(clause[[symbol_idx]]) == length(restringent)) { - # If the lengths match, then the clause is a superset of the unit (since the intersections are equal) - # the clause is therefore subsumed by the unit + # If the lengths match, then the clause is a superset of the restringent (since the intersections are equal) + # the clause is therefore subsumed by the restringent -- unit elimination or subsumption elimination + # + # We do not need to check for clause_ext subsumption: if that were the case, hidden literal addition would get the clause. eliminate_clause_update_sr(clause_idx) return(NULL) } @@ -168,21 +157,22 @@ simplify_cnf = function(entries, universe) { # is_not_subset_of was built, because unit-propagation could be cascading from a unit elimination. if (meta_idx > meta_idx_outer) return(FALSE) - if (!is_unit_propagation) { - # we are not propagating units, so we need to update the subset relations in the other direction. - # we do this first, in case on_updated_subset_relations gets too eager later - # No need to compare against meta_idx_outer, since not_subset_count will be NA for larger indices.. - idx_to_check = which(!is.na(not_subset_count[, meta_idx]) & available %in% symbol_registry[[symbol]]) - for (other_meta_idx in idx_to_check) { - # was the other a subset of us before? that could have changed now. - if (!is_not_subset_of[[other_meta_idx]][meta_idx, symbol] && !all(entries[[available[[other_meta_idx]]]][[symbol]] %in% entries[[clause_idx]][[symbol]])) { - is_not_subset_of[[other_meta_idx]][meta_idx, symbol] <<- TRUE - # no need to call on_updated_subset_relations, since we are increasing rowsums, not decreasing them - not_subset_count[other_meta_idx, meta_idx] <<- not_subset_count[other_meta_idx, meta_idx] + 1L - # no need to call the higher order self subsumption elimination handler here, since we need to do this anyways further down. - } - } - } + ### TODO: I think this is not needed when we keep extended clauses + # if (!is_unit_propagation) { + # # we are not propagating units, so we need to update the subset relations in the other direction. + # # we do this first, in case on_updated_subset_relations gets too eager later + # # No need to compare against meta_idx_outer, since not_subset_count will be NA for larger indices.. + # idx_to_check = which(!is.na(not_subset_count[, meta_idx]) & available %in% symbol_registry[[symbol]]) + # for (other_meta_idx in idx_to_check) { + # # was the other a subset of us before? that could have changed now. + # if (!is_not_subset_of[[other_meta_idx]][meta_idx, symbol] && !all(entries[[available[[other_meta_idx]]]][[symbol]] %in% entries[[clause_idx]][[symbol]])) { + # is_not_subset_of[[other_meta_idx]][meta_idx, symbol] <<- TRUE + # # no need to call on_updated_subset_relations, since we are increasing rowsums, not decreasing them + # not_subset_count[other_meta_idx, meta_idx] <<- not_subset_count[other_meta_idx, meta_idx] + 1L + # # no need to call the higher order self subsumption elimination handler here, since we need to do this anyways further down. + # } + # } + # } is_not_subset_of_col = match(symbol, colnames(is_not_subset_of[[meta_idx]])) # * We could now be a subset of things that we were not a subset of before, so we only need to check the TRUE entries and may be setting them to FALSE. @@ -192,10 +182,10 @@ simplify_cnf = function(entries, universe) { # In particular, we do not need to worry that some other clause that was formerly our subset ceases to be our subset, since that other clause # will also be restricted by the unit. # * We can only ever set those entries to FALSE for which the other clause is in the symbol registry for the current symbol - # --> hence `available %in% symbol_registry[[symbol]]` + # --> hence `available %in% symbol_registry_ext[[symbol]]` # * We only need to check up to the point where we have built is_not_subset_of # --> hence the is.na() - rows_to_check = which(!is.na(not_subset_count[meta_idx, ]) & is_not_subset_of[[meta_idx]][, is_not_subset_of_col] & available %in% symbol_registry[[symbol]]) + rows_to_check = which(!is.na(not_subset_count[meta_idx, ]) & is_not_subset_of[[meta_idx]][, is_not_subset_of_col] & available %in% symbol_registry_ext[[symbol]]) for (other_meta_idx in rows_to_check) { clause_idx_other = available[[other_meta_idx]] # while we only get here for rows that are in the symbol_registry and therefore not eliminated / units, we need to check again since on_updated_subset_relations() @@ -205,7 +195,7 @@ simplify_cnf = function(entries, universe) { # when we get here, that means that the symbol exists both in clause_idx and in other_ref_this symbol, *and* we have seen both clauses # in the is_not_subset_of building process. # If this were not the case, then we would not need to change anything. - other_clause_range = entries[[available[[other_meta_idx]]]][[symbol]] + other_clause_range = entries_ext[[other_meta_idx]][[symbol]] if (!all(entries[[clause_idx]][[symbol]] %in% other_clause_range)) next # we are now a subset (and most likely were not before) @@ -241,6 +231,10 @@ simplify_cnf = function(entries, universe) { # (since it is now a unit) sr = symbol_registry[[names(clause)]] symbol_registry[[names(clause)]] = sr[sr != clause_idx] + if (!is.null(symbol_registry_ext)) { + sr = symbol_registry_ext[[symbol]] + symbol_registry_ext[[symbol]] = sr[sr != clause_idx] + } if (register_unit(clause_idx)) return(TRUE) # forward signal from register_unit: contradiction return(NULL) # clause was turned into a unit } @@ -259,15 +253,17 @@ simplify_cnf = function(entries, universe) { not_subset_count[meta_idx, rows_changed] <<- not_subset_count[meta_idx, rows_changed] - 1L others_ref_this_symbol = available_inverse[sr] # only where we have already set up is_not_subset_of - for (meta_idx_other in others_ref_this_symbol[!is.na(not_subset_count[others_ref_this_symbol, meta_idx])]) { - if (!is_not_subset_of[[meta_idx_other]][meta_idx, symbol]) { - is_not_subset_of[[meta_idx_other]][meta_idx, symbol] <<- TRUE - not_subset_count[meta_idx_other, meta_idx] <<- not_subset_count[meta_idx_other, meta_idx] + 1L - } - } + ## TODO: I think the following is not necessary, since we keep clause_ext now + # for (meta_idx_other in others_ref_this_symbol[!is.na(not_subset_count[others_ref_this_symbol, meta_idx])]) { + # if (!is_not_subset_of[[meta_idx_other]][meta_idx, symbol]) { + # is_not_subset_of[[meta_idx_other]][meta_idx, symbol] <<- TRUE + # not_subset_count[meta_idx_other, meta_idx] <<- not_subset_count[meta_idx_other, meta_idx] + 1L + # } + # } # we could have some leftover TRUEs from eliminated or unit-ed clauses rows_changed_ids = available[rows_changed] for (meta_idx_other in rows_changed[!eliminated[rows_changed_ids] & !is_unit[rows_changed_ids] & rows_changed <= meta_idx_outer]) { + ## TODO: the following comment is obsolete, see above # We have to do this *after* we set the corresponding values to TRUE for others_ref_this_symbol, # since calling this could realistically change the symbol registry (e.g. if it leads to a symbol # being eliminated from other clauses). @@ -435,18 +431,21 @@ simplify_cnf = function(entries, universe) { try_sse_2nd_order = function(meta_idx_oneend, meta_idx_twoends, meta_idx_target, symbol_intersect, symbol_target) { ## assuming that symbol_target exists in meta_idx_target ## assuming that meta_idx_oneend and meta_idx_twoends both have symbol_intersect, and that at least meta_idx_twoends has symbol_target - if (!all(is_not_subset_of[[meta_idx_target]][c(meta_idx_oneend, meta_idx_twoends), symbol_target])) return(FALSE) + # The following does not work any more, since is_not_subset_of relates to larger versions of the oneend / twoend clauses + # if (!all(is_not_subset_of[[meta_idx_target]][c(meta_idx_oneend, meta_idx_twoends), symbol_target])) return(FALSE) idx_oneend = available[[meta_idx_oneend]] idx_twoends = available[[meta_idx_twoends]] idx_target = available[[meta_idx_target]] + # The following is already checked before we all here # if (any(eliminated[c(idx_oneend, idx_twoends, idx_target)]) || any(is_unit[c(idx_oneend, idx_twoends, idx_target)])) return(FALSE) clause_oneend = entries[[idx_oneend]] clause_twoends = entries[[idx_twoends]] - # only proceed if clause_oneend and clause_twoends are disjoint outside of clause_target, with respect to symbol_intersect + # only proceed if clause_oneend and clause_twoends are disjoint outside of clause_target, with respect to symbol_intersect. + # Here, we can use the "extended" version of clause_target. clause_oneend_symbol_intersect = clause_oneend[[symbol_intersect]] if (any(clause_oneend_symbol_intersect %in% clause_twoends[[symbol_intersect]] & - !clause_oneend_symbol_intersect %in% entries[[idx_target]][[symbol_intersect]])) { + !clause_oneend_symbol_intersect %in% entries_ext[[meta_idx_target]][[symbol_intersect]])) { return(FALSE) } apply_domain_restriction(idx_target, symbol_target, char_union(clause_oneend[[symbol_target]], clause_twoends[[symbol_target]]), FALSE) @@ -461,6 +460,12 @@ simplify_cnf = function(entries, universe) { sr = symbol_registry[[s]] symbol_registry[[s]] = sr[sr != clause_idx] } + if (!is.null(symbol_registry_ext)) { + for (s in names(entries[[clause_idx]])) { + sr = symbol_registry_ext[[s]] + symbol_registry_ext[[s]] = sr[sr != clause_idx] + } + } } # process units: @@ -527,15 +532,19 @@ simplify_cnf = function(entries, universe) { # This is the same as sum(is_not_subset_of[[i]][j, ]) not_subset_count = matrix(NA_integer_, nrow = length(available), ncol = length(available)) + # symbol registry for 'extended' clauses + symbol_registry_ext = list2env(as.list(symbol_registry, all.names = TRUE), parent = emptyenv()) + + entries_ext = entries[available] for (meta_idx_outer in seq_along(available)) { clause_idx = available[[meta_idx_outer]] if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) next # may happen if we somehow turn something into a unit that eliminates a later clause clause = entries[[clause_idx]] - # is_not_subset_of[[i]][j, k] records whether for symbol k, clause i is not a subset of clause j + # is_not_subset_of[[i]][j, k] records whether for symbol k, clause i is not a subset of clause_ext j # If k is not in clause i, then var(i, k) is trivially a subset of var(j, k), so this is interpreted as FALSE. - # If k is not in clause j but is in clause i, then var(i, k) is not a subset of var(j, k), so this is interpreted as TRUE. + # If k is not in clause_ext j but is in clause i, then var(i, k) is not a subset of var(j, k), so this is interpreted as TRUE. # We initialize with TRUE and then search for instances where a symbol k is in both clauses i and j, and where var(i, k) *is* a subset of var(j, k). # In that case, we set the entry to FALSE. is_not_subset_of[[meta_idx_outer]] = matrix( @@ -551,28 +560,51 @@ simplify_cnf = function(entries, universe) { for (meta_idx_inner in seq_len(meta_idx_outer - 1L)) { ## need to refresh clause here, since it might have been shortened by unit propagation in an earlier iteration clause = entries[[clause_idx]] + clause_ext = entries_ext[[clause_idx]] clause_idx_inner = available[[meta_idx_inner]] if (eliminated[[clause_idx_inner]] || is_unit[[clause_idx_inner]]) next clause_inner = entries[[clause_idx_inner]] + clause_ext_inner = entries_ext[[clause_idx_inner]] # note that even though we sort entries at the beginning, we can *not* rely on clause_inner to have smaller or equal length than clause, # since unit elimination can change the length of clauses - sci = names(clause_inner) - sci_sc_map = match(sci, names(clause), nomatch = 0L) + sci = names(clause_ext_inner) + sci_sc_map = match(sci, names(clause_ext), nomatch = 0L) sci_names_in_common = which(sci_sc_map != 0L) + sci_nonext_map = match(sci, names(clause_inner), nomatch = 0L) + sci_sc_nonext_map = match(sci, names(clause), nomatch = 0L) # symbols that are not in common trivially get the matrix entry TRUE # (they are not subsets of their counterpart in the other clause, since the other ones are empty) - for (symbol_idx_inner in sci_names_in_common) { - symbol_idx_outer = sci_sc_map[[symbol_idx_inner]] - symbol = sci[[symbol_idx_inner]] + for (symbol_idx_ext_inner in sci_names_in_common) { + symbol_idx_inner = sci_nonext_map[[symbol_idx_ext_inner]] + symbol_idx_outer = sci_sc_nonext_map[[symbol_idx_ext_inner]] + if (symbol_idx_inner == 0L && symbol_idx_outer == 0L) next + symbol_idx_ext_outer = sci_sc_map[[symbol_idx_ext_inner]] # the only one (besides symbol_idx_ext_inner) guaranteed to be non-0 + symbol = sci[[symbol_idx_ext_inner]] - range_inner = clause_inner[[symbol_idx_inner]] - range_outer = clause[[symbol_idx_outer]] - inner_subset_of_outer = all(range_inner %in% range_outer) - outer_subset_of_inner = (inner_subset_of_outer && length(range_outer) == length(range_inner)) || all(range_outer %in% range_inner) + range_ext_inner = clause_ext_inner[[symbol_idx_ext_inner]] + range_ext_outer = clause_ext[[symbol_idx_ext_outer]] + + + inner_subset_of_outer = if (symbol_idx_inner == 0L) { + TRUE + } else { + range_inner = clause_inner[[symbol_idx_inner]] + all(range_inner %in% range_ext_outer) + } + outer_subset_of_inner = if (symbol_idx_outer == 0L) { + TRUE + } else { + range_outer = clause[[symbol_idx_outer]] + # if inner_subset_of_outer is TRUE and range_inner has the same length as range_ext_outer, then + # all(range_inner %in% range_ext_outer) lets us conclude that they are equal. + # However, that only works if symbol_idx_inner is != 0, otherwise range_inner is not defined. + # If we can not onclude equality, we have to do another (expensive) all()-subset-check. + (inner_subset_of_outer && symbol_idx_inner != 0L && length(range_ext_outer) == length(range_inner)) || all(range_outer %in% range_ext_inner) + } if (inner_subset_of_outer) { # Avoid assigning TRUE to matrix that is initialized with TRUE. # We index by column name here, since it is possible that clauses were shortened by @@ -618,7 +650,7 @@ simplify_cnf = function(entries, universe) { # iterating from large to small entries for (clause_idx in remaining_nonunit_entries) { - clause = entries[[clause_idx]] + clause = entries_ext[[clause_idx]] # index inside `is_not_subset_of` meta_idx = available_inverse[[clause_idx]] diff --git a/attic/CnfFormula_simplify_greedy.R b/attic/CnfFormula_simplify_greedy.R index 00d64bad2..e119c52bb 100644 --- a/attic/CnfFormula_simplify_greedy.R +++ b/attic/CnfFormula_simplify_greedy.R @@ -297,6 +297,7 @@ simplify_cnf_greedy = function(entries, universe) { if (meta_idx > meta_idx_outer) return(FALSE) is_not_subset_of_col = match(symbol, colnames(is_not_subset_of[[meta_idx]])) + ## TODO: I THINK the available_ext %in% symbol_registry_ext[[symbol]] in the following line is a bug, since we are *also* a subset of empty clauses. rows_changed = which(is_not_subset_of[[meta_idx]][, is_not_subset_of_col] & available_ext %in% symbol_registry_ext[[symbol]] & !is.na(not_subset_count[meta_idx, ])) not_subset_count[meta_idx, rows_changed] <<- not_subset_count[meta_idx, rows_changed] - 1L is_not_subset_of[[meta_idx]][, is_not_subset_of_col] <<- FALSE From bed7a3bb187f19e9acb873d454c90a2ef0e9e72f Mon Sep 17 00:00:00 2001 From: mb706 Date: Mon, 23 Sep 2024 21:59:50 +0200 Subject: [PATCH 77/87] a few bugfixes --- R/CnfFormula_simplify1.R | 19 +++++++++++-------- 1 file changed, 11 insertions(+), 8 deletions(-) diff --git a/R/CnfFormula_simplify1.R b/R/CnfFormula_simplify1.R index f7e69b708..7b1f9972b 100644 --- a/R/CnfFormula_simplify1.R +++ b/R/CnfFormula_simplify1.R @@ -540,7 +540,7 @@ simplify_cnf = function(entries, universe) { for (meta_idx_outer in seq_along(available)) { clause_idx = available[[meta_idx_outer]] if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) next # may happen if we somehow turn something into a unit that eliminates a later clause - clause = entries[[clause_idx]] + clause_ext = entries_ext[[meta_idx_outer]] # is_not_subset_of[[i]][j, k] records whether for symbol k, clause i is not a subset of clause_ext j # If k is not in clause i, then var(i, k) is trivially a subset of var(j, k), so this is interpreted as FALSE. @@ -550,8 +550,11 @@ simplify_cnf = function(entries, universe) { is_not_subset_of[[meta_idx_outer]] = matrix( TRUE, nrow = length(available), # indexed by meta_idx! - ncol = length(clause), - dimnames = list(NULL, names(clause)) + ncol = length(clause_ext), + # using clause_ext for symbol names, because we can rely on names(clause_ext) being a superset of names(clause). + # It could have happened that clause shrinked already in previous loops, even if SSE does not jump ahead in the loop, + # from unit propagation. So we may waste a bit of memory here, but in return we can easier index the inso-matrices further down. + dimnames = list(NULL, names(clause_ext)) ) # we are not a subset of ourselves # (this prevents us from checking this later in on_updated_subset_relations; if we do check it there, we would eliminate the clause from itself) @@ -560,11 +563,11 @@ simplify_cnf = function(entries, universe) { for (meta_idx_inner in seq_len(meta_idx_outer - 1L)) { ## need to refresh clause here, since it might have been shortened by unit propagation in an earlier iteration clause = entries[[clause_idx]] - clause_ext = entries_ext[[clause_idx]] + clause_ext = entries_ext[[meta_idx_outer]] clause_idx_inner = available[[meta_idx_inner]] if (eliminated[[clause_idx_inner]] || is_unit[[clause_idx_inner]]) next clause_inner = entries[[clause_idx_inner]] - clause_ext_inner = entries_ext[[clause_idx_inner]] + clause_ext_inner = entries_ext[[meta_idx_inner]] # note that even though we sort entries at the beginning, we can *not* rely on clause_inner to have smaller or equal length than clause, # since unit elimination can change the length of clauses @@ -609,10 +612,10 @@ simplify_cnf = function(entries, universe) { # Avoid assigning TRUE to matrix that is initialized with TRUE. # We index by column name here, since it is possible that clauses were shortened by # unit propagation or self subsumption elimination somewhere on the way here - is_not_subset_of[[meta_idx_inner]][meta_idx_outer, symbol] = FALSE + is_not_subset_of[[meta_idx_inner]][meta_idx_outer, symbol_idx_ext_inner] = FALSE } if (outer_subset_of_inner) { - is_not_subset_of[[meta_idx_outer]][meta_idx_inner, symbol] = FALSE + is_not_subset_of[[meta_idx_outer]][meta_idx_inner, symbol_idx_ext_outer] = FALSE } } # prefer to eliminate the outer loopo clause first, since we have already @@ -650,10 +653,10 @@ simplify_cnf = function(entries, universe) { # iterating from large to small entries for (clause_idx in remaining_nonunit_entries) { - clause = entries_ext[[clause_idx]] # index inside `is_not_subset_of` meta_idx = available_inverse[[clause_idx]] + clause = entries_ext[[meta_idx]] remaining_other_entries = remaining_nonunit_entries[remaining_nonunit_entries != clause_idx] # we keep track of which clauses were used for HLA, since every other clause can only do that once. From c6e0919a45a7bd00b55d1512651c4e1bacc70279 Mon Sep 17 00:00:00 2001 From: mb706 Date: Mon, 23 Sep 2024 23:00:25 +0200 Subject: [PATCH 78/87] learned something new --- R/CnfFormula_simplify1.R | 159 ++--- attic/CnfFormula_simplify_halfgreedy.R | 782 +++++++++++++++++++++++++ attic/experiments.R | 54 ++ attic/mvsat.mv | 9 + tests/testthat/test_CnfFormula.R | 16 + 5 files changed, 923 insertions(+), 97 deletions(-) create mode 100644 attic/CnfFormula_simplify_halfgreedy.R diff --git a/R/CnfFormula_simplify1.R b/R/CnfFormula_simplify1.R index 7b1f9972b..dc400f1d5 100644 --- a/R/CnfFormula_simplify1.R +++ b/R/CnfFormula_simplify1.R @@ -58,7 +58,6 @@ simplify_cnf = function(entries, universe) { # maps symbol name -> the index of all non-unit clauses that refer to it symbol_registry = new.env(parent = emptyenv()) - symbol_registry_ext = NULL # registry for "extended" clauses (i.e. clauses where no self-subsumption elimination was applied) is_not_subset_of = NULL # see further down @@ -105,13 +104,27 @@ simplify_cnf = function(entries, universe) { eliminated[[unit_idx]] <<- TRUE } # The symbol registry is empty at the start; the following happens when new units are added later - + use_inso = FALSE + if (!is.null(is_not_subset_of)) { + # if we have the is_not_subset_of matrix, we can use it to skip some checks + unit_idx_meta = available_inverse[[unit_idx]] + use_inso = unit_idx_meta <= meta_idx_outer # .. but only if we have built the matrix up to the current index + if (use_inso) { + # if the unit is a subset of the other clause, we will never skip. + inso_column = is_not_subset_of[[unit_idx_meta]][, nu] + } + } for (s_clause_idx in symbol_registry[[nu]]) { # could have been eliminated by subsumption elimination during unit propagation of another clause # (we are not afraid of is_unit here, since we are the unit for the symbol here -- everything else that has the # symbol gets eliminated) if (eliminated[[s_clause_idx]]) next - + if (use_inso) { + # if we already know that s_clause_idx[[nu]] is a subset of unit_idx, we can skip this + # exception: unit_idx is *also* a subset, implying equality, in which case we will do subsumption elimination. + s_clause_idx_meta = available_inverse[[s_clause_idx]] + if (s_clause_idx_meta <= meta_idx_outer && inso_column[[s_clause_idx_meta]] && !is_not_subset_of[[s_clause_idx_meta]][unit_idx_meta, nu]) next + } adr = apply_domain_restriction(s_clause_idx, nu, unit_domains[[nu]], TRUE) if (identical(adr, TRUE)) return(TRUE) # forward contradiction signal } @@ -131,10 +144,8 @@ simplify_cnf = function(entries, universe) { clause_symbol_length_before = length(clause[[symbol_idx]]) clause[[symbol_idx]] = char_intersect(clause[[symbol_idx]], restringent) if (length(clause[[symbol_idx]]) == length(restringent)) { - # If the lengths match, then the clause is a superset of the restringent (since the intersections are equal) - # the clause is therefore subsumed by the restringent -- unit elimination or subsumption elimination - # - # We do not need to check for clause_ext subsumption: if that were the case, hidden literal addition would get the clause. + # If the lengths match, then the clause is a superset of the unit (since the intersections are equal) + # the clause is therefore subsumed by the unit eliminate_clause_update_sr(clause_idx) return(NULL) } @@ -157,22 +168,21 @@ simplify_cnf = function(entries, universe) { # is_not_subset_of was built, because unit-propagation could be cascading from a unit elimination. if (meta_idx > meta_idx_outer) return(FALSE) - ### TODO: I think this is not needed when we keep extended clauses - # if (!is_unit_propagation) { - # # we are not propagating units, so we need to update the subset relations in the other direction. - # # we do this first, in case on_updated_subset_relations gets too eager later - # # No need to compare against meta_idx_outer, since not_subset_count will be NA for larger indices.. - # idx_to_check = which(!is.na(not_subset_count[, meta_idx]) & available %in% symbol_registry[[symbol]]) - # for (other_meta_idx in idx_to_check) { - # # was the other a subset of us before? that could have changed now. - # if (!is_not_subset_of[[other_meta_idx]][meta_idx, symbol] && !all(entries[[available[[other_meta_idx]]]][[symbol]] %in% entries[[clause_idx]][[symbol]])) { - # is_not_subset_of[[other_meta_idx]][meta_idx, symbol] <<- TRUE - # # no need to call on_updated_subset_relations, since we are increasing rowsums, not decreasing them - # not_subset_count[other_meta_idx, meta_idx] <<- not_subset_count[other_meta_idx, meta_idx] + 1L - # # no need to call the higher order self subsumption elimination handler here, since we need to do this anyways further down. - # } - # } - # } + if (!is_unit_propagation) { + # we are not propagating units, so we need to update the subset relations in the other direction. + # we do this first, in case on_updated_subset_relations gets too eager later + # No need to compare against meta_idx_outer, since not_subset_count will be NA for larger indices.. + idx_to_check = which(!is.na(not_subset_count[, meta_idx]) & available %in% symbol_registry[[symbol]]) + for (other_meta_idx in idx_to_check) { + # was the other a subset of us before? that could have changed now. + if (!is_not_subset_of[[other_meta_idx]][meta_idx, symbol] && !all(entries[[available[[other_meta_idx]]]][[symbol]] %in% entries[[clause_idx]][[symbol]])) { + is_not_subset_of[[other_meta_idx]][meta_idx, symbol] <<- TRUE + # no need to call on_updated_subset_relations, since we are increasing rowsums, not decreasing them + not_subset_count[other_meta_idx, meta_idx] <<- not_subset_count[other_meta_idx, meta_idx] + 1L + # no need to call the higher order self subsumption elimination handler here, since we need to do this anyways further down. + } + } + } is_not_subset_of_col = match(symbol, colnames(is_not_subset_of[[meta_idx]])) # * We could now be a subset of things that we were not a subset of before, so we only need to check the TRUE entries and may be setting them to FALSE. @@ -182,10 +192,10 @@ simplify_cnf = function(entries, universe) { # In particular, we do not need to worry that some other clause that was formerly our subset ceases to be our subset, since that other clause # will also be restricted by the unit. # * We can only ever set those entries to FALSE for which the other clause is in the symbol registry for the current symbol - # --> hence `available %in% symbol_registry_ext[[symbol]]` + # --> hence `available %in% symbol_registry[[symbol]]` # * We only need to check up to the point where we have built is_not_subset_of # --> hence the is.na() - rows_to_check = which(!is.na(not_subset_count[meta_idx, ]) & is_not_subset_of[[meta_idx]][, is_not_subset_of_col] & available %in% symbol_registry_ext[[symbol]]) + rows_to_check = which(!is.na(not_subset_count[meta_idx, ]) & is_not_subset_of[[meta_idx]][, is_not_subset_of_col] & available %in% symbol_registry[[symbol]]) for (other_meta_idx in rows_to_check) { clause_idx_other = available[[other_meta_idx]] # while we only get here for rows that are in the symbol_registry and therefore not eliminated / units, we need to check again since on_updated_subset_relations() @@ -195,7 +205,7 @@ simplify_cnf = function(entries, universe) { # when we get here, that means that the symbol exists both in clause_idx and in other_ref_this symbol, *and* we have seen both clauses # in the is_not_subset_of building process. # If this were not the case, then we would not need to change anything. - other_clause_range = entries_ext[[other_meta_idx]][[symbol]] + other_clause_range = entries[[available[[other_meta_idx]]]][[symbol]] if (!all(entries[[clause_idx]][[symbol]] %in% other_clause_range)) next # we are now a subset (and most likely were not before) @@ -231,10 +241,6 @@ simplify_cnf = function(entries, universe) { # (since it is now a unit) sr = symbol_registry[[names(clause)]] symbol_registry[[names(clause)]] = sr[sr != clause_idx] - if (!is.null(symbol_registry_ext)) { - sr = symbol_registry_ext[[symbol]] - symbol_registry_ext[[symbol]] = sr[sr != clause_idx] - } if (register_unit(clause_idx)) return(TRUE) # forward signal from register_unit: contradiction return(NULL) # clause was turned into a unit } @@ -253,17 +259,15 @@ simplify_cnf = function(entries, universe) { not_subset_count[meta_idx, rows_changed] <<- not_subset_count[meta_idx, rows_changed] - 1L others_ref_this_symbol = available_inverse[sr] # only where we have already set up is_not_subset_of - ## TODO: I think the following is not necessary, since we keep clause_ext now - # for (meta_idx_other in others_ref_this_symbol[!is.na(not_subset_count[others_ref_this_symbol, meta_idx])]) { - # if (!is_not_subset_of[[meta_idx_other]][meta_idx, symbol]) { - # is_not_subset_of[[meta_idx_other]][meta_idx, symbol] <<- TRUE - # not_subset_count[meta_idx_other, meta_idx] <<- not_subset_count[meta_idx_other, meta_idx] + 1L - # } - # } + for (meta_idx_other in others_ref_this_symbol[!is.na(not_subset_count[others_ref_this_symbol, meta_idx])]) { + if (!is_not_subset_of[[meta_idx_other]][meta_idx, symbol]) { + is_not_subset_of[[meta_idx_other]][meta_idx, symbol] <<- TRUE + not_subset_count[meta_idx_other, meta_idx] <<- not_subset_count[meta_idx_other, meta_idx] + 1L + } + } # we could have some leftover TRUEs from eliminated or unit-ed clauses rows_changed_ids = available[rows_changed] for (meta_idx_other in rows_changed[!eliminated[rows_changed_ids] & !is_unit[rows_changed_ids] & rows_changed <= meta_idx_outer]) { - ## TODO: the following comment is obsolete, see above # We have to do this *after* we set the corresponding values to TRUE for others_ref_this_symbol, # since calling this could realistically change the symbol registry (e.g. if it leads to a symbol # being eliminated from other clauses). @@ -431,21 +435,18 @@ simplify_cnf = function(entries, universe) { try_sse_2nd_order = function(meta_idx_oneend, meta_idx_twoends, meta_idx_target, symbol_intersect, symbol_target) { ## assuming that symbol_target exists in meta_idx_target ## assuming that meta_idx_oneend and meta_idx_twoends both have symbol_intersect, and that at least meta_idx_twoends has symbol_target - # The following does not work any more, since is_not_subset_of relates to larger versions of the oneend / twoend clauses - # if (!all(is_not_subset_of[[meta_idx_target]][c(meta_idx_oneend, meta_idx_twoends), symbol_target])) return(FALSE) + if (!all(is_not_subset_of[[meta_idx_target]][c(meta_idx_oneend, meta_idx_twoends), symbol_target])) return(FALSE) idx_oneend = available[[meta_idx_oneend]] idx_twoends = available[[meta_idx_twoends]] idx_target = available[[meta_idx_target]] - # The following is already checked before we all here # if (any(eliminated[c(idx_oneend, idx_twoends, idx_target)]) || any(is_unit[c(idx_oneend, idx_twoends, idx_target)])) return(FALSE) clause_oneend = entries[[idx_oneend]] clause_twoends = entries[[idx_twoends]] - # only proceed if clause_oneend and clause_twoends are disjoint outside of clause_target, with respect to symbol_intersect. - # Here, we can use the "extended" version of clause_target. + # only proceed if clause_oneend and clause_twoends are disjoint outside of clause_target, with respect to symbol_intersect clause_oneend_symbol_intersect = clause_oneend[[symbol_intersect]] if (any(clause_oneend_symbol_intersect %in% clause_twoends[[symbol_intersect]] & - !clause_oneend_symbol_intersect %in% entries_ext[[meta_idx_target]][[symbol_intersect]])) { + !clause_oneend_symbol_intersect %in% entries[[idx_target]][[symbol_intersect]])) { return(FALSE) } apply_domain_restriction(idx_target, symbol_target, char_union(clause_oneend[[symbol_target]], clause_twoends[[symbol_target]]), FALSE) @@ -460,12 +461,6 @@ simplify_cnf = function(entries, universe) { sr = symbol_registry[[s]] symbol_registry[[s]] = sr[sr != clause_idx] } - if (!is.null(symbol_registry_ext)) { - for (s in names(entries[[clause_idx]])) { - sr = symbol_registry_ext[[s]] - symbol_registry_ext[[s]] = sr[sr != clause_idx] - } - } } # process units: @@ -532,29 +527,22 @@ simplify_cnf = function(entries, universe) { # This is the same as sum(is_not_subset_of[[i]][j, ]) not_subset_count = matrix(NA_integer_, nrow = length(available), ncol = length(available)) - # symbol registry for 'extended' clauses - symbol_registry_ext = list2env(as.list(symbol_registry, all.names = TRUE), parent = emptyenv()) - - entries_ext = entries[available] for (meta_idx_outer in seq_along(available)) { clause_idx = available[[meta_idx_outer]] if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) next # may happen if we somehow turn something into a unit that eliminates a later clause - clause_ext = entries_ext[[meta_idx_outer]] + clause = entries[[clause_idx]] - # is_not_subset_of[[i]][j, k] records whether for symbol k, clause i is not a subset of clause_ext j + # is_not_subset_of[[i]][j, k] records whether for symbol k, clause i is not a subset of clause j # If k is not in clause i, then var(i, k) is trivially a subset of var(j, k), so this is interpreted as FALSE. - # If k is not in clause_ext j but is in clause i, then var(i, k) is not a subset of var(j, k), so this is interpreted as TRUE. + # If k is not in clause j but is in clause i, then var(i, k) is not a subset of var(j, k), so this is interpreted as TRUE. # We initialize with TRUE and then search for instances where a symbol k is in both clauses i and j, and where var(i, k) *is* a subset of var(j, k). # In that case, we set the entry to FALSE. is_not_subset_of[[meta_idx_outer]] = matrix( TRUE, nrow = length(available), # indexed by meta_idx! - ncol = length(clause_ext), - # using clause_ext for symbol names, because we can rely on names(clause_ext) being a superset of names(clause). - # It could have happened that clause shrinked already in previous loops, even if SSE does not jump ahead in the loop, - # from unit propagation. So we may waste a bit of memory here, but in return we can easier index the inso-matrices further down. - dimnames = list(NULL, names(clause_ext)) + ncol = length(clause), + dimnames = list(NULL, names(clause)) ) # we are not a subset of ourselves # (this prevents us from checking this later in on_updated_subset_relations; if we do check it there, we would eliminate the clause from itself) @@ -563,59 +551,36 @@ simplify_cnf = function(entries, universe) { for (meta_idx_inner in seq_len(meta_idx_outer - 1L)) { ## need to refresh clause here, since it might have been shortened by unit propagation in an earlier iteration clause = entries[[clause_idx]] - clause_ext = entries_ext[[meta_idx_outer]] clause_idx_inner = available[[meta_idx_inner]] if (eliminated[[clause_idx_inner]] || is_unit[[clause_idx_inner]]) next clause_inner = entries[[clause_idx_inner]] - clause_ext_inner = entries_ext[[meta_idx_inner]] # note that even though we sort entries at the beginning, we can *not* rely on clause_inner to have smaller or equal length than clause, # since unit elimination can change the length of clauses - sci = names(clause_ext_inner) - sci_sc_map = match(sci, names(clause_ext), nomatch = 0L) + sci = names(clause_inner) + sci_sc_map = match(sci, names(clause), nomatch = 0L) sci_names_in_common = which(sci_sc_map != 0L) - sci_nonext_map = match(sci, names(clause_inner), nomatch = 0L) - sci_sc_nonext_map = match(sci, names(clause), nomatch = 0L) # symbols that are not in common trivially get the matrix entry TRUE # (they are not subsets of their counterpart in the other clause, since the other ones are empty) - for (symbol_idx_ext_inner in sci_names_in_common) { - symbol_idx_inner = sci_nonext_map[[symbol_idx_ext_inner]] - symbol_idx_outer = sci_sc_nonext_map[[symbol_idx_ext_inner]] - if (symbol_idx_inner == 0L && symbol_idx_outer == 0L) next - symbol_idx_ext_outer = sci_sc_map[[symbol_idx_ext_inner]] # the only one (besides symbol_idx_ext_inner) guaranteed to be non-0 - symbol = sci[[symbol_idx_ext_inner]] + for (symbol_idx_inner in sci_names_in_common) { + symbol_idx_outer = sci_sc_map[[symbol_idx_inner]] + symbol = sci[[symbol_idx_inner]] + range_inner = clause_inner[[symbol_idx_inner]] + range_outer = clause[[symbol_idx_outer]] - range_ext_inner = clause_ext_inner[[symbol_idx_ext_inner]] - range_ext_outer = clause_ext[[symbol_idx_ext_outer]] - - - inner_subset_of_outer = if (symbol_idx_inner == 0L) { - TRUE - } else { - range_inner = clause_inner[[symbol_idx_inner]] - all(range_inner %in% range_ext_outer) - } - outer_subset_of_inner = if (symbol_idx_outer == 0L) { - TRUE - } else { - range_outer = clause[[symbol_idx_outer]] - # if inner_subset_of_outer is TRUE and range_inner has the same length as range_ext_outer, then - # all(range_inner %in% range_ext_outer) lets us conclude that they are equal. - # However, that only works if symbol_idx_inner is != 0, otherwise range_inner is not defined. - # If we can not onclude equality, we have to do another (expensive) all()-subset-check. - (inner_subset_of_outer && symbol_idx_inner != 0L && length(range_ext_outer) == length(range_inner)) || all(range_outer %in% range_ext_inner) - } + inner_subset_of_outer = all(range_inner %in% range_outer) + outer_subset_of_inner = (inner_subset_of_outer && length(range_outer) == length(range_inner)) || all(range_outer %in% range_inner) if (inner_subset_of_outer) { # Avoid assigning TRUE to matrix that is initialized with TRUE. # We index by column name here, since it is possible that clauses were shortened by # unit propagation or self subsumption elimination somewhere on the way here - is_not_subset_of[[meta_idx_inner]][meta_idx_outer, symbol_idx_ext_inner] = FALSE + is_not_subset_of[[meta_idx_inner]][meta_idx_outer, symbol] = FALSE } if (outer_subset_of_inner) { - is_not_subset_of[[meta_idx_outer]][meta_idx_inner, symbol_idx_ext_outer] = FALSE + is_not_subset_of[[meta_idx_outer]][meta_idx_inner, symbol] = FALSE } } # prefer to eliminate the outer loopo clause first, since we have already @@ -653,10 +618,10 @@ simplify_cnf = function(entries, universe) { # iterating from large to small entries for (clause_idx in remaining_nonunit_entries) { + clause = entries[[clause_idx]] # index inside `is_not_subset_of` meta_idx = available_inverse[[clause_idx]] - clause = entries_ext[[meta_idx]] remaining_other_entries = remaining_nonunit_entries[remaining_nonunit_entries != clause_idx] # we keep track of which clauses were used for HLA, since every other clause can only do that once. diff --git a/attic/CnfFormula_simplify_halfgreedy.R b/attic/CnfFormula_simplify_halfgreedy.R new file mode 100644 index 000000000..7b1f9972b --- /dev/null +++ b/attic/CnfFormula_simplify_halfgreedy.R @@ -0,0 +1,782 @@ + + +simplify_cnf = function(entries, universe) { + ################################# + # Some vocabulary: + # - `entries` is a list of `clauses`, which are named lists. + # - `clauses`' names are `symbols`, the values are the `ranges` of the symbols within that clause + # - `unit`: clause with single symbol + # Glossary of operations: + # - `unit propagation`: ranges of a symbol within a unit constitute the entire possible range of that symbol, + # so all clauses with that symbol are restricted to those values + # - `subsumption elimination`: if all ranges of all symbols within one clause are subsets of those ranges in another clause, + # then the other clause can be removed + # - `self-subsumption elimination`: if the ranges of all except one symbol within one clause are a subset of those ranges + # in another clause, then the remaining symbol in the latter clause can be intersected with the remaining symbol. + # - `hidden literal addition` (HLA): if the ranges of all except one symbol within one clause are a subset of those ranges + # in another clause, then the *complement* of the remaining symbol in the former clause can be added to the latter clause. + # This is basically the reverse of self-subsumption elimination. We do not use this to change clauses directly; + # the point here is that the resulting clause, even if applied repeatedly, is logically equivalent to the original clause within the formula: + # - `hidden subsumption elimination`: if applying HLA results in a clause that can be subsumed, the original clause can be removed. + # - `hidden tautology elimination`: if applying HLA results in a clause that is a tautology, the original clause can be removed. + # Note: 'Clause Elimination Procedures for CNF Formulas' by Marijn Heule et al. calls this "Asymmetric Hidden Literal Addition". + ################################# + + ######################## + ## Helper functions ## + ######################## + + # faster intersect, setdiff etc. that rely on x, y being characters with no duplicates + char_intersect = function(x, y) x[x %in% y] + char_setdiff = function(x, y) x[!x %in% y] + char_union = function(x, y) c(x, y[!y %in% x]) + # construct the CnfFormula return object + return_entries = function(entries) { + structure( + if (!length(entries)) TRUE else entries, + universe = universe, + class = "CnfFormula" + ) + } + + if (is.logical(entries)) return(return_entries(entries)) + + ######################## + ## Variable setup ## + ######################## + + entries = entries[order(lengths(entries))] + + is_unit = lengths(entries) == 1L + eliminated = logical(length(entries)) + + # maps symbol name -> the index of unit clauses + unit_registry = new.env(parent = emptyenv()) + + # maps symbol name -> their current domain + unit_domains = new.env(parent = emptyenv()) + + # maps symbol name -> the index of all non-unit clauses that refer to it + symbol_registry = new.env(parent = emptyenv()) + symbol_registry_ext = NULL # registry for "extended" clauses (i.e. clauses where no self-subsumption elimination was applied) + + is_not_subset_of = NULL # see further down + + ################################## + ## Event-driven clause handling ## + ################################## + # The following functions process the CNF clauses in various ways, + # depending on the current state of the entries. + # The state of the entries is updated in-place. + # The functions are then called in a loop, but they may also call each other. + # It is therefore important that they make the global state consistent before + # calling other functions, and that they are aware of how the global state *can* + # have changed upon their return. + # - entries[[clause_idx]] should be updated if necessary before other fns are called + # - symbol_registry[[symbol]] could have been updated + # - eliminated[[clause_idx]] could have been set to TRUE + # Since functions can call each other in different ways, `eliminated` could have changed even for clauses + # for which the other functions were not called. + + # Register a clause as a unit: + # - check if there is already a unit for this symbol + # - if not, add it to the unit registry + # - otherwise, intersect unit domains (and exit on contradiction) + # - apply unit propagation + # - We do *not* update the sybmol registry here; if the clause is registered for a given symbol, + # it has to be removed from there *before* calling this function. + register_unit = function(unit_idx) { + unit = entries[[unit_idx]] + nu = names(unit) + ur = unit_registry[[nu]] + if (is.null(ur)) { + unit_registry[[nu]] = unit_idx # environment assignment + unit_domains[[nu]] = unit[[1L]] # environment assignment + # this is init'd TRUE for those w/ length 1 at the start, we set it to TRUE for clauses where symbols were eliminated + is_unit[[unit_idx]] <<- TRUE + } else { + # two units refer to the same symbol + # -> we keep the one we saw before but update it to the intersection. + # the current one is eliminated + prev_unit = unit_domains[[nu]] + unit_isct = prev_unit[prev_unit %in% unit[[1L]]] + if (!length(unit_isct)) return(TRUE) # signal that we have a contradiction and can exit + entries[[ur]][[1L]] <<- (unit_domains[[nu]] = unit_isct) # update the *old* unit and unit_domains in one go. unit_domains is updated by-reference (environment) + eliminated[[unit_idx]] <<- TRUE + } + # The symbol registry is empty at the start; the following happens when new units are added later + + for (s_clause_idx in symbol_registry[[nu]]) { + # could have been eliminated by subsumption elimination during unit propagation of another clause + # (we are not afraid of is_unit here, since we are the unit for the symbol here -- everything else that has the + # symbol gets eliminated) + if (eliminated[[s_clause_idx]]) next + + adr = apply_domain_restriction(s_clause_idx, nu, unit_domains[[nu]], TRUE) + if (identical(adr, TRUE)) return(TRUE) # forward contradiction signal + } + FALSE # no contradiction + } + + # restrict the symbol in the clause to a given domain, e.g. a unit + # - clause_idx: index in entries + # - symbol: name of symbol to restrict + # - restringent: domain to restrict to + # returns TRUE if a contradiction was detected, NULL if the clause was eliminated + apply_domain_restriction = function(clause_idx, symbol, restringent, is_unit_propagation) { + clause = entries[[clause_idx]] + symbol_idx = match(symbol, names(clause)) + if (is.na(symbol_idx)) return(FALSE) + + clause_symbol_length_before = length(clause[[symbol_idx]]) + clause[[symbol_idx]] = char_intersect(clause[[symbol_idx]], restringent) + if (length(clause[[symbol_idx]]) == length(restringent)) { + # If the lengths match, then the clause is a superset of the restringent (since the intersections are equal) + # the clause is therefore subsumed by the restringent -- unit elimination or subsumption elimination + # + # We do not need to check for clause_ext subsumption: if that were the case, hidden literal addition would get the clause. + eliminate_clause_update_sr(clause_idx) + return(NULL) + } + # clause was not changed + if (length(clause[[symbol_idx]]) == clause_symbol_length_before) return(FALSE) + if (!length(clause[[symbol_idx]])) { + # the symbol is not in the clause anymore + return(eliminate_symbol_from_clause(clause_idx, symbol)) + } + # clause was changed. + # We don't need to do this when we go the eliminate_symbol_from_clause route, since that will update the clause in any case. + entries[[clause_idx]] <<- clause + + # We need to update the subset relations matrix, if it exists + if (is.null(is_not_subset_of)) return(FALSE) + + meta_idx = available_inverse[[clause_idx]] + # meta_idx_outer is the index up to which we have built is_not_subset_of; if meta_idx > meta_idx_outer, then we haven't seen the clause yet. + # we are not relying on the fact that as soon as is_not_subset_of is non-null, we will only get here for clauses for which + # is_not_subset_of was built, because unit-propagation could be cascading from a unit elimination. + if (meta_idx > meta_idx_outer) return(FALSE) + + ### TODO: I think this is not needed when we keep extended clauses + # if (!is_unit_propagation) { + # # we are not propagating units, so we need to update the subset relations in the other direction. + # # we do this first, in case on_updated_subset_relations gets too eager later + # # No need to compare against meta_idx_outer, since not_subset_count will be NA for larger indices.. + # idx_to_check = which(!is.na(not_subset_count[, meta_idx]) & available %in% symbol_registry[[symbol]]) + # for (other_meta_idx in idx_to_check) { + # # was the other a subset of us before? that could have changed now. + # if (!is_not_subset_of[[other_meta_idx]][meta_idx, symbol] && !all(entries[[available[[other_meta_idx]]]][[symbol]] %in% entries[[clause_idx]][[symbol]])) { + # is_not_subset_of[[other_meta_idx]][meta_idx, symbol] <<- TRUE + # # no need to call on_updated_subset_relations, since we are increasing rowsums, not decreasing them + # not_subset_count[other_meta_idx, meta_idx] <<- not_subset_count[other_meta_idx, meta_idx] + 1L + # # no need to call the higher order self subsumption elimination handler here, since we need to do this anyways further down. + # } + # } + # } + + is_not_subset_of_col = match(symbol, colnames(is_not_subset_of[[meta_idx]])) + # * We could now be a subset of things that we were not a subset of before, so we only need to check the TRUE entries and may be setting them to FALSE. + # --> hence `is_not_subset_of[meta_idx][is_not_subset_of[meta_idx]` + # Note: we cannot address is_not_subset_of by symbol_idx, since clauses may get shorter but is_not_subset_of stays the same! + # * If this is unit propagation, we do not need to check other entries, since apply_domain_restriction happens to all clauses in a row, so the counter-side is updated in time. + # In particular, we do not need to worry that some other clause that was formerly our subset ceases to be our subset, since that other clause + # will also be restricted by the unit. + # * We can only ever set those entries to FALSE for which the other clause is in the symbol registry for the current symbol + # --> hence `available %in% symbol_registry_ext[[symbol]]` + # * We only need to check up to the point where we have built is_not_subset_of + # --> hence the is.na() + rows_to_check = which(!is.na(not_subset_count[meta_idx, ]) & is_not_subset_of[[meta_idx]][, is_not_subset_of_col] & available %in% symbol_registry_ext[[symbol]]) + for (other_meta_idx in rows_to_check) { + clause_idx_other = available[[other_meta_idx]] + # while we only get here for rows that are in the symbol_registry and therefore not eliminated / units, we need to check again since on_updated_subset_relations() + # can change this during the loop. + if (eliminated[[clause_idx_other]] || is_unit[[clause_idx_other]]) next + + # when we get here, that means that the symbol exists both in clause_idx and in other_ref_this symbol, *and* we have seen both clauses + # in the is_not_subset_of building process. + # If this were not the case, then we would not need to change anything. + other_clause_range = entries_ext[[other_meta_idx]][[symbol]] + if (!all(entries[[clause_idx]][[symbol]] %in% other_clause_range)) next + + # we are now a subset (and most likely were not before) + # ("most likely" because it could probably happen that we re-enter this part through some cascading elimination / propagation) + if (!is_not_subset_of[[meta_idx]][other_meta_idx, is_not_subset_of_col]) next + is_not_subset_of[[meta_idx]][other_meta_idx, is_not_subset_of_col] <<- FALSE + not_subset_count[meta_idx, other_meta_idx] <<- (rowsum = not_subset_count[meta_idx, other_meta_idx] - 1L) + if (rowsum > 2L) next + ousr = on_updated_subset_relations(meta_idx, other_meta_idx) + if (identical(ousr, TRUE)) return(TRUE) # forward contradiction signal. We don't care if other_meta_idx was eliminated. + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) return(NULL) # need to check more directly if things escalated somehow and clause_idx was eliminated indirectly + } + # call on_domain_changed_handle_2nd_order_sse + # it is not a waste w/r/t the 'on_updated_subset_relations' call, since that one only deals with clauses for which the symbol is set to FALSE now, + # i.e. precisely the other clauses. + on_update_range(meta_idx, symbol) + } + + # eliminate `symbol` from `clause_idx` + # returns 'NULL' for turned into a unit or eliminated, 'TRUE' for contradiction, 'FALSE' for nothing happened + eliminate_symbol_from_clause = function(clause_idx, symbol) { + clause = entries[[clause_idx]] + clause[[symbol]] = NULL + if (!length(clause)) return(TRUE) # signal that we have a contradiction and can exit + # remove from symbol registry of the symbol that went to 0 + sr = symbol_registry[[symbol]] + symbol_registry[[symbol]] = sr[sr != clause_idx] + + entries[[clause_idx]] <<- clause + if (length(clause) == 1) { + # new unit ahoy + # remove from symbol registry of the symbol that remains in the clause + # (since it is now a unit) + sr = symbol_registry[[names(clause)]] + symbol_registry[[names(clause)]] = sr[sr != clause_idx] + if (!is.null(symbol_registry_ext)) { + sr = symbol_registry_ext[[symbol]] + symbol_registry_ext[[symbol]] = sr[sr != clause_idx] + } + if (register_unit(clause_idx)) return(TRUE) # forward signal from register_unit: contradiction + return(NULL) # clause was turned into a unit + } + # clause was not turned into a unit, so we need to fill in is_not_subset_of + if (is.null(is_not_subset_of)) return(FALSE) # we have not started filling this one in + + meta_idx = available_inverse[[clause_idx]] + # meta_idx_outer is the index up to which we have built is_not_subset_of; if meta_idx > meta_idx_outer, then we haven't seen the clause yet. + # we are not relying on the fact that as soon as is_not_subset_of is non-null, we will only get here for clauses for which + # this was built, because it could be cascading from a unit elimination. + if (meta_idx > meta_idx_outer) return(FALSE) + + is_not_subset_of_col = match(symbol, colnames(is_not_subset_of[[meta_idx]])) + rows_changed = which(is_not_subset_of[[meta_idx]][, is_not_subset_of_col] & !is.na(not_subset_count[meta_idx, ])) + is_not_subset_of[[meta_idx]][, is_not_subset_of_col] <<- FALSE + not_subset_count[meta_idx, rows_changed] <<- not_subset_count[meta_idx, rows_changed] - 1L + others_ref_this_symbol = available_inverse[sr] + # only where we have already set up is_not_subset_of + ## TODO: I think the following is not necessary, since we keep clause_ext now + # for (meta_idx_other in others_ref_this_symbol[!is.na(not_subset_count[others_ref_this_symbol, meta_idx])]) { + # if (!is_not_subset_of[[meta_idx_other]][meta_idx, symbol]) { + # is_not_subset_of[[meta_idx_other]][meta_idx, symbol] <<- TRUE + # not_subset_count[meta_idx_other, meta_idx] <<- not_subset_count[meta_idx_other, meta_idx] + 1L + # } + # } + # we could have some leftover TRUEs from eliminated or unit-ed clauses + rows_changed_ids = available[rows_changed] + for (meta_idx_other in rows_changed[!eliminated[rows_changed_ids] & !is_unit[rows_changed_ids] & rows_changed <= meta_idx_outer]) { + ## TODO: the following comment is obsolete, see above + # We have to do this *after* we set the corresponding values to TRUE for others_ref_this_symbol, + # since calling this could realistically change the symbol registry (e.g. if it leads to a symbol + # being eliminated from other clauses). + clause_idx_other = available[[meta_idx_other]] + # while we *do* restrict meta_idx_other in the for loop already, eliminated and is_unit can still change during the loop, so check here again + if (eliminated[[clause_idx_other]] || is_unit[[clause_idx_other]]) next + if (not_subset_count[meta_idx, meta_idx_other] > 2L) next + ousr = on_updated_subset_relations(meta_idx, meta_idx_other) + if (identical(ousr, TRUE)) return(TRUE) + # on_updated_subset_relations could cascade down to eliminating meta_idx (i.e. clause_idx) + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) return(NULL) + } + FALSE + } + + # returns 'NULL' when meta_idx_other was eliminated (or possibly turned into a unit), + # 'TRUE' for contradiction, 'FALSE' for nothing changed + on_updated_subset_relations = function(meta_idx, meta_idx_other) { + # the row `meta_idx_other` of `is_not_subset_of[[meta_idx]]` has been updated. + # we now check whether we can apply subsumption elimination, or at least self-subsumption elimination, on `meta_idx`. + rowsum = not_subset_count[meta_idx, meta_idx_other] + if (rowsum > 2L) return(FALSE) # nothing to do + if (rowsum == 2L) { + hs2oo = handle_sse_2nd_order_twoend(meta_idx, meta_idx_other, NULL) + if (identical(hs2oo, TRUE)) return(TRUE) + clause_other = available[[meta_idx_other]] + if (eliminated[[clause_other]] || is_unit[[clause_other]]) return(NULL) + return(FALSE) + } + if (rowsum == 0) { + eliminate_clause_update_sr(available[[meta_idx_other]]) + return(NULL) + } + # rowsum == 1 + symbol_to_restrict = colnames(is_not_subset_of[[meta_idx]])[is_not_subset_of[[meta_idx]][meta_idx_other, ]] + # update clause and sc! + + # note we update meta_idx_other: we are currently subset of that other clause w/r/t all except one symbol. + # we can therefore intersect that last symbol in the other clause with the range of that symbol in the current clause. + # apply_domain_restriction will take care of eliminating the symbol if the range becomes empty. + # It could in theory even do subsumption, but we have already taken care of that above. + adr = apply_domain_restriction(available[[meta_idx_other]], symbol_to_restrict, entries[[available[[meta_idx]]]][[symbol_to_restrict]], FALSE) + if (is.null(adr)) return(NULL) + if (adr) return(TRUE) + clause_idx = available[[meta_idx]] + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) return(FALSE) + hs2oo = handle_sse_2nd_order_oneend(meta_idx, meta_idx_other, symbol_to_restrict) + if (identical(hs2oo, TRUE)) return(TRUE) + clause_other = available[[meta_idx_other]] + if (eliminated[[clause_other]] || is_unit[[clause_other]]) return(NULL) + FALSE + } + + # second order self-subsumption elimination + # this is called whenever the range of symbol in meta_idx shrinks, opening up the possibility for 2nd order self-subsumption. + # meta_idx is the clause that will remove symbol range from other clauses. + # returns NULL if meta_idx was eliminated, FALSE if no contradiction, TRUE if contradiction + on_update_range = function(meta_idx, symbol) { + ## assuming the symbol exists in meta_idx + # availability of symbol in the other clause is not necessary here! + # units don't need to be treated separately: + # - since they only work with 2 length-2-clauses that have both the same symbol: the one of the unit, and another one; in the other one they must be disjoint. + # - because of this, they will HS-eliminate the unit. + + inso_symbol_col = match(symbol, colnames(is_not_subset_of[[meta_idx]])) + potential_targets = which(is_not_subset_of[[meta_idx]][, inso_symbol_col] & !eliminated[available] & !is_unit[available] & !is.na(not_subset_count[meta_idx, ])) + + targets_while_oneend = potential_targets[not_subset_count[meta_idx, potential_targets] == 1L] + + for (meta_idx_target in targets_while_oneend) { + hs2oo = handle_sse_2nd_order_oneend(meta_idx, meta_idx_target, symbol) + if (is.null(hs2oo)) return(NULL) # meta_idx eliminated + if (hs2oo) return(TRUE) + } + targets_while_twoend = potential_targets[not_subset_count[meta_idx, potential_targets] == 2L] + for (meta_idx_target in targets_while_twoend) { + hs2oo = handle_sse_2nd_order_twoend(meta_idx, meta_idx_target, symbol) + if (is.null(hs2oo)) return(NULL) # meta_idx eliminated + if (hs2oo) return(TRUE) + } + FALSE + } + + # meta_idx is not subset of meta_idx_target over 'symbol'. + # check if there are other clauses that are non-subsets of meta_idx_target for two symbols, one of which is 'symbol' as well. + # return NULL if clause_idx is eliminated. + handle_sse_2nd_order_oneend = function(meta_idx, meta_idx_target, symbol) { + # we don't need to check whether symbol is in meta_idx, since then it will automatically not be a non-subset of target + inso_symbol_col = match(symbol, colnames(is_not_subset_of[[meta_idx]])) + clause_idx = available[[meta_idx]] + symbol_clauses = symbol_registry[[symbol]] + symbol_clauses_meta = available_inverse[symbol_clauses] + + clause_idx_target = available[[meta_idx_target]] + # intersect on symbol with some other clause that has not_subset_count == 2, and where the target symbol is present in the garget + if (eliminated[[clause_idx_target]] || is_unit[[clause_idx_target]]) return(FALSE) + twoends = symbol_clauses_meta[not_subset_count[symbol_clauses_meta, meta_idx_target] == 2L] + for (meta_idx_twoend in twoends[!is.na(twoends)]) { # twoends is NA for clauses that have not been processed yet + # in every loop iteration, check our conditions again, since anything can happen when we do sse: + # target exists, is not a unit (these are checked outside the for loop as well as with `ts2o`), and exactly one symbol ("symbol") of meta_idx does not cover it. + if (not_subset_count[meta_idx, meta_idx_target] != 1L || !is_not_subset_of[[meta_idx]][meta_idx_target, inso_symbol_col]) break + clause_idx_twoend = available[[meta_idx_twoend]] + # now check that the meta_idx_twoend is still valid: + # exists, not a unit, it does not cover the target with exactly two symbols, one of which is `symbol` + if (eliminated[[clause_idx_twoend]] || is_unit[[clause_idx_twoend]] || + not_subset_count[meta_idx_twoend, meta_idx_target] != 2L) { + next + } + symbol_target = colnames(is_not_subset_of[[meta_idx_twoend]])[is_not_subset_of[[meta_idx_twoend]][meta_idx_target, ]] + symbol_target = symbol_target[symbol_target != symbol] + if (length(symbol_target) != 1L) next # this can happen if a previous loop changed the clause in some way + if (!symbol_target %in% names(entries[[clause_idx_target]])) next + # `symbol_target` is two symbols here: target and intersect + ts2o = try_sse_2nd_order(meta_idx, meta_idx_twoend, meta_idx_target, symbol, symbol_target) + if (identical(ts2o, TRUE)) return(TRUE) + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) return(NULL) + if (is.null(ts2o)) return(FALSE) # target was eliminated + } + FALSE + } + + handle_sse_2nd_order_twoend = function(meta_idx, meta_idx_target, symbol) { + clause_idx = available[[meta_idx]] + + clause_idx_target = available[[meta_idx_target]] + # check that meta_idx_target is still valid: not eliminated, not a unit, not_subset_count 2 w/r/t the target, one of which is still the symbol itself. + if (eliminated[[clause_idx_target]] || is_unit[[clause_idx_target]] || not_subset_count[meta_idx, meta_idx_target] != 2) return(FALSE) + inso_symbols_cols = which(is_not_subset_of[[meta_idx]][meta_idx_target, ]) + symbols_twoend = colnames(is_not_subset_of[[meta_idx]])[inso_symbols_cols] + if (!is.null(symbol) && !symbol %in% symbols_twoend) return(FALSE) + for (symbol_inner_idx in 1:2) { + symbol_inner = symbols_twoend[[symbol_inner_idx]] # the intersection symbol + symbol_other = symbols_twoend[[3 - symbol_inner_idx]] + # symbol_other must be present in the target clause, otherwise we can skip. + if (!symbol_other %in% names(entries[[clause_idx_target]])) next + symbol_inner_clauses_meta = available_inverse[symbol_registry[[symbol_inner]]] + # 'oneends' may either have 1 or 2 non-subset symbols, with both symbols equal in the latter case. + # We do this in both inner loops, since we switch on which one of them is the target. + oneends = symbol_inner_clauses_meta[not_subset_count[symbol_inner_clauses_meta, meta_idx_target] <= 2L] + for (meta_idx_oneend in oneends[!is.na(oneends)]) { # oneends is NA for clauses that have not been processed yet + # check if the twoend-bit broke + if (not_subset_count[meta_idx, meta_idx_target] != 2 || !all(is_not_subset_of[[meta_idx]][meta_idx_target, inso_symbols_cols])) break + + # check if theoneend-bit broke + clause_idx_oneend = available[[meta_idx_oneend]] + if (eliminated[[clause_idx_oneend]] || is_unit[[clause_idx_oneend]]) next + # so the 'oneend' thing may also overlap with 'twoend' on the other symbol. + # The trouble is that we cannot rely on both symbols being in is_not_subset_of[[meta_idx_oneend]]. + # We therefore get the columns, with '0' if one of the symbols is not there, and then check whether the two columns are the only + # two that are TRUE (where the sum may be either 1 or 2). + symbols_twoend_idx = match(symbols_twoend, colnames(is_not_subset_of[[meta_idx_oneend]]), nomatch = 0L) + if (not_subset_count[meta_idx_oneend, meta_idx_target] != sum(is_not_subset_of[[meta_idx_oneend]][meta_idx_target, symbols_twoend_idx])) { + next + } + if (!symbol_other %in% names(entries[[clause_idx_target]])) next + ts2o = try_sse_2nd_order(meta_idx_oneend, meta_idx, meta_idx_target, symbol_inner, symbol_other) + if (identical(ts2o, TRUE)) return(TRUE) + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) return(NULL) + if (is.null(ts2o)) return(FALSE) # target was eliminated + } + } + FALSE + } + + try_sse_2nd_order = function(meta_idx_oneend, meta_idx_twoends, meta_idx_target, symbol_intersect, symbol_target) { + ## assuming that symbol_target exists in meta_idx_target + ## assuming that meta_idx_oneend and meta_idx_twoends both have symbol_intersect, and that at least meta_idx_twoends has symbol_target + # The following does not work any more, since is_not_subset_of relates to larger versions of the oneend / twoend clauses + # if (!all(is_not_subset_of[[meta_idx_target]][c(meta_idx_oneend, meta_idx_twoends), symbol_target])) return(FALSE) + idx_oneend = available[[meta_idx_oneend]] + idx_twoends = available[[meta_idx_twoends]] + idx_target = available[[meta_idx_target]] + # The following is already checked before we all here + # if (any(eliminated[c(idx_oneend, idx_twoends, idx_target)]) || any(is_unit[c(idx_oneend, idx_twoends, idx_target)])) return(FALSE) + clause_oneend = entries[[idx_oneend]] + clause_twoends = entries[[idx_twoends]] + + # only proceed if clause_oneend and clause_twoends are disjoint outside of clause_target, with respect to symbol_intersect. + # Here, we can use the "extended" version of clause_target. + clause_oneend_symbol_intersect = clause_oneend[[symbol_intersect]] + if (any(clause_oneend_symbol_intersect %in% clause_twoends[[symbol_intersect]] & + !clause_oneend_symbol_intersect %in% entries_ext[[meta_idx_target]][[symbol_intersect]])) { + return(FALSE) + } + apply_domain_restriction(idx_target, symbol_target, char_union(clause_oneend[[symbol_target]], clause_twoends[[symbol_target]]), FALSE) + } + + # mark a clause as eliminated and update symbol registry + # This is relatively safe to call, since it does not modify any other clauses and does not create new units or subset relationships. + eliminate_clause_update_sr = function(clause_idx) { + if (is_unit[[clause_idx]]) stop("Bug in the code, this should never happen.") + eliminated[[clause_idx]] <<- TRUE + for (s in names(entries[[clause_idx]])) { + sr = symbol_registry[[s]] + symbol_registry[[s]] = sr[sr != clause_idx] + } + if (!is.null(symbol_registry_ext)) { + for (s in names(entries[[clause_idx]])) { + sr = symbol_registry_ext[[s]] + symbol_registry_ext[[s]] = sr[sr != clause_idx] + } + } + } + + # process units: + # - populate unit_domains + # - start populating symbol_registry; it gets finished later down with non-units + # - also reduce duplicate units and replace them with their intersection + unit_queue = which(is_unit) + for (unit_idx in unit_queue) { + if (register_unit(unit_idx)) return(return_entries(FALSE)) + } + + # if there were only units, we are done + if (length(unit_queue) == length(entries)) return(return_entries(entries[!eliminated])) + + # process non-units: + # - eliminate entries subsumed by units + # - populate symbol_registry + # we sorted clauses by length, so we can skip ahead by length(unit_queue) + # At this point, everything after the unit_queue is not (yet) a unit. + # The seq.int here is "dangerous" and only allowed because we checked for length(unit_queue) == length(entries) above. + for (clause_idx in seq.int(length(unit_queue) + 1L, length(entries))) { + + # intersect with units and eliminate subsumed clauses + clause_symbol_isct = char_intersect(names(entries[[clause_idx]]), names(unit_domains)) + # apply unit-propagation early, since we otherwise run the risk of adding the clause + # to lots of symbol registry entries, only to remove it again right away + for (symbol in clause_symbol_isct) { + adr = apply_domain_restriction(clause_idx, symbol, unit_domains[[symbol]], TRUE) + if (is.null(adr)) break + if (adr) return(return_entries(FALSE)) + } + + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) next # could happen from unit propagation + + # do cache `clause = entries[[clause_idx]]` and refer to names(clause) here, + # since apply_domain_restriction might have removed symbols from the clause + for (symbol in names(entries[[clause_idx]])) { + sr_entry = symbol_registry[[symbol]] + if (is.null(sr_entry)) { + symbol_registry[[symbol]] = clause_idx + } else { + symbol_registry[[symbol]][[length(sr_entry) + 1L]] = clause_idx + } + } + } + + + # let's start with (self)-subsumption. + # this can also create new units etc. + + # we don't need to check for units, upon registration they are automatically removed, and they cannot help with self-subsumption or HLA + available = which(!(eliminated | is_unit)) + available_inverse = match(seq_along(entries), available) + + # record for each clause whether it is a subset of another clause. + # we record this for each symbol separately, so when a symbol gets self-subsumed, we can re-check others more quickly. + # Default is FALSE (not not a subset, i.e. it is a subset), this aligns with absent columns (which are subsets of everything) + # + # note that as soon as is_not_subset_of is non-null, some other functions assume that meta_idx_outer is also defined. + is_not_subset_of = vector("list", length(available)) + # not_subset_count[i, j]: how many symbols of clause i are not subset of clause j? + # if this is 1, we can do self-subsumption elimination and HLA. + # if this is 2, we can do self-subsumption with resolution. + # This is the same as sum(is_not_subset_of[[i]][j, ]) + not_subset_count = matrix(NA_integer_, nrow = length(available), ncol = length(available)) + + # symbol registry for 'extended' clauses + symbol_registry_ext = list2env(as.list(symbol_registry, all.names = TRUE), parent = emptyenv()) + + entries_ext = entries[available] + + for (meta_idx_outer in seq_along(available)) { + clause_idx = available[[meta_idx_outer]] + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) next # may happen if we somehow turn something into a unit that eliminates a later clause + clause_ext = entries_ext[[meta_idx_outer]] + + # is_not_subset_of[[i]][j, k] records whether for symbol k, clause i is not a subset of clause_ext j + # If k is not in clause i, then var(i, k) is trivially a subset of var(j, k), so this is interpreted as FALSE. + # If k is not in clause_ext j but is in clause i, then var(i, k) is not a subset of var(j, k), so this is interpreted as TRUE. + # We initialize with TRUE and then search for instances where a symbol k is in both clauses i and j, and where var(i, k) *is* a subset of var(j, k). + # In that case, we set the entry to FALSE. + is_not_subset_of[[meta_idx_outer]] = matrix( + TRUE, + nrow = length(available), # indexed by meta_idx! + ncol = length(clause_ext), + # using clause_ext for symbol names, because we can rely on names(clause_ext) being a superset of names(clause). + # It could have happened that clause shrinked already in previous loops, even if SSE does not jump ahead in the loop, + # from unit propagation. So we may waste a bit of memory here, but in return we can easier index the inso-matrices further down. + dimnames = list(NULL, names(clause_ext)) + ) + # we are not a subset of ourselves + # (this prevents us from checking this later in on_updated_subset_relations; if we do check it there, we would eliminate the clause from itself) + is_not_subset_of[[meta_idx_outer]][meta_idx_outer, ] = FALSE + + for (meta_idx_inner in seq_len(meta_idx_outer - 1L)) { + ## need to refresh clause here, since it might have been shortened by unit propagation in an earlier iteration + clause = entries[[clause_idx]] + clause_ext = entries_ext[[meta_idx_outer]] + clause_idx_inner = available[[meta_idx_inner]] + if (eliminated[[clause_idx_inner]] || is_unit[[clause_idx_inner]]) next + clause_inner = entries[[clause_idx_inner]] + clause_ext_inner = entries_ext[[meta_idx_inner]] + # note that even though we sort entries at the beginning, we can *not* rely on clause_inner to have smaller or equal length than clause, + # since unit elimination can change the length of clauses + + sci = names(clause_ext_inner) + sci_sc_map = match(sci, names(clause_ext), nomatch = 0L) + sci_names_in_common = which(sci_sc_map != 0L) + sci_nonext_map = match(sci, names(clause_inner), nomatch = 0L) + sci_sc_nonext_map = match(sci, names(clause), nomatch = 0L) + + # symbols that are not in common trivially get the matrix entry TRUE + # (they are not subsets of their counterpart in the other clause, since the other ones are empty) + + for (symbol_idx_ext_inner in sci_names_in_common) { + symbol_idx_inner = sci_nonext_map[[symbol_idx_ext_inner]] + symbol_idx_outer = sci_sc_nonext_map[[symbol_idx_ext_inner]] + if (symbol_idx_inner == 0L && symbol_idx_outer == 0L) next + symbol_idx_ext_outer = sci_sc_map[[symbol_idx_ext_inner]] # the only one (besides symbol_idx_ext_inner) guaranteed to be non-0 + symbol = sci[[symbol_idx_ext_inner]] + + + range_ext_inner = clause_ext_inner[[symbol_idx_ext_inner]] + range_ext_outer = clause_ext[[symbol_idx_ext_outer]] + + + inner_subset_of_outer = if (symbol_idx_inner == 0L) { + TRUE + } else { + range_inner = clause_inner[[symbol_idx_inner]] + all(range_inner %in% range_ext_outer) + } + outer_subset_of_inner = if (symbol_idx_outer == 0L) { + TRUE + } else { + range_outer = clause[[symbol_idx_outer]] + # if inner_subset_of_outer is TRUE and range_inner has the same length as range_ext_outer, then + # all(range_inner %in% range_ext_outer) lets us conclude that they are equal. + # However, that only works if symbol_idx_inner is != 0, otherwise range_inner is not defined. + # If we can not onclude equality, we have to do another (expensive) all()-subset-check. + (inner_subset_of_outer && symbol_idx_inner != 0L && length(range_ext_outer) == length(range_inner)) || all(range_outer %in% range_ext_inner) + } + if (inner_subset_of_outer) { + # Avoid assigning TRUE to matrix that is initialized with TRUE. + # We index by column name here, since it is possible that clauses were shortened by + # unit propagation or self subsumption elimination somewhere on the way here + is_not_subset_of[[meta_idx_inner]][meta_idx_outer, symbol_idx_ext_inner] = FALSE + } + if (outer_subset_of_inner) { + is_not_subset_of[[meta_idx_outer]][meta_idx_inner, symbol_idx_ext_outer] = FALSE + } + } + # prefer to eliminate the outer loopo clause first, since we have already + # done more work for the inner loop clause (which comes earlier in 'entries') + not_subset_count[meta_idx_outer, meta_idx_inner] = sum(is_not_subset_of[[meta_idx_outer]][meta_idx_inner, ]) + rowsum = sum(is_not_subset_of[[meta_idx_inner]][meta_idx_outer, ]) + not_subset_count[meta_idx_inner, meta_idx_outer] = rowsum + if (rowsum <= 2) { + ousr = on_updated_subset_relations(meta_idx_inner, meta_idx_outer) + if (is.null(ousr)) break + if (ousr) return(return_entries(FALSE)) + if (eliminated[[clause_idx_inner]] || is_unit[[clause_idx_inner]]) next # yes this can happen. + } + # need to get rowsum back again, since the call above could have changed something! + rowsum = not_subset_count[meta_idx_outer, meta_idx_inner] + if (rowsum <= 2) { + ousr = on_updated_subset_relations(meta_idx_outer, meta_idx_inner) + if (identical(ousr, TRUE)) return(return_entries(FALSE)) + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) break # probably this can happen if things cascade onwards when updating clause_inner + if (is.null(ousr)) next + } + } + } + + # Now for the big one: Asymmetric Hidden Literal Addition (Marijn et al.) + + # First, we do non-units, then we do units separately. + # We go big to small, since eliminating one clause could prevent us from eliminating other clauses, and all things being equal, we prefer eliminating long ones. + + # We only loop over the entries that have not been eliminated yet. + # We update `remaining_nonunit_entries` inside the loop whenever a clause is eliminated. + remaining_entries = which(!eliminated)[order(lengths(entries[!eliminated]), decreasing = TRUE)] + remaining_nonunit_entries = remaining_entries[seq_len(length(remaining_entries) - length(unit_domains))] + remaining_unit_entries = if (length(unit_domains)) remaining_entries[seq.int(length(remaining_entries) - length(unit_domains) + 1L, length(remaining_entries))] + + # iterating from large to small entries + for (clause_idx in remaining_nonunit_entries) { + + # index inside `is_not_subset_of` + meta_idx = available_inverse[[clause_idx]] + clause = entries_ext[[meta_idx]] + remaining_other_entries = remaining_nonunit_entries[remaining_nonunit_entries != clause_idx] + + # we keep track of which clauses were used for HLA, since every other clause can only do that once. + was_used = logical(length(remaining_other_entries)) + + # for each of the other clauses, how many of their symbols are not a subset of the current clause? + not_subset_count_current = not_subset_count[available_inverse[remaining_other_entries], meta_idx] + # for (roe_idx in seq_along(remaining_other_entries)) { + # # if we had set up is_not_subset_of as a 3-dim array, then the following could just have been a colSums over is_not_subset_of[, meta_idx, ] + # # However, that array would take a lot of memory: N_clauses^2 x N_all_symbols; The current setup has N_clauses^2 x max(N_symbols_per_clause) + # other_clause_idx = remaining_other_entries[[roe_idx]] + # meta_idx_other = available_inverse[[other_clause_idx]] + # not_subset_count[[roe_idx]] = sum(is_not_subset_of[[meta_idx_other]][meta_idx, ]) + # } + repeat { + # we do HLA by looking for a clause that is a subset of the current clause w/r/t all except one symbol. + # We also only consider every clause at most once, since it won't have anything else to add a second time. + # No need to check for == 0 here: if it was the case before, then we eliminated the clause already. If it becomes the case during the loop, we check + # for it further down. + hla_clause_idx = match(TRUE, not_subset_count_current == 1L & !was_used) + if (is.na(hla_clause_idx)) break # no more clauses to consider: all are either used or have no_subset_count > 1 + clause_idx_other = remaining_other_entries[[hla_clause_idx]] + meta_idx_other = available_inverse[[clause_idx_other]] + symbol = colnames(is_not_subset_of[[meta_idx_other]])[is_not_subset_of[[meta_idx_other]][meta_idx, ]] + range_old = clause[[symbol]] + # new range of the symbol inside the clause: Union of old range and complement of that symbol's range in the other clause. + range_new = c(range_old, char_setdiff(universe[[symbol]], c(range_old, entries[[clause_idx_other]][[symbol]]))) + if (length(range_new) == length(universe[[symbol]])) { + # hidden tautology elimination + + # We still need the symbol registry (see below), so this can not be replaced by just `eliminated[[clause_idx]] = TRUE` + eliminate_clause_update_sr(clause_idx) + remaining_nonunit_entries = remaining_other_entries + break + } + # Now loop over clauses that also use the symbol, checking if they have one less `not_subset_count_current` because of that + # Note we do not need to check subsumption w/r/t units any more: All symbols are proper subsets w/r/t units at this point, + # so if adding the complement of one symbol to another made it a superset of a unit, the result was a tautology already. + for (updating_clause_meta_idx in available_inverse[symbol_registry[[symbol]]]) { + # we don't want to skip 'was_used' here, since we might still do hidden subsumption elimination with them. + if (is_not_subset_of[[updating_clause_meta_idx]][meta_idx, symbol] && + all(entries[[available[[updating_clause_meta_idx]]]][[symbol]] %in% range_new)) { + is_not_subset_of[[updating_clause_meta_idx]][meta_idx, symbol] = FALSE + roe_idx = match(available[[updating_clause_meta_idx]], remaining_other_entries) # I wished I didn't have to do this + not_subset_count_current[[roe_idx]] = not_subset_count_current[[roe_idx]] - 1L + if (not_subset_count_current[[roe_idx]] == 0L) { + # hidden subsumption elimination + eliminate_clause_update_sr(clause_idx) + remaining_nonunit_entries = remaining_other_entries + break + } + } + } + if (eliminated[[clause_idx]]) break # the break inside the for-loop above will not break the repeat loop + was_used[[hla_clause_idx]] = TRUE + clause[[symbol]] = range_new + } + } + + # We now do the same thing as above, only for units. + # Units are different, because they don't have the `is_not_subset_of` matrices. These are trivially constructed from + # The symbol registry: "is_not_subset_of" for unit relating to symbol `s` is TRUE for all symbols in a clause that are not `s`. + # We deliberately make use of `remaining_nonunit_entries` here, which has been updated in the loop above as nonunit-clauses were eliminated + delayedAssign("roe_inverse", match(seq_along(entries), remaining_nonunit_entries)) # only do this match()-call if it is actually needed + for (clause_idx in remaining_unit_entries) { + clause = entries[[clause_idx]] + unitsymbol = names(clause) + was_used = logical(length(remaining_nonunit_entries)) + # every clause that is not yet eliminated is a proper subset of the current unit. + # If it is length N and contains the unit symbol, then N - 1 of its symbols are not subsets; + # otherwise (if it does not contain the unit symbol), all N symbols are not subsets. + not_subset_count = lengths(entries[remaining_nonunit_entries]) - (remaining_nonunit_entries %in% symbol_registry[[unitsymbol]]) + + # corresponding to `is_not_subset_of` matrix; only construct this for entries where it is needed. + is_not_subset_of_unit = vector("list", length(remaining_nonunit_entries)) + + # The following loop is mostly identical to the loop above, only for units. + repeat { + hla_clause_idx = match(TRUE, not_subset_count == 1L & !was_used) + if (is.na(hla_clause_idx)) break # no more clauses to consider: all are either used or have no_subset_count > 1 + clause_idx_other = remaining_nonunit_entries[[hla_clause_idx]] + clause_other = entries[[clause_idx_other]] + if (is.null(is_not_subset_of_unit[[hla_clause_idx]])) { + is_not_subset_of_unit[[hla_clause_idx]] = structure(names(clause_other) != unitsymbol, names = names(clause_other)) + } + is_not_subset_entry = is_not_subset_of_unit[[hla_clause_idx]] + symbol = names(is_not_subset_entry)[is_not_subset_entry] + range_old = clause[[symbol]] + range_new = c(range_old, char_setdiff(universe[[symbol]], c(range_old, clause_other[[symbol]]))) + if (length(range_new) == length(universe[[symbol]])) { + # hidden tautology elimination + # no more need to update the unit registry + eliminated[[clause_idx]] = TRUE + break + } + # Now loop over clauses that also use the symbol, checking if they have one less `not_subset_count` because of that + for (updating_clause_idx in symbol_registry[[symbol]]) { + updating_hla_clause_idx = roe_inverse[[updating_clause_idx]] + if (is.null(is_not_subset_of_unit[[updating_hla_clause_idx]])) { + # Dynamically construct this entry if it is not set yet. + # We could delay this further, but that would make things even more complicated + updating_clause = entries[[updating_clause_idx]] + is_not_subset_of_unit[[updating_hla_clause_idx]] = structure(names(updating_clause) != unitsymbol, names = names(updating_clause)) + } + if (is_not_subset_of_unit[[updating_hla_clause_idx]][[symbol]] && + all(entries[[updating_clause_idx]][[symbol]] %in% range_new)) { + is_not_subset_of_unit[[updating_hla_clause_idx]][[symbol]] = FALSE + not_subset_count[[updating_hla_clause_idx]] = not_subset_count[[updating_hla_clause_idx]] - 1L + if (not_subset_count[[updating_hla_clause_idx]] == 0) { + # hidden subsumption elimination + eliminated[[clause_idx]] = TRUE + break + } + } + } + if (eliminated[[clause_idx]]) break # the break inside the for-loop above will not break the repeat loop + was_used[[hla_clause_idx]] = TRUE + clause[[symbol]] = range_new + } + } + + return_entries(entries[!eliminated]) +} diff --git a/attic/experiments.R b/attic/experiments.R index 25ef2923e..c72ac7e3d 100644 --- a/attic/experiments.R +++ b/attic/experiments.R @@ -1255,6 +1255,60 @@ e1 e2 +ex <- quote( + (W %among% "q" & W %among% c("r", "q") | (Y %among% "w" | W %among% c("q", "r"))) & + (X %among% c("s", "t") | X %among% "t" | W %among% "p" & X %among% c("s", "u")) | + + ((W %among% "q" | Z %among% c("z", "a")) & (Y %among% "v" | Z %among% c("a", "z")) | (Y %among% "w" & W %among% "p" | Z %among% c("z", "a") & X %among% c("t", "s"))) +) +evaluate_expression(ex, assignment) +eval(ex) |> formula_to_expression() |> evaluate_expression(assignment) + + +e1 <- (W %among% "q" & W %among% c("r", "q") | (Y %among% "w" | W %among% c("q", "r"))) & + (X %among% c("s", "t") | X %among% "t" | W %among% "p" & X %among% c("s", "u")) +e2 <- ((W %among% "q" | Z %among% c("z", "a")) & (Y %among% "v" | Z %among% c("a", "z")) | (Y %among% "w" & W %among% "p" | Z %among% c("z", "a") & X %among% c("t", "s"))) + +e1 |> formula_to_expression() |> evaluate_expression(assignment) +e2 |> formula_to_expression() |> evaluate_expression(assignment) +(e1 | e2) |> formula_to_expression() |> evaluate_expression(assignment) + +e1 +e2 +e1 | e2 +assignment + + +[[1]] +CnfClause: + Z ∈ {z, a} | Y ∈ {w} | W ∈ {q, r} + +[[2]] +CnfClause: + Z ∈ {z, a} | Y ∈ {w} | W ∈ {p, q} | X ∈ {s, t} + +[[3]] +CnfClause: + Z ∈ {a, z} | W ∈ {p} | Y ∈ {v} | X ∈ {s, t} + + + +1. clause 1 is a subset of clause 2 outside of W, it does SSE and removes W == p. Now clause 1 depends on Y=={w} being present. +2. clause 3 is a subset of clause 2 outside of Y, it does SSE and removes W == y. + +u = CnfUniverse() +A = CnfSymbol(u, "A", c("a1", "a2", "a3")) +B = CnfSymbol(u, "B", c("b1", "b2", "b3")) +C = CnfSymbol(u, "C", c("c1", "c2", "c3")) + + CnfFormula(list((A %among% "a1" | B %among% "b1" | C %among% "c1"), + (A %among% "a1" | B %among% "b2"), + (A %among% "a2" | B %among% "b1"))) + + + + + (V3 %among% c("v3_3", "v3_4") | V1 %among% "v1_2" | (V1 %among% "v1_1" | V1 %among% c("v1_1", "v1_5", "v1_4"))) & ((V1 %among% "v1_3" | V4 %among% "v4_3") & (V1 %among% c("v1_5", "v1_3", "v1_4", "v1_1") | V4 %among% "v4_3")) & (V3 %among% diff --git a/attic/mvsat.mv b/attic/mvsat.mv index 613cdc850..066ab7ffb 100644 --- a/attic/mvsat.mv +++ b/attic/mvsat.mv @@ -215,3 +215,12 @@ # - problem: this would make unit handling weird, since we get new units that can now still be self-subsumed. # - wehn we have that, we can also make sure 2nd order things only run after the initial 1st order things have all run, since we can then expect # fewer range changes and hende fewer updates; that probably gives a lot of performance benefit. +# - NO this does not work. Example case: +# 1. CnfFormula(list((A %among% "a1" | B %among% "b1" | C %among% "c1"), +# 2. (A %among% "a1" | B %among% "b2"), +# 3. (A %among% "a2" | B %among% "b1"))) +# Clause 2 can remove "B" from clause 1 through SSE. +# If we keep the memory of the larger clasue 1, then 3 can also remove "A" from 1. +# The result contains the unit C = "c1"; however, A = "a1", B = "b1", C = "c2" would have satisfied the original formula. +# +# diff --git a/tests/testthat/test_CnfFormula.R b/tests/testthat/test_CnfFormula.R index 76a397390..1e5d6f9f7 100644 --- a/tests/testthat/test_CnfFormula.R +++ b/tests/testthat/test_CnfFormula.R @@ -800,4 +800,20 @@ test_that("Constructed test cases", { expect_set_equal(unlist(lapply(as.list(simplified2), function(x) unclass(x)$B)), c("b1", "b2", "b3", "b3")) expect_set_equal(unlist(lapply(as.list(simplified3), function(x) unclass(x)$B)), c("b1", "b2", "b3", "b3")) + + original = quote( + (A %among% "a2" | B %among% "b1") & + (A %among% "a1" | B %among% "b2") & + (A %among% "a1" | B %among% "b1"| C %among% "c1") + ) + + simplified = CnfFormula(list( + CnfClause(list(CnfAtom(A, c("a2")), CnfAtom(B, c("b1")))), + CnfClause(list(CnfAtom(A, c("a1")), CnfAtom(B, c("b2")))), + CnfClause(list(CnfAtom(A, c("a1")), CnfAtom(B, c("b1")), CnfAtom(C, c("c1")))) + )) + + expect_equal(evaluate_expression(formula_to_expression(simplified), assignments), + evaluate_expression(original, assignments)) + }) From 9848ebabce5e0cd6e3a2027448e1134227f9d2d3 Mon Sep 17 00:00:00 2001 From: mb706 Date: Tue, 24 Sep 2024 00:25:24 +0200 Subject: [PATCH 79/87] delayed 2nd order sse --- R/CnfFormula_simplify1.R | 63 ++++++++++++++++++++++++++++------------ 1 file changed, 45 insertions(+), 18 deletions(-) diff --git a/R/CnfFormula_simplify1.R b/R/CnfFormula_simplify1.R index dc400f1d5..7aae90e96 100644 --- a/R/CnfFormula_simplify1.R +++ b/R/CnfFormula_simplify1.R @@ -213,15 +213,15 @@ simplify_cnf = function(entries, universe) { if (!is_not_subset_of[[meta_idx]][other_meta_idx, is_not_subset_of_col]) next is_not_subset_of[[meta_idx]][other_meta_idx, is_not_subset_of_col] <<- FALSE not_subset_count[meta_idx, other_meta_idx] <<- (rowsum = not_subset_count[meta_idx, other_meta_idx] - 1L) - if (rowsum > 2L) next - ousr = on_updated_subset_relations(meta_idx, other_meta_idx) + if (rowsum > 1L + second_order_enabled) next + ousr = on_updated_subset_relations(meta_idx, other_meta_idx, FALSE) if (identical(ousr, TRUE)) return(TRUE) # forward contradiction signal. We don't care if other_meta_idx was eliminated. if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) return(NULL) # need to check more directly if things escalated somehow and clause_idx was eliminated indirectly } # call on_domain_changed_handle_2nd_order_sse # it is not a waste w/r/t the 'on_updated_subset_relations' call, since that one only deals with clauses for which the symbol is set to FALSE now, # i.e. precisely the other clauses. - on_update_range(meta_idx, symbol) + if (second_order_enabled) on_update_range(meta_idx, symbol) else FALSE } # eliminate `symbol` from `clause_idx` @@ -274,8 +274,8 @@ simplify_cnf = function(entries, universe) { clause_idx_other = available[[meta_idx_other]] # while we *do* restrict meta_idx_other in the for loop already, eliminated and is_unit can still change during the loop, so check here again if (eliminated[[clause_idx_other]] || is_unit[[clause_idx_other]]) next - if (not_subset_count[meta_idx, meta_idx_other] > 2L) next - ousr = on_updated_subset_relations(meta_idx, meta_idx_other) + if (not_subset_count[meta_idx, meta_idx_other] > 1L + second_order_enabled) next + ousr = on_updated_subset_relations(meta_idx, meta_idx_other, FALSE) if (identical(ousr, TRUE)) return(TRUE) # on_updated_subset_relations could cascade down to eliminating meta_idx (i.e. clause_idx) if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) return(NULL) @@ -285,12 +285,13 @@ simplify_cnf = function(entries, universe) { # returns 'NULL' when meta_idx_other was eliminated (or possibly turned into a unit), # 'TRUE' for contradiction, 'FALSE' for nothing changed - on_updated_subset_relations = function(meta_idx, meta_idx_other) { + on_updated_subset_relations = function(meta_idx, meta_idx_other, second_order_only) { # the row `meta_idx_other` of `is_not_subset_of[[meta_idx]]` has been updated. # we now check whether we can apply subsumption elimination, or at least self-subsumption elimination, on `meta_idx`. rowsum = not_subset_count[meta_idx, meta_idx_other] - if (rowsum > 2L) return(FALSE) # nothing to do + if (rowsum > 1L + second_order_enabled) return(FALSE) # nothing to do if (rowsum == 2L) { + # we only get here when second_order_enabled is TRUE hs2oo = handle_sse_2nd_order_twoend(meta_idx, meta_idx_other, NULL) if (identical(hs2oo, TRUE)) return(TRUE) clause_other = available[[meta_idx_other]] @@ -305,13 +306,17 @@ simplify_cnf = function(entries, universe) { symbol_to_restrict = colnames(is_not_subset_of[[meta_idx]])[is_not_subset_of[[meta_idx]][meta_idx_other, ]] # update clause and sc! - # note we update meta_idx_other: we are currently subset of that other clause w/r/t all except one symbol. - # we can therefore intersect that last symbol in the other clause with the range of that symbol in the current clause. - # apply_domain_restriction will take care of eliminating the symbol if the range becomes empty. - # It could in theory even do subsumption, but we have already taken care of that above. - adr = apply_domain_restriction(available[[meta_idx_other]], symbol_to_restrict, entries[[available[[meta_idx]]]][[symbol_to_restrict]], FALSE) - if (is.null(adr)) return(NULL) - if (adr) return(TRUE) + if (!second_order_only) { + # note we update meta_idx_other: we are currently subset of that other clause w/r/t all except one symbol. + # we can therefore intersect that last symbol in the other clause with the range of that symbol in the current clause. + # apply_domain_restriction will take care of eliminating the symbol if the range becomes empty. + # It could in theory even do subsumption, but we have already taken care of that above. + adr = apply_domain_restriction(available[[meta_idx_other]], symbol_to_restrict, entries[[available[[meta_idx]]]][[symbol_to_restrict]], FALSE) + if (is.null(adr)) return(NULL) + if (adr) return(TRUE) + if (!second_order_enabled) return(FALSE) + } + if (!second_order_enabled_matrix[meta_idx, meta_idx_other]) return(FALSE) clause_idx = available[[meta_idx]] if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) return(FALSE) hs2oo = handle_sse_2nd_order_oneend(meta_idx, meta_idx_other, symbol_to_restrict) @@ -338,12 +343,14 @@ simplify_cnf = function(entries, universe) { targets_while_oneend = potential_targets[not_subset_count[meta_idx, potential_targets] == 1L] for (meta_idx_target in targets_while_oneend) { + if (!second_order_enabled_matrix[meta_idx, meta_idx_target]) next hs2oo = handle_sse_2nd_order_oneend(meta_idx, meta_idx_target, symbol) if (is.null(hs2oo)) return(NULL) # meta_idx eliminated if (hs2oo) return(TRUE) } targets_while_twoend = potential_targets[not_subset_count[meta_idx, potential_targets] == 2L] for (meta_idx_target in targets_while_twoend) { + if (!second_order_enabled_matrix[meta_idx, meta_idx_target]) next hs2oo = handle_sse_2nd_order_twoend(meta_idx, meta_idx_target, symbol) if (is.null(hs2oo)) return(NULL) # meta_idx eliminated if (hs2oo) return(TRUE) @@ -527,6 +534,11 @@ simplify_cnf = function(entries, universe) { # This is the same as sum(is_not_subset_of[[i]][j, ]) not_subset_count = matrix(NA_integer_, nrow = length(available), ncol = length(available)) + # whether second-order subsumption is enabled for the pair + # We only enable it after the initial first-order checks are done, to reduce 2nd order calls as much as possible. + second_order_enabled = FALSE + second_order_enabled_matrix = matrix(FALSE, nrow = length(available), ncol = length(available)) + for (meta_idx_outer in seq_along(available)) { clause_idx = available[[meta_idx_outer]] @@ -588,16 +600,16 @@ simplify_cnf = function(entries, universe) { not_subset_count[meta_idx_outer, meta_idx_inner] = sum(is_not_subset_of[[meta_idx_outer]][meta_idx_inner, ]) rowsum = sum(is_not_subset_of[[meta_idx_inner]][meta_idx_outer, ]) not_subset_count[meta_idx_inner, meta_idx_outer] = rowsum - if (rowsum <= 2) { - ousr = on_updated_subset_relations(meta_idx_inner, meta_idx_outer) + if (rowsum <= 1) { + ousr = on_updated_subset_relations(meta_idx_inner, meta_idx_outer, FALSE) if (is.null(ousr)) break if (ousr) return(return_entries(FALSE)) if (eliminated[[clause_idx_inner]] || is_unit[[clause_idx_inner]]) next # yes this can happen. } # need to get rowsum back again, since the call above could have changed something! rowsum = not_subset_count[meta_idx_outer, meta_idx_inner] - if (rowsum <= 2) { - ousr = on_updated_subset_relations(meta_idx_outer, meta_idx_inner) + if (rowsum <= 1) { + ousr = on_updated_subset_relations(meta_idx_outer, meta_idx_inner, FALSE) if (identical(ousr, TRUE)) return(return_entries(FALSE)) if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) break # probably this can happen if things cascade onwards when updating clause_inner if (is.null(ousr)) next @@ -605,6 +617,21 @@ simplify_cnf = function(entries, universe) { } } + second_order_enabled = TRUE + second_order_enabled_matrix = not_subset_count > 2L # allow cascading of indirect SSE, except for the combinations where we trigger it manually (otherwise we'd be running them twice) + # alternatively, we could also enable none of the cascading in the beginning and have a nested loop in the following, where we 'repeat' until there are no more rowsum <= 2L + # That would probably give uns less cascading, but we'd have to run 'which()' on a N^2 matrix potentially many times. + sse_to_trigger = which(not_subset_count <= 2L, arr.ind = TRUE) + for (sse_idx in seq_len(nrow(sse_to_trigger))) { + meta_idx = sse_to_trigger[sse_idx, 1L] + meta_idx_other = sse_to_trigger[sse_idx, 2L] + second_order_enabled_matrix[meta_idx, meta_idx_other] = TRUE + on_updated_subset_relations(meta_idx, meta_idx_other, TRUE) + } + + + + # Now for the big one: Asymmetric Hidden Literal Addition (Marijn et al.) # First, we do non-units, then we do units separately. From 5925da0113726c1f6c2b90815b8b8b0efd805d48 Mon Sep 17 00:00:00 2001 From: mb706 Date: Tue, 24 Sep 2024 00:59:49 +0200 Subject: [PATCH 80/87] local tests pass --- R/CnfFormula_simplify1.R | 13 +++++++--- attic/experiments.R | 30 +++++++++++++++++++++++ tests/testthat/test_CnfFormula_simplify.R | 1 - 3 files changed, 39 insertions(+), 5 deletions(-) diff --git a/R/CnfFormula_simplify1.R b/R/CnfFormula_simplify1.R index 7aae90e96..4cee6a104 100644 --- a/R/CnfFormula_simplify1.R +++ b/R/CnfFormula_simplify1.R @@ -619,19 +619,24 @@ simplify_cnf = function(entries, universe) { second_order_enabled = TRUE second_order_enabled_matrix = not_subset_count > 2L # allow cascading of indirect SSE, except for the combinations where we trigger it manually (otherwise we'd be running them twice) + # we need to make sure we don't trigger for eliminated / unit clauses, so we set them to TRUE here. + # This means all remaining entries of the second_order_enabled_matrix are exactly the ones for which we trigger on_updated_subset_relations() manually. + meta_disabled = eliminated[available] | is_unit[available] + second_order_enabled_matrix[meta_disabled, ] = TRUE + second_order_enabled_matrix[, meta_disabled] = TRUE # alternatively, we could also enable none of the cascading in the beginning and have a nested loop in the following, where we 'repeat' until there are no more rowsum <= 2L # That would probably give uns less cascading, but we'd have to run 'which()' on a N^2 matrix potentially many times. - sse_to_trigger = which(not_subset_count <= 2L, arr.ind = TRUE) + + sse_to_trigger = which(!second_order_enabled_matrix, arr.ind = TRUE) for (sse_idx in seq_len(nrow(sse_to_trigger))) { meta_idx = sse_to_trigger[sse_idx, 1L] meta_idx_other = sse_to_trigger[sse_idx, 2L] + if (eliminated[[available[[meta_idx]]]] || is_unit[[available[[meta_idx]]]] || eliminated[[available[[meta_idx_other]]]] || is_unit[[available[[meta_idx_other]]]]) next second_order_enabled_matrix[meta_idx, meta_idx_other] = TRUE - on_updated_subset_relations(meta_idx, meta_idx_other, TRUE) + if (identical(on_updated_subset_relations(meta_idx, meta_idx_other, TRUE), TRUE)) return(return_entries(FALSE)) } - - # Now for the big one: Asymmetric Hidden Literal Addition (Marijn et al.) # First, we do non-units, then we do units separately. diff --git a/attic/experiments.R b/attic/experiments.R index c72ac7e3d..1aa5a3e35 100644 --- a/attic/experiments.R +++ b/attic/experiments.R @@ -1245,6 +1245,8 @@ meta_idx_inner c lapply(seq_along(eliminated), function(x) if (eliminated[[x]]) FALSE else structure(entries[[x]], class = "CnfClause")) + + entries[!eliminated] |> lapply(structure, class = "CnfClause") which(eliminated) @@ -1307,6 +1309,34 @@ C = CnfSymbol(u, "C", c("c1", "c2", "c3")) +quote( + (W %among% "p" | Y %among% "x") | + Y %among% "x" & W %among% "p" +) |> eval() |> formula_to_expression() |> evaluate_expression(assignment) + + +(W %among% "p" | Y %among% "x") + + Y %among% "x" & W %among% "p" + + +e1 <- (W %among% "p" | Y %among% "x") +e2 <- Y %among% "x" & W %among% "p" + +e1 +e2 + +e1 | e2 + + + + assignment + + + (W %among% "p" | Y %among% "x" | + Y %among% "x" & W %among% "p") + + diff --git a/tests/testthat/test_CnfFormula_simplify.R b/tests/testthat/test_CnfFormula_simplify.R index fae8fe3f9..d59fcf739 100644 --- a/tests/testthat/test_CnfFormula_simplify.R +++ b/tests/testthat/test_CnfFormula_simplify.R @@ -68,7 +68,6 @@ test_that("CnfFormula Regression Tests", { paste(capture.output(print(assignment)), collapse = "\n"), deparse1(simplified) )) - } dti <- as.data.table(stats) From 00d84d283056fa81105f9c748c270fc746e3f751 Mon Sep 17 00:00:00 2001 From: mb706 Date: Tue, 24 Sep 2024 04:20:58 +0200 Subject: [PATCH 81/87] possible big efficiency gain for late 2nd order self subsumption --- R/CnfFormula_simplify1.R | 6 ++++-- attic/experiments.R | 9 ++++++++- 2 files changed, 12 insertions(+), 3 deletions(-) diff --git a/R/CnfFormula_simplify1.R b/R/CnfFormula_simplify1.R index 4cee6a104..98e046a8a 100644 --- a/R/CnfFormula_simplify1.R +++ b/R/CnfFormula_simplify1.R @@ -291,7 +291,8 @@ simplify_cnf = function(entries, universe) { rowsum = not_subset_count[meta_idx, meta_idx_other] if (rowsum > 1L + second_order_enabled) return(FALSE) # nothing to do if (rowsum == 2L) { - # we only get here when second_order_enabled is TRUE + # we usually don't get here when we are second_order_only; however, it may be possible that a oneend clause + # gets turned into a twoend clause during 2nd order triggering before it gets triggered itself. hs2oo = handle_sse_2nd_order_twoend(meta_idx, meta_idx_other, NULL) if (identical(hs2oo, TRUE)) return(TRUE) clause_other = available[[meta_idx_other]] @@ -618,7 +619,8 @@ simplify_cnf = function(entries, universe) { } second_order_enabled = TRUE - second_order_enabled_matrix = not_subset_count > 2L # allow cascading of indirect SSE, except for the combinations where we trigger it manually (otherwise we'd be running them twice) + second_order_enabled_matrix = not_subset_count != 1L # allow cascading of indirect SSE, except for the combinations where we trigger it manually (otherwise we'd be running them twice) + # We only trigger oneend-clauses, because every oneend clauses looks for all available twoend-clauses by itself. # we need to make sure we don't trigger for eliminated / unit clauses, so we set them to TRUE here. # This means all remaining entries of the second_order_enabled_matrix are exactly the ones for which we trigger on_updated_subset_relations() manually. meta_disabled = eliminated[available] | is_unit[available] diff --git a/attic/experiments.R b/attic/experiments.R index 1aa5a3e35..3d970ff84 100644 --- a/attic/experiments.R +++ b/attic/experiments.R @@ -1246,7 +1246,7 @@ c lapply(seq_along(eliminated), function(x) if (eliminated[[x]]) FALSE else structure(entries[[x]], class = "CnfClause")) - +prof entries[!eliminated] |> lapply(structure, class = "CnfClause") which(eliminated) @@ -1419,3 +1419,10 @@ e1 | e2 "v3_3", "v3_4", "v3_5") & V4 %among% c("v4_4", "v4_5", "v4_3", "v4_2") | V2 %among% c("v2_4", "v2_5", "v2_2", "v2_3") & V4 %among% c("v4_1", "v4_5", "v4_3")))))) + +u = CnfUniverse() +CnfSymbol(u, "A", c("T", "F")) +CnfSymbol(u, "B", c("T", "F")) +CnfSymbol(u, "C", c("T", "F")) +replicate(4, gc()) +profvis::profvis(replicate(3000, { !!(((u$A %among% "T" | u$B %among% "F") & (u$A %among% "F" | u$C %among% "T") & (u$B %among% "T" | u$C %among% "F"))) ; NULL }) -> ., simplify = FALSE) From 9a254b73d5c63b5a04a9160c5adb54526ee657a9 Mon Sep 17 00:00:00 2001 From: mb706 Date: Tue, 24 Sep 2024 13:44:22 +0200 Subject: [PATCH 82/87] bugfix --- R/CnfFormula_simplify1.R | 5 +++-- attic/experiments.R | 18 ++++++++++++++++++ tests/testthat/test_CnfFormula.R | 15 +++++++++++++++ 3 files changed, 36 insertions(+), 2 deletions(-) diff --git a/R/CnfFormula_simplify1.R b/R/CnfFormula_simplify1.R index 98e046a8a..7d7239d1c 100644 --- a/R/CnfFormula_simplify1.R +++ b/R/CnfFormula_simplify1.R @@ -619,8 +619,9 @@ simplify_cnf = function(entries, universe) { } second_order_enabled = TRUE - second_order_enabled_matrix = not_subset_count != 1L # allow cascading of indirect SSE, except for the combinations where we trigger it manually (otherwise we'd be running them twice) - # We only trigger oneend-clauses, because every oneend clauses looks for all available twoend-clauses by itself. + second_order_enabled_matrix = not_subset_count != 2L # allow cascading of indirect SSE, except for the combinations where we trigger it manually (otherwise we'd be running them twice) + # We only trigger twoend-clauses, because every twoend clauses looks for all available oneend-clauses by itself. + # We can not do oneend-clauses-only, since twoend-clauses also look for other twoend-clauses that have common overlap. # we need to make sure we don't trigger for eliminated / unit clauses, so we set them to TRUE here. # This means all remaining entries of the second_order_enabled_matrix are exactly the ones for which we trigger on_updated_subset_relations() manually. meta_disabled = eliminated[available] | is_unit[available] diff --git a/attic/experiments.R b/attic/experiments.R index 3d970ff84..5ed3a13b8 100644 --- a/attic/experiments.R +++ b/attic/experiments.R @@ -1426,3 +1426,21 @@ CnfSymbol(u, "B", c("T", "F")) CnfSymbol(u, "C", c("T", "F")) replicate(4, gc()) profvis::profvis(replicate(3000, { !!(((u$A %among% "T" | u$B %among% "F") & (u$A %among% "F" | u$C %among% "T") & (u$B %among% "T" | u$C %among% "F"))) ; NULL }) -> ., simplify = FALSE) + + + + + +e1 <- (V4 %among% c("v4_3", "v4_1") | V2 %among% c("v2_1", "v2_3")) & + (V2 %among% c("v2_2", "v2_1") | V4 %among% "v4_3") & ((V3 %among% + c("v3_1", "v3_3") | V4 %among% c("v4_3", "v4_2")) & (V2 %among% + "v2_3" | V4 %among% "v4_2")) + +e2 <- (V4 %among% c("v4_3", "v4_2" +) & V3 %among% c("v3_2", "v3_3") & (V2 %among% "v2_2" & V3 %among% + c("v3_1", "v3_3")) | V4 %among% "v4_1" & V4 %among% c("v4_2", +"v4_1") & (V3 %among% "v3_3" & V4 %among% "v4_1")) + +e1 & e2 + + diff --git a/tests/testthat/test_CnfFormula.R b/tests/testthat/test_CnfFormula.R index 1e5d6f9f7..0fad2ae19 100644 --- a/tests/testthat/test_CnfFormula.R +++ b/tests/testthat/test_CnfFormula.R @@ -816,4 +816,19 @@ test_that("Constructed test cases", { expect_equal(evaluate_expression(formula_to_expression(simplified), assignments), evaluate_expression(original, assignments)) + + e1 <- (V4 %among% c("v4_3", "v4_1") | V2 %among% c("v2_1", "v2_3")) & + (V2 %among% c("v2_2", "v2_1") | V4 %among% "v4_3") & ((V3 %among% + c("v3_1", "v3_3") | V4 %among% c("v4_3", "v4_2")) & (V2 %among% + "v2_3" | V4 %among% "v4_2")) + + e2 <- (V4 %among% c("v4_3", "v4_2") & V3 %among% c("v3_2", "v3_3") & (V2 %among% "v2_2" & V3 %among% + c("v3_1", "v3_3")) | V4 %among% "v4_1" & V4 %among% c("v4_2", + "v4_1") & (V3 %among% "v3_3" & V4 %among% "v4_1")) + + expect_false(is.logical(e1)) + expect_false(is.logical(e2)) + expect_true(is.logical(e1 & e2)) # this contradiction should be recognized from 2nd order self subsumption elimination + expect_false(e1 & e2) + }) From 9780921777e45dc0b3cd9bea1d0273177d325b93 Mon Sep 17 00:00:00 2001 From: mb706 Date: Tue, 24 Sep 2024 13:48:31 +0200 Subject: [PATCH 83/87] test fix --- tests/testthat/test_CnfFormula.R | 16 ++++++++-------- 1 file changed, 8 insertions(+), 8 deletions(-) diff --git a/tests/testthat/test_CnfFormula.R b/tests/testthat/test_CnfFormula.R index 0fad2ae19..10a60018f 100644 --- a/tests/testthat/test_CnfFormula.R +++ b/tests/testthat/test_CnfFormula.R @@ -817,14 +817,14 @@ test_that("Constructed test cases", { evaluate_expression(original, assignments)) - e1 <- (V4 %among% c("v4_3", "v4_1") | V2 %among% c("v2_1", "v2_3")) & - (V2 %among% c("v2_2", "v2_1") | V4 %among% "v4_3") & ((V3 %among% - c("v3_1", "v3_3") | V4 %among% c("v4_3", "v4_2")) & (V2 %among% - "v2_3" | V4 %among% "v4_2")) - - e2 <- (V4 %among% c("v4_3", "v4_2") & V3 %among% c("v3_2", "v3_3") & (V2 %among% "v2_2" & V3 %among% - c("v3_1", "v3_3")) | V4 %among% "v4_1" & V4 %among% c("v4_2", - "v4_1") & (V3 %among% "v3_3" & V4 %among% "v4_1")) + e1 <- (D %among% c("d3", "d1") | B %among% c("b1", "b3")) & + (B %among% c("b1", "b2") | D %among% c("d3")) & ((C %among% + c("c1", "c3") | D %among% c("d3", "d2")) & (B %among% + "b3" | D %among% "d2")) + + e2 <- (D %among% c("d3", "d2") & C %among% c("c2", "c3") & (B %among% "b2" & C %among% + c("c1", "c3")) | D %among% "d1" & D %among% c("d2", + "d1") & (C %among% "c3" & D %among% "d1")) expect_false(is.logical(e1)) expect_false(is.logical(e2)) From 51d28ee13b8d956acf1640e515b602c4a1fe1993 Mon Sep 17 00:00:00 2001 From: mb706 Date: Tue, 24 Sep 2024 14:20:48 +0200 Subject: [PATCH 84/87] moving files --- DESCRIPTION | 2 - R/CnfFormula_simplify.R | 951 ++++++++++++++++++++++------ R/CnfFormula_simplify1.R | 782 ----------------------- attic/CnfFormula_simplify.R | 201 ++++++ {R => attic}/CnfFormula_simplify2.R | 0 5 files changed, 967 insertions(+), 969 deletions(-) delete mode 100644 R/CnfFormula_simplify1.R create mode 100644 attic/CnfFormula_simplify.R rename {R => attic}/CnfFormula_simplify2.R (100%) diff --git a/DESCRIPTION b/DESCRIPTION index 42d096484..a856345cc 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -102,8 +102,6 @@ Collate: 'CnfClause.R' 'CnfFormula.R' 'CnfFormula_simplify.R' - 'CnfFormula_simplify1.R' - 'CnfFormula_simplify2.R' 'CnfSymbol.R' 'CnfUniverse.R' 'Graph.R' diff --git a/R/CnfFormula_simplify.R b/R/CnfFormula_simplify.R index f3661001d..7d7239d1c 100644 --- a/R/CnfFormula_simplify.R +++ b/R/CnfFormula_simplify.R @@ -1,201 +1,782 @@ +simplify_cnf = function(entries, universe) { + ################################# + # Some vocabulary: + # - `entries` is a list of `clauses`, which are named lists. + # - `clauses`' names are `symbols`, the values are the `ranges` of the symbols within that clause + # - `unit`: clause with single symbol + # Glossary of operations: + # - `unit propagation`: ranges of a symbol within a unit constitute the entire possible range of that symbol, + # so all clauses with that symbol are restricted to those values + # - `subsumption elimination`: if all ranges of all symbols within one clause are subsets of those ranges in another clause, + # then the other clause can be removed + # - `self-subsumption elimination`: if the ranges of all except one symbol within one clause are a subset of those ranges + # in another clause, then the remaining symbol in the latter clause can be intersected with the remaining symbol. + # - `hidden literal addition` (HLA): if the ranges of all except one symbol within one clause are a subset of those ranges + # in another clause, then the *complement* of the remaining symbol in the former clause can be added to the latter clause. + # This is basically the reverse of self-subsumption elimination. We do not use this to change clauses directly; + # the point here is that the resulting clause, even if applied repeatedly, is logically equivalent to the original clause within the formula: + # - `hidden subsumption elimination`: if applying HLA results in a clause that can be subsumed, the original clause can be removed. + # - `hidden tautology elimination`: if applying HLA results in a clause that is a tautology, the original clause can be removed. + # Note: 'Clause Elimination Procedures for CNF Formulas' by Marijn Heule et al. calls this "Asymmetric Hidden Literal Addition". + ################################# + ######################## + ## Helper functions ## + ######################## + # faster intersect, setdiff etc. that rely on x, y being characters with no duplicates + char_intersect = function(x, y) x[x %in% y] + char_setdiff = function(x, y) x[!x %in% y] + char_union = function(x, y) c(x, y[!y %in% x]) + # construct the CnfFormula return object + return_entries = function(entries) { + structure( + if (!length(entries)) TRUE else entries, + universe = universe, + class = "CnfFormula" + ) + } -simplify_cnf_1 = function(entries, universe) { - return_false = structure( - FALSE, - universe = universe, - class = "CnfFormula" - ) - - # can we do unit elimination? - # if we are already TRUE or FALSE no simplification is necessary - # this only works if there actually are units. - can_simplify = !is.logical(entries) - # likewise, if there is only one clause left, no simplification is necessary. - - units = list() - - while (can_simplify && length(entries) > 1) { - # we do the following until we are sure there are no more simplifications to be made. - # this is the case if we have not meaningfully simplified anything in the last iteration. - can_simplify = FALSE - # sort clauses by length, since (1) length-1-clauses are special, and (2) short clauses can only ever subsume longer ones - entries = entries[order(lengths(entries))] - # Let sum(A) be the symbols in clause A, and val(A, s) be the values of symbol s admitted in clause A. - if (any(lengths(entries) == 1)) { - for (i in seq_along(entries)) { - ei = entries[[i]] - # If |sym(A)| == 1, sym(A) == {s} and s is in sym(B), then val(B, s) <- intersect(val(A, s), val(B, s)) ("unit propagation") - # units is a named list of symbols in size-one-clauses, together with their values. - # We iterate over all symbols in ei that are also in units, and intersect their values. - for (unit_symbol in intersect(names(ei), names(units))) { - length_before_ei = length(ei[[unit_symbol]]) - length_before_unit = length(units[[unit_symbol]]) - intersection = intersect(units[[unit_symbol]], ei[[unit_symbol]]) - ei[[unit_symbol]] = intersection - if (length(ei) == 1 && length(intersection) != length_before_unit) { - # we made a unit shorter, this means we need to simplify the entry from which units[[unit_symbol]] came - can_simplify = TRUE - } - if (!length(ei[[unit_symbol]])) { - ei[[unit_symbol]] = NULL - } - if (!length(ei)) { - return(return_false) - } - if (length(intersection) != length_before_ei) { - # need to store changed ei entry only if its length changed; otherwise we know the intersection did not do anything. - entries[[i]] = ei - } + if (is.logical(entries)) return(return_entries(entries)) + + ######################## + ## Variable setup ## + ######################## + + entries = entries[order(lengths(entries))] + + is_unit = lengths(entries) == 1L + eliminated = logical(length(entries)) + + # maps symbol name -> the index of unit clauses + unit_registry = new.env(parent = emptyenv()) + + # maps symbol name -> their current domain + unit_domains = new.env(parent = emptyenv()) + + # maps symbol name -> the index of all non-unit clauses that refer to it + symbol_registry = new.env(parent = emptyenv()) + + is_not_subset_of = NULL # see further down + + ################################## + ## Event-driven clause handling ## + ################################## + # The following functions process the CNF clauses in various ways, + # depending on the current state of the entries. + # The state of the entries is updated in-place. + # The functions are then called in a loop, but they may also call each other. + # It is therefore important that they make the global state consistent before + # calling other functions, and that they are aware of how the global state *can* + # have changed upon their return. + # - entries[[clause_idx]] should be updated if necessary before other fns are called + # - symbol_registry[[symbol]] could have been updated + # - eliminated[[clause_idx]] could have been set to TRUE + # Since functions can call each other in different ways, `eliminated` could have changed even for clauses + # for which the other functions were not called. + + # Register a clause as a unit: + # - check if there is already a unit for this symbol + # - if not, add it to the unit registry + # - otherwise, intersect unit domains (and exit on contradiction) + # - apply unit propagation + # - We do *not* update the sybmol registry here; if the clause is registered for a given symbol, + # it has to be removed from there *before* calling this function. + register_unit = function(unit_idx) { + unit = entries[[unit_idx]] + nu = names(unit) + ur = unit_registry[[nu]] + if (is.null(ur)) { + unit_registry[[nu]] = unit_idx # environment assignment + unit_domains[[nu]] = unit[[1L]] # environment assignment + # this is init'd TRUE for those w/ length 1 at the start, we set it to TRUE for clauses where symbols were eliminated + is_unit[[unit_idx]] <<- TRUE + } else { + # two units refer to the same symbol + # -> we keep the one we saw before but update it to the intersection. + # the current one is eliminated + prev_unit = unit_domains[[nu]] + unit_isct = prev_unit[prev_unit %in% unit[[1L]]] + if (!length(unit_isct)) return(TRUE) # signal that we have a contradiction and can exit + entries[[ur]][[1L]] <<- (unit_domains[[nu]] = unit_isct) # update the *old* unit and unit_domains in one go. unit_domains is updated by-reference (environment) + eliminated[[unit_idx]] <<- TRUE + } + # The symbol registry is empty at the start; the following happens when new units are added later + use_inso = FALSE + if (!is.null(is_not_subset_of)) { + # if we have the is_not_subset_of matrix, we can use it to skip some checks + unit_idx_meta = available_inverse[[unit_idx]] + use_inso = unit_idx_meta <= meta_idx_outer # .. but only if we have built the matrix up to the current index + if (use_inso) { + # if the unit is a subset of the other clause, we will never skip. + inso_column = is_not_subset_of[[unit_idx_meta]][, nu] + } + } + for (s_clause_idx in symbol_registry[[nu]]) { + # could have been eliminated by subsumption elimination during unit propagation of another clause + # (we are not afraid of is_unit here, since we are the unit for the symbol here -- everything else that has the + # symbol gets eliminated) + if (eliminated[[s_clause_idx]]) next + if (use_inso) { + # if we already know that s_clause_idx[[nu]] is a subset of unit_idx, we can skip this + # exception: unit_idx is *also* a subset, implying equality, in which case we will do subsumption elimination. + s_clause_idx_meta = available_inverse[[s_clause_idx]] + if (s_clause_idx_meta <= meta_idx_outer && inso_column[[s_clause_idx_meta]] && !is_not_subset_of[[s_clause_idx_meta]][unit_idx_meta, nu]) next + } + adr = apply_domain_restriction(s_clause_idx, nu, unit_domains[[nu]], TRUE) + if (identical(adr, TRUE)) return(TRUE) # forward contradiction signal + } + FALSE # no contradiction + } + + # restrict the symbol in the clause to a given domain, e.g. a unit + # - clause_idx: index in entries + # - symbol: name of symbol to restrict + # - restringent: domain to restrict to + # returns TRUE if a contradiction was detected, NULL if the clause was eliminated + apply_domain_restriction = function(clause_idx, symbol, restringent, is_unit_propagation) { + clause = entries[[clause_idx]] + symbol_idx = match(symbol, names(clause)) + if (is.na(symbol_idx)) return(FALSE) + + clause_symbol_length_before = length(clause[[symbol_idx]]) + clause[[symbol_idx]] = char_intersect(clause[[symbol_idx]], restringent) + if (length(clause[[symbol_idx]]) == length(restringent)) { + # If the lengths match, then the clause is a superset of the unit (since the intersections are equal) + # the clause is therefore subsumed by the unit + eliminate_clause_update_sr(clause_idx) + return(NULL) + } + # clause was not changed + if (length(clause[[symbol_idx]]) == clause_symbol_length_before) return(FALSE) + if (!length(clause[[symbol_idx]])) { + # the symbol is not in the clause anymore + return(eliminate_symbol_from_clause(clause_idx, symbol)) + } + # clause was changed. + # We don't need to do this when we go the eliminate_symbol_from_clause route, since that will update the clause in any case. + entries[[clause_idx]] <<- clause + + # We need to update the subset relations matrix, if it exists + if (is.null(is_not_subset_of)) return(FALSE) + + meta_idx = available_inverse[[clause_idx]] + # meta_idx_outer is the index up to which we have built is_not_subset_of; if meta_idx > meta_idx_outer, then we haven't seen the clause yet. + # we are not relying on the fact that as soon as is_not_subset_of is non-null, we will only get here for clauses for which + # is_not_subset_of was built, because unit-propagation could be cascading from a unit elimination. + if (meta_idx > meta_idx_outer) return(FALSE) + + if (!is_unit_propagation) { + # we are not propagating units, so we need to update the subset relations in the other direction. + # we do this first, in case on_updated_subset_relations gets too eager later + # No need to compare against meta_idx_outer, since not_subset_count will be NA for larger indices.. + idx_to_check = which(!is.na(not_subset_count[, meta_idx]) & available %in% symbol_registry[[symbol]]) + for (other_meta_idx in idx_to_check) { + # was the other a subset of us before? that could have changed now. + if (!is_not_subset_of[[other_meta_idx]][meta_idx, symbol] && !all(entries[[available[[other_meta_idx]]]][[symbol]] %in% entries[[clause_idx]][[symbol]])) { + is_not_subset_of[[other_meta_idx]][meta_idx, symbol] <<- TRUE + # no need to call on_updated_subset_relations, since we are increasing rowsums, not decreasing them + not_subset_count[other_meta_idx, meta_idx] <<- not_subset_count[other_meta_idx, meta_idx] + 1L + # no need to call the higher order self subsumption elimination handler here, since we need to do this anyways further down. } - if (length(ei) == 1) { - # even if names(ei) is already in units, at this point ei[[1]] is the intersection of the values - units[[names(ei)]] = ei[[1]] + } + } + + is_not_subset_of_col = match(symbol, colnames(is_not_subset_of[[meta_idx]])) + # * We could now be a subset of things that we were not a subset of before, so we only need to check the TRUE entries and may be setting them to FALSE. + # --> hence `is_not_subset_of[meta_idx][is_not_subset_of[meta_idx]` + # Note: we cannot address is_not_subset_of by symbol_idx, since clauses may get shorter but is_not_subset_of stays the same! + # * If this is unit propagation, we do not need to check other entries, since apply_domain_restriction happens to all clauses in a row, so the counter-side is updated in time. + # In particular, we do not need to worry that some other clause that was formerly our subset ceases to be our subset, since that other clause + # will also be restricted by the unit. + # * We can only ever set those entries to FALSE for which the other clause is in the symbol registry for the current symbol + # --> hence `available %in% symbol_registry[[symbol]]` + # * We only need to check up to the point where we have built is_not_subset_of + # --> hence the is.na() + rows_to_check = which(!is.na(not_subset_count[meta_idx, ]) & is_not_subset_of[[meta_idx]][, is_not_subset_of_col] & available %in% symbol_registry[[symbol]]) + for (other_meta_idx in rows_to_check) { + clause_idx_other = available[[other_meta_idx]] + # while we only get here for rows that are in the symbol_registry and therefore not eliminated / units, we need to check again since on_updated_subset_relations() + # can change this during the loop. + if (eliminated[[clause_idx_other]] || is_unit[[clause_idx_other]]) next + + # when we get here, that means that the symbol exists both in clause_idx and in other_ref_this symbol, *and* we have seen both clauses + # in the is_not_subset_of building process. + # If this were not the case, then we would not need to change anything. + other_clause_range = entries[[available[[other_meta_idx]]]][[symbol]] + if (!all(entries[[clause_idx]][[symbol]] %in% other_clause_range)) next + + # we are now a subset (and most likely were not before) + # ("most likely" because it could probably happen that we re-enter this part through some cascading elimination / propagation) + if (!is_not_subset_of[[meta_idx]][other_meta_idx, is_not_subset_of_col]) next + is_not_subset_of[[meta_idx]][other_meta_idx, is_not_subset_of_col] <<- FALSE + not_subset_count[meta_idx, other_meta_idx] <<- (rowsum = not_subset_count[meta_idx, other_meta_idx] - 1L) + if (rowsum > 1L + second_order_enabled) next + ousr = on_updated_subset_relations(meta_idx, other_meta_idx, FALSE) + if (identical(ousr, TRUE)) return(TRUE) # forward contradiction signal. We don't care if other_meta_idx was eliminated. + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) return(NULL) # need to check more directly if things escalated somehow and clause_idx was eliminated indirectly + } + # call on_domain_changed_handle_2nd_order_sse + # it is not a waste w/r/t the 'on_updated_subset_relations' call, since that one only deals with clauses for which the symbol is set to FALSE now, + # i.e. precisely the other clauses. + if (second_order_enabled) on_update_range(meta_idx, symbol) else FALSE + } + + # eliminate `symbol` from `clause_idx` + # returns 'NULL' for turned into a unit or eliminated, 'TRUE' for contradiction, 'FALSE' for nothing happened + eliminate_symbol_from_clause = function(clause_idx, symbol) { + clause = entries[[clause_idx]] + clause[[symbol]] = NULL + if (!length(clause)) return(TRUE) # signal that we have a contradiction and can exit + # remove from symbol registry of the symbol that went to 0 + sr = symbol_registry[[symbol]] + symbol_registry[[symbol]] = sr[sr != clause_idx] + + entries[[clause_idx]] <<- clause + if (length(clause) == 1) { + # new unit ahoy + # remove from symbol registry of the symbol that remains in the clause + # (since it is now a unit) + sr = symbol_registry[[names(clause)]] + symbol_registry[[names(clause)]] = sr[sr != clause_idx] + if (register_unit(clause_idx)) return(TRUE) # forward signal from register_unit: contradiction + return(NULL) # clause was turned into a unit + } + # clause was not turned into a unit, so we need to fill in is_not_subset_of + if (is.null(is_not_subset_of)) return(FALSE) # we have not started filling this one in + + meta_idx = available_inverse[[clause_idx]] + # meta_idx_outer is the index up to which we have built is_not_subset_of; if meta_idx > meta_idx_outer, then we haven't seen the clause yet. + # we are not relying on the fact that as soon as is_not_subset_of is non-null, we will only get here for clauses for which + # this was built, because it could be cascading from a unit elimination. + if (meta_idx > meta_idx_outer) return(FALSE) + + is_not_subset_of_col = match(symbol, colnames(is_not_subset_of[[meta_idx]])) + rows_changed = which(is_not_subset_of[[meta_idx]][, is_not_subset_of_col] & !is.na(not_subset_count[meta_idx, ])) + is_not_subset_of[[meta_idx]][, is_not_subset_of_col] <<- FALSE + not_subset_count[meta_idx, rows_changed] <<- not_subset_count[meta_idx, rows_changed] - 1L + others_ref_this_symbol = available_inverse[sr] + # only where we have already set up is_not_subset_of + for (meta_idx_other in others_ref_this_symbol[!is.na(not_subset_count[others_ref_this_symbol, meta_idx])]) { + if (!is_not_subset_of[[meta_idx_other]][meta_idx, symbol]) { + is_not_subset_of[[meta_idx_other]][meta_idx, symbol] <<- TRUE + not_subset_count[meta_idx_other, meta_idx] <<- not_subset_count[meta_idx_other, meta_idx] + 1L + } + } + # we could have some leftover TRUEs from eliminated or unit-ed clauses + rows_changed_ids = available[rows_changed] + for (meta_idx_other in rows_changed[!eliminated[rows_changed_ids] & !is_unit[rows_changed_ids] & rows_changed <= meta_idx_outer]) { + # We have to do this *after* we set the corresponding values to TRUE for others_ref_this_symbol, + # since calling this could realistically change the symbol registry (e.g. if it leads to a symbol + # being eliminated from other clauses). + clause_idx_other = available[[meta_idx_other]] + # while we *do* restrict meta_idx_other in the for loop already, eliminated and is_unit can still change during the loop, so check here again + if (eliminated[[clause_idx_other]] || is_unit[[clause_idx_other]]) next + if (not_subset_count[meta_idx, meta_idx_other] > 1L + second_order_enabled) next + ousr = on_updated_subset_relations(meta_idx, meta_idx_other, FALSE) + if (identical(ousr, TRUE)) return(TRUE) + # on_updated_subset_relations could cascade down to eliminating meta_idx (i.e. clause_idx) + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) return(NULL) + } + FALSE + } + + # returns 'NULL' when meta_idx_other was eliminated (or possibly turned into a unit), + # 'TRUE' for contradiction, 'FALSE' for nothing changed + on_updated_subset_relations = function(meta_idx, meta_idx_other, second_order_only) { + # the row `meta_idx_other` of `is_not_subset_of[[meta_idx]]` has been updated. + # we now check whether we can apply subsumption elimination, or at least self-subsumption elimination, on `meta_idx`. + rowsum = not_subset_count[meta_idx, meta_idx_other] + if (rowsum > 1L + second_order_enabled) return(FALSE) # nothing to do + if (rowsum == 2L) { + # we usually don't get here when we are second_order_only; however, it may be possible that a oneend clause + # gets turned into a twoend clause during 2nd order triggering before it gets triggered itself. + hs2oo = handle_sse_2nd_order_twoend(meta_idx, meta_idx_other, NULL) + if (identical(hs2oo, TRUE)) return(TRUE) + clause_other = available[[meta_idx_other]] + if (eliminated[[clause_other]] || is_unit[[clause_other]]) return(NULL) + return(FALSE) + } + if (rowsum == 0) { + eliminate_clause_update_sr(available[[meta_idx_other]]) + return(NULL) + } + # rowsum == 1 + symbol_to_restrict = colnames(is_not_subset_of[[meta_idx]])[is_not_subset_of[[meta_idx]][meta_idx_other, ]] + # update clause and sc! + + if (!second_order_only) { + # note we update meta_idx_other: we are currently subset of that other clause w/r/t all except one symbol. + # we can therefore intersect that last symbol in the other clause with the range of that symbol in the current clause. + # apply_domain_restriction will take care of eliminating the symbol if the range becomes empty. + # It could in theory even do subsumption, but we have already taken care of that above. + adr = apply_domain_restriction(available[[meta_idx_other]], symbol_to_restrict, entries[[available[[meta_idx]]]][[symbol_to_restrict]], FALSE) + if (is.null(adr)) return(NULL) + if (adr) return(TRUE) + if (!second_order_enabled) return(FALSE) + } + if (!second_order_enabled_matrix[meta_idx, meta_idx_other]) return(FALSE) + clause_idx = available[[meta_idx]] + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) return(FALSE) + hs2oo = handle_sse_2nd_order_oneend(meta_idx, meta_idx_other, symbol_to_restrict) + if (identical(hs2oo, TRUE)) return(TRUE) + clause_other = available[[meta_idx_other]] + if (eliminated[[clause_other]] || is_unit[[clause_other]]) return(NULL) + FALSE + } + + # second order self-subsumption elimination + # this is called whenever the range of symbol in meta_idx shrinks, opening up the possibility for 2nd order self-subsumption. + # meta_idx is the clause that will remove symbol range from other clauses. + # returns NULL if meta_idx was eliminated, FALSE if no contradiction, TRUE if contradiction + on_update_range = function(meta_idx, symbol) { + ## assuming the symbol exists in meta_idx + # availability of symbol in the other clause is not necessary here! + # units don't need to be treated separately: + # - since they only work with 2 length-2-clauses that have both the same symbol: the one of the unit, and another one; in the other one they must be disjoint. + # - because of this, they will HS-eliminate the unit. + + inso_symbol_col = match(symbol, colnames(is_not_subset_of[[meta_idx]])) + potential_targets = which(is_not_subset_of[[meta_idx]][, inso_symbol_col] & !eliminated[available] & !is_unit[available] & !is.na(not_subset_count[meta_idx, ])) + + targets_while_oneend = potential_targets[not_subset_count[meta_idx, potential_targets] == 1L] + + for (meta_idx_target in targets_while_oneend) { + if (!second_order_enabled_matrix[meta_idx, meta_idx_target]) next + hs2oo = handle_sse_2nd_order_oneend(meta_idx, meta_idx_target, symbol) + if (is.null(hs2oo)) return(NULL) # meta_idx eliminated + if (hs2oo) return(TRUE) + } + targets_while_twoend = potential_targets[not_subset_count[meta_idx, potential_targets] == 2L] + for (meta_idx_target in targets_while_twoend) { + if (!second_order_enabled_matrix[meta_idx, meta_idx_target]) next + hs2oo = handle_sse_2nd_order_twoend(meta_idx, meta_idx_target, symbol) + if (is.null(hs2oo)) return(NULL) # meta_idx eliminated + if (hs2oo) return(TRUE) + } + FALSE + } + + # meta_idx is not subset of meta_idx_target over 'symbol'. + # check if there are other clauses that are non-subsets of meta_idx_target for two symbols, one of which is 'symbol' as well. + # return NULL if clause_idx is eliminated. + handle_sse_2nd_order_oneend = function(meta_idx, meta_idx_target, symbol) { + # we don't need to check whether symbol is in meta_idx, since then it will automatically not be a non-subset of target + inso_symbol_col = match(symbol, colnames(is_not_subset_of[[meta_idx]])) + clause_idx = available[[meta_idx]] + symbol_clauses = symbol_registry[[symbol]] + symbol_clauses_meta = available_inverse[symbol_clauses] + + clause_idx_target = available[[meta_idx_target]] + # intersect on symbol with some other clause that has not_subset_count == 2, and where the target symbol is present in the garget + if (eliminated[[clause_idx_target]] || is_unit[[clause_idx_target]]) return(FALSE) + twoends = symbol_clauses_meta[not_subset_count[symbol_clauses_meta, meta_idx_target] == 2L] + for (meta_idx_twoend in twoends[!is.na(twoends)]) { # twoends is NA for clauses that have not been processed yet + # in every loop iteration, check our conditions again, since anything can happen when we do sse: + # target exists, is not a unit (these are checked outside the for loop as well as with `ts2o`), and exactly one symbol ("symbol") of meta_idx does not cover it. + if (not_subset_count[meta_idx, meta_idx_target] != 1L || !is_not_subset_of[[meta_idx]][meta_idx_target, inso_symbol_col]) break + clause_idx_twoend = available[[meta_idx_twoend]] + # now check that the meta_idx_twoend is still valid: + # exists, not a unit, it does not cover the target with exactly two symbols, one of which is `symbol` + if (eliminated[[clause_idx_twoend]] || is_unit[[clause_idx_twoend]] || + not_subset_count[meta_idx_twoend, meta_idx_target] != 2L) { + next + } + symbol_target = colnames(is_not_subset_of[[meta_idx_twoend]])[is_not_subset_of[[meta_idx_twoend]][meta_idx_target, ]] + symbol_target = symbol_target[symbol_target != symbol] + if (length(symbol_target) != 1L) next # this can happen if a previous loop changed the clause in some way + if (!symbol_target %in% names(entries[[clause_idx_target]])) next + # `symbol_target` is two symbols here: target and intersect + ts2o = try_sse_2nd_order(meta_idx, meta_idx_twoend, meta_idx_target, symbol, symbol_target) + if (identical(ts2o, TRUE)) return(TRUE) + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) return(NULL) + if (is.null(ts2o)) return(FALSE) # target was eliminated + } + FALSE + } + + handle_sse_2nd_order_twoend = function(meta_idx, meta_idx_target, symbol) { + clause_idx = available[[meta_idx]] + + clause_idx_target = available[[meta_idx_target]] + # check that meta_idx_target is still valid: not eliminated, not a unit, not_subset_count 2 w/r/t the target, one of which is still the symbol itself. + if (eliminated[[clause_idx_target]] || is_unit[[clause_idx_target]] || not_subset_count[meta_idx, meta_idx_target] != 2) return(FALSE) + inso_symbols_cols = which(is_not_subset_of[[meta_idx]][meta_idx_target, ]) + symbols_twoend = colnames(is_not_subset_of[[meta_idx]])[inso_symbols_cols] + if (!is.null(symbol) && !symbol %in% symbols_twoend) return(FALSE) + for (symbol_inner_idx in 1:2) { + symbol_inner = symbols_twoend[[symbol_inner_idx]] # the intersection symbol + symbol_other = symbols_twoend[[3 - symbol_inner_idx]] + # symbol_other must be present in the target clause, otherwise we can skip. + if (!symbol_other %in% names(entries[[clause_idx_target]])) next + symbol_inner_clauses_meta = available_inverse[symbol_registry[[symbol_inner]]] + # 'oneends' may either have 1 or 2 non-subset symbols, with both symbols equal in the latter case. + # We do this in both inner loops, since we switch on which one of them is the target. + oneends = symbol_inner_clauses_meta[not_subset_count[symbol_inner_clauses_meta, meta_idx_target] <= 2L] + for (meta_idx_oneend in oneends[!is.na(oneends)]) { # oneends is NA for clauses that have not been processed yet + # check if the twoend-bit broke + if (not_subset_count[meta_idx, meta_idx_target] != 2 || !all(is_not_subset_of[[meta_idx]][meta_idx_target, inso_symbols_cols])) break + + # check if theoneend-bit broke + clause_idx_oneend = available[[meta_idx_oneend]] + if (eliminated[[clause_idx_oneend]] || is_unit[[clause_idx_oneend]]) next + # so the 'oneend' thing may also overlap with 'twoend' on the other symbol. + # The trouble is that we cannot rely on both symbols being in is_not_subset_of[[meta_idx_oneend]]. + # We therefore get the columns, with '0' if one of the symbols is not there, and then check whether the two columns are the only + # two that are TRUE (where the sum may be either 1 or 2). + symbols_twoend_idx = match(symbols_twoend, colnames(is_not_subset_of[[meta_idx_oneend]]), nomatch = 0L) + if (not_subset_count[meta_idx_oneend, meta_idx_target] != sum(is_not_subset_of[[meta_idx_oneend]][meta_idx_target, symbols_twoend_idx])) { + next } + if (!symbol_other %in% names(entries[[clause_idx_target]])) next + ts2o = try_sse_2nd_order(meta_idx_oneend, meta_idx, meta_idx_target, symbol_inner, symbol_other) + if (identical(ts2o, TRUE)) return(TRUE) + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) return(NULL) + if (is.null(ts2o)) return(FALSE) # target was eliminated } - if (can_simplify) next - } - - entries = entries[order(lengths(entries))] # removing units may have changed the order - eliminated = logical(length(entries)) - for (i in seq_along(entries)) { - if (eliminated[[i]]) next # can only happen if we do the hidden subsumption elimination, which searches forward - ei = entries[[i]] - # If sym(A) is a subset of sym(B) and for each s in sym(A), val(A, s) is a subset of val(B, s), then A implies B, so B can be removed ("subsumption elimination"). - for (j in seq_along(entries)) { - if (j == i) next - if (eliminated[[j]]) next - ej = entries[[j]] - if (length(ej) > length(ei)) break # we can't just do j in 1:(i-1), since some clauses have the same length, in which case we need to check subsumption. - name_overlap = names(ej) %in% names(ei) - if (all(name_overlap) && all(sapply(names(ej), function(s) all(ej[[s]] %in% ei[[s]])))) { - # can't do entries[[i]] = NULL, since we are iterating over entries; the entries[[i]] would break. - eliminated[[i]] = TRUE - break + } + FALSE + } + + try_sse_2nd_order = function(meta_idx_oneend, meta_idx_twoends, meta_idx_target, symbol_intersect, symbol_target) { + ## assuming that symbol_target exists in meta_idx_target + ## assuming that meta_idx_oneend and meta_idx_twoends both have symbol_intersect, and that at least meta_idx_twoends has symbol_target + if (!all(is_not_subset_of[[meta_idx_target]][c(meta_idx_oneend, meta_idx_twoends), symbol_target])) return(FALSE) + idx_oneend = available[[meta_idx_oneend]] + idx_twoends = available[[meta_idx_twoends]] + idx_target = available[[meta_idx_target]] + # if (any(eliminated[c(idx_oneend, idx_twoends, idx_target)]) || any(is_unit[c(idx_oneend, idx_twoends, idx_target)])) return(FALSE) + clause_oneend = entries[[idx_oneend]] + clause_twoends = entries[[idx_twoends]] + + # only proceed if clause_oneend and clause_twoends are disjoint outside of clause_target, with respect to symbol_intersect + clause_oneend_symbol_intersect = clause_oneend[[symbol_intersect]] + if (any(clause_oneend_symbol_intersect %in% clause_twoends[[symbol_intersect]] & + !clause_oneend_symbol_intersect %in% entries[[idx_target]][[symbol_intersect]])) { + return(FALSE) + } + apply_domain_restriction(idx_target, symbol_target, char_union(clause_oneend[[symbol_target]], clause_twoends[[symbol_target]]), FALSE) + } + + # mark a clause as eliminated and update symbol registry + # This is relatively safe to call, since it does not modify any other clauses and does not create new units or subset relationships. + eliminate_clause_update_sr = function(clause_idx) { + if (is_unit[[clause_idx]]) stop("Bug in the code, this should never happen.") + eliminated[[clause_idx]] <<- TRUE + for (s in names(entries[[clause_idx]])) { + sr = symbol_registry[[s]] + symbol_registry[[s]] = sr[sr != clause_idx] + } + } + + # process units: + # - populate unit_domains + # - start populating symbol_registry; it gets finished later down with non-units + # - also reduce duplicate units and replace them with their intersection + unit_queue = which(is_unit) + for (unit_idx in unit_queue) { + if (register_unit(unit_idx)) return(return_entries(FALSE)) + } + + # if there were only units, we are done + if (length(unit_queue) == length(entries)) return(return_entries(entries[!eliminated])) + + # process non-units: + # - eliminate entries subsumed by units + # - populate symbol_registry + # we sorted clauses by length, so we can skip ahead by length(unit_queue) + # At this point, everything after the unit_queue is not (yet) a unit. + # The seq.int here is "dangerous" and only allowed because we checked for length(unit_queue) == length(entries) above. + for (clause_idx in seq.int(length(unit_queue) + 1L, length(entries))) { + + # intersect with units and eliminate subsumed clauses + clause_symbol_isct = char_intersect(names(entries[[clause_idx]]), names(unit_domains)) + # apply unit-propagation early, since we otherwise run the risk of adding the clause + # to lots of symbol registry entries, only to remove it again right away + for (symbol in clause_symbol_isct) { + adr = apply_domain_restriction(clause_idx, symbol, unit_domains[[symbol]], TRUE) + if (is.null(adr)) break + if (adr) return(return_entries(FALSE)) + } + + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) next # could happen from unit propagation + + # do cache `clause = entries[[clause_idx]]` and refer to names(clause) here, + # since apply_domain_restriction might have removed symbols from the clause + for (symbol in names(entries[[clause_idx]])) { + sr_entry = symbol_registry[[symbol]] + if (is.null(sr_entry)) { + symbol_registry[[symbol]] = clause_idx + } else { + symbol_registry[[symbol]][[length(sr_entry) + 1L]] = clause_idx + } + } + } + + + # let's start with (self)-subsumption. + # this can also create new units etc. + + # we don't need to check for units, upon registration they are automatically removed, and they cannot help with self-subsumption or HLA + available = which(!(eliminated | is_unit)) + available_inverse = match(seq_along(entries), available) + + # record for each clause whether it is a subset of another clause. + # we record this for each symbol separately, so when a symbol gets self-subsumed, we can re-check others more quickly. + # Default is FALSE (not not a subset, i.e. it is a subset), this aligns with absent columns (which are subsets of everything) + # + # note that as soon as is_not_subset_of is non-null, some other functions assume that meta_idx_outer is also defined. + is_not_subset_of = vector("list", length(available)) + # not_subset_count[i, j]: how many symbols of clause i are not subset of clause j? + # if this is 1, we can do self-subsumption elimination and HLA. + # if this is 2, we can do self-subsumption with resolution. + # This is the same as sum(is_not_subset_of[[i]][j, ]) + not_subset_count = matrix(NA_integer_, nrow = length(available), ncol = length(available)) + + # whether second-order subsumption is enabled for the pair + # We only enable it after the initial first-order checks are done, to reduce 2nd order calls as much as possible. + second_order_enabled = FALSE + second_order_enabled_matrix = matrix(FALSE, nrow = length(available), ncol = length(available)) + + + for (meta_idx_outer in seq_along(available)) { + clause_idx = available[[meta_idx_outer]] + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) next # may happen if we somehow turn something into a unit that eliminates a later clause + clause = entries[[clause_idx]] + + # is_not_subset_of[[i]][j, k] records whether for symbol k, clause i is not a subset of clause j + # If k is not in clause i, then var(i, k) is trivially a subset of var(j, k), so this is interpreted as FALSE. + # If k is not in clause j but is in clause i, then var(i, k) is not a subset of var(j, k), so this is interpreted as TRUE. + # We initialize with TRUE and then search for instances where a symbol k is in both clauses i and j, and where var(i, k) *is* a subset of var(j, k). + # In that case, we set the entry to FALSE. + is_not_subset_of[[meta_idx_outer]] = matrix( + TRUE, + nrow = length(available), # indexed by meta_idx! + ncol = length(clause), + dimnames = list(NULL, names(clause)) + ) + # we are not a subset of ourselves + # (this prevents us from checking this later in on_updated_subset_relations; if we do check it there, we would eliminate the clause from itself) + is_not_subset_of[[meta_idx_outer]][meta_idx_outer, ] = FALSE + + for (meta_idx_inner in seq_len(meta_idx_outer - 1L)) { + ## need to refresh clause here, since it might have been shortened by unit propagation in an earlier iteration + clause = entries[[clause_idx]] + clause_idx_inner = available[[meta_idx_inner]] + if (eliminated[[clause_idx_inner]] || is_unit[[clause_idx_inner]]) next + clause_inner = entries[[clause_idx_inner]] + # note that even though we sort entries at the beginning, we can *not* rely on clause_inner to have smaller or equal length than clause, + # since unit elimination can change the length of clauses + + sci = names(clause_inner) + sci_sc_map = match(sci, names(clause), nomatch = 0L) + sci_names_in_common = which(sci_sc_map != 0L) + + # symbols that are not in common trivially get the matrix entry TRUE + # (they are not subsets of their counterpart in the other clause, since the other ones are empty) + + for (symbol_idx_inner in sci_names_in_common) { + symbol_idx_outer = sci_sc_map[[symbol_idx_inner]] + symbol = sci[[symbol_idx_inner]] + + range_inner = clause_inner[[symbol_idx_inner]] + range_outer = clause[[symbol_idx_outer]] + + inner_subset_of_outer = all(range_inner %in% range_outer) + outer_subset_of_inner = (inner_subset_of_outer && length(range_outer) == length(range_inner)) || all(range_outer %in% range_inner) + if (inner_subset_of_outer) { + # Avoid assigning TRUE to matrix that is initialized with TRUE. + # We index by column name here, since it is possible that clauses were shortened by + # unit propagation or self subsumption elimination somewhere on the way here + is_not_subset_of[[meta_idx_inner]][meta_idx_outer, symbol] = FALSE } - if (j >= i) next # everything that follows already checks in both directions in case of equal lengths. - # simple self subsumption and hidden subsumption elimination - # HSE: - # if s is in sym(A) and sym(B), and val(A, s) and val(B, s) are disjoint, then (A - s | B - s) is implied, - # and all superset clauses of (A - s | B - s) can be removed. - # we could also do this for higher order terms, intersection over X of val(X, s) == 0 etc., but this gets more complex. - # tbh, I am not sure if this is actually worth it - # SSE: If val(A, s) and val(B, s) are disjoint, and A - s is a subset of B - s, then A & B <=> A & (B - s) - - which_name_overlap = which(name_overlap) - # - build the union of values of overlapping symbols - # - in the innerloop we will check that most of this is a subset of any other clause - # - "most of" here means: all but the one symbol s where the values are disjoint - # - use delayedAssign to avoid computation if there is no overlap with empty intersect - delayedAssign("cnames", union(names(ei), names(ej))) - - # Putting ei[[s2]] first on purpose, since union() preserves the order of the first argument. - # If and only if ej[-s] is a subset of ei[-s], then cunion[-s] will be the same as ei[-s]. - delayedAssign("cunion", sapply(cnames, function(s2) union(ei[[s2]], ej[[s2]]), simplify = FALSE)) - - nameshift = 0 # in case we eliminate names from ej, we need to shift the indices for later loops iterations - for (no in which_name_overlap) { - s = names(ej)[[no - nameshift]] - # intersection is not 0 --> try next one - if (length(intersect(ej[[s]], ei[[s]]))) next - cnames_s = setdiff(cnames, s) - - # Let's try self subsumption elimination first - if (length(cnames) == length(ei)) { - # cnames is the union of symbols in ei and ej. - # If length(cnames) is different from max(length(ei), length(ej)), then ei and ej can not be subsets of one another. - # Since j < i, length(ej) <= length(ei). - - # ej is usually smaller than ei, so often only ej can be a subset of ei. - # They may, however, have the same number of terms, in which case the reverse is also possible. - # Use 'c()' to drop attributes from ei here. - ei_without_s = ei[cnames_s] - do_sse = identical(cunion[cnames_s], c(ei_without_s)) - # if they have the same number of terms, ei could be a subset of ej. - # However, then we can not rely on the order of values in the union being correct. - do_sse_reverse = (!do_sse && (length(ei) == length(ej)) && - all(sapply(cnames_s, function(s2) all(ei[[s2]] %in% ej[[s2]])))) - if (do_sse_reverse) { - # ei is a subset of ej - # --> eliminate s from ej - ej[[s]] = NULL - new_entry = entries[[j]] = ej - dont_eliminate = j - nameshift = nameshift + 1 - } else if (do_sse) { - # ej is a subset of ei - # --> eliminate s from ei - new_entry = entries[[i]] = ei = ei_without_s - dont_eliminate = i - } - - if (do_sse || do_sse_reverse) { - - if (length(new_entry) == 1) { - # we have a unit clause now - - # It could happen that we eliminate the entry further, in which - # case units[[]] would get stale, but then we return_false anyway. - units[[names(new_entry)]] = new_entry[[1]] - can_simplify = TRUE # do unit elimination all over again - ## TODO: we could probably make this more efficient by only unit-eliminating the terms that are new - } - - if (!length(new_entry)) { - # we have a contradiction now - # Maybe this could happen if we SS-Eliminate multiple symbols from a clause in a row. - return(return_false) - } - - # What can have happened now is that the newly created element can eliminate other elements. - # If it can eliminate the current element i, that means it is a subset of ei, which only happens if ej\s is a subset of ei\s. However, in that case, we always want to keep element i. - # We therefore only need to loop up to i - 1. - # The loop is similar to the subsumption elimination loop; only in this case, we check if we can eliminate the elements that come before i, not like above where we check if we can eliminate i. - - # loop down from large to small, since then we can break once we find a clause with insufficient entries - for (k in rev(seq_len(i - 1))) { - if (k == dont_eliminate || eliminated[[k]]) next - ek = entries[[k]] - if (length(ek) < length(new_entry)) break # once we reached entries that are shorter than the new_entry, we won't find anything longer any more and we can break - if (all(cnames_s %in% names(ek)) && all(sapply(cnames_s, function(s2) all(new_entry[[s2]] %in% ek[[s2]])))) { - eliminated[[k]] = TRUE - } - } - if (eliminated[[j]]) break # we eliminated one of the entries we are currently looking at, no more need to look at other symbols - next - } - } - # Hidden Subsumption Elimination - # - # We only do this if self subsumption elimination did not occur. - # - # We eliminate based on an implied clause (A - s | B - s) - # Since we will forget about this clause after this iteration, we have to eliminate all clauses with size larger or equal to ||A | B|| - 1 - # loop down from large to small, since then we can break once we find a clause with insufficient entries - for (k in rev(seq_along(entries))) { - if (k == i || k == j || eliminated[[k]]) next - ek = entries[[k]] - # all of cnames_s must be in ek, otherwise we can't eliminate - # since we are looping down from large to small ek, we can break once this is not the case - if (length(ek) < length(cnames) - 1) break - if (all(cnames_s %in% names(ek)) && all(sapply(cnames_s, function(s2) all(cunion[[s2]] %in% ek[[s2]])))) { - eliminated[[k]] = TRUE - } - } + if (outer_subset_of_inner) { + is_not_subset_of[[meta_idx_outer]][meta_idx_inner, symbol] = FALSE } + } + # prefer to eliminate the outer loopo clause first, since we have already + # done more work for the inner loop clause (which comes earlier in 'entries') + not_subset_count[meta_idx_outer, meta_idx_inner] = sum(is_not_subset_of[[meta_idx_outer]][meta_idx_inner, ]) + rowsum = sum(is_not_subset_of[[meta_idx_inner]][meta_idx_outer, ]) + not_subset_count[meta_idx_inner, meta_idx_outer] = rowsum + if (rowsum <= 1) { + ousr = on_updated_subset_relations(meta_idx_inner, meta_idx_outer, FALSE) + if (is.null(ousr)) break + if (ousr) return(return_entries(FALSE)) + if (eliminated[[clause_idx_inner]] || is_unit[[clause_idx_inner]]) next # yes this can happen. + } + # need to get rowsum back again, since the call above could have changed something! + rowsum = not_subset_count[meta_idx_outer, meta_idx_inner] + if (rowsum <= 1) { + ousr = on_updated_subset_relations(meta_idx_outer, meta_idx_inner, FALSE) + if (identical(ousr, TRUE)) return(return_entries(FALSE)) + if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) break # probably this can happen if things cascade onwards when updating clause_inner + if (is.null(ousr)) next + } + } + } + + second_order_enabled = TRUE + second_order_enabled_matrix = not_subset_count != 2L # allow cascading of indirect SSE, except for the combinations where we trigger it manually (otherwise we'd be running them twice) + # We only trigger twoend-clauses, because every twoend clauses looks for all available oneend-clauses by itself. + # We can not do oneend-clauses-only, since twoend-clauses also look for other twoend-clauses that have common overlap. + # we need to make sure we don't trigger for eliminated / unit clauses, so we set them to TRUE here. + # This means all remaining entries of the second_order_enabled_matrix are exactly the ones for which we trigger on_updated_subset_relations() manually. + meta_disabled = eliminated[available] | is_unit[available] + second_order_enabled_matrix[meta_disabled, ] = TRUE + second_order_enabled_matrix[, meta_disabled] = TRUE + # alternatively, we could also enable none of the cascading in the beginning and have a nested loop in the following, where we 'repeat' until there are no more rowsum <= 2L + # That would probably give uns less cascading, but we'd have to run 'which()' on a N^2 matrix potentially many times. + + sse_to_trigger = which(!second_order_enabled_matrix, arr.ind = TRUE) + for (sse_idx in seq_len(nrow(sse_to_trigger))) { + meta_idx = sse_to_trigger[sse_idx, 1L] + meta_idx_other = sse_to_trigger[sse_idx, 2L] + if (eliminated[[available[[meta_idx]]]] || is_unit[[available[[meta_idx]]]] || eliminated[[available[[meta_idx_other]]]] || is_unit[[available[[meta_idx_other]]]]) next + second_order_enabled_matrix[meta_idx, meta_idx_other] = TRUE + if (identical(on_updated_subset_relations(meta_idx, meta_idx_other, TRUE), TRUE)) return(return_entries(FALSE)) + } + + + # Now for the big one: Asymmetric Hidden Literal Addition (Marijn et al.) + + # First, we do non-units, then we do units separately. + # We go big to small, since eliminating one clause could prevent us from eliminating other clauses, and all things being equal, we prefer eliminating long ones. + + # We only loop over the entries that have not been eliminated yet. + # We update `remaining_nonunit_entries` inside the loop whenever a clause is eliminated. + remaining_entries = which(!eliminated)[order(lengths(entries[!eliminated]), decreasing = TRUE)] + remaining_nonunit_entries = remaining_entries[seq_len(length(remaining_entries) - length(unit_domains))] + remaining_unit_entries = if (length(unit_domains)) remaining_entries[seq.int(length(remaining_entries) - length(unit_domains) + 1L, length(remaining_entries))] + + # iterating from large to small entries + for (clause_idx in remaining_nonunit_entries) { + clause = entries[[clause_idx]] + + # index inside `is_not_subset_of` + meta_idx = available_inverse[[clause_idx]] + remaining_other_entries = remaining_nonunit_entries[remaining_nonunit_entries != clause_idx] + + # we keep track of which clauses were used for HLA, since every other clause can only do that once. + was_used = logical(length(remaining_other_entries)) + # for each of the other clauses, how many of their symbols are not a subset of the current clause? + not_subset_count_current = not_subset_count[available_inverse[remaining_other_entries], meta_idx] + # for (roe_idx in seq_along(remaining_other_entries)) { + # # if we had set up is_not_subset_of as a 3-dim array, then the following could just have been a colSums over is_not_subset_of[, meta_idx, ] + # # However, that array would take a lot of memory: N_clauses^2 x N_all_symbols; The current setup has N_clauses^2 x max(N_symbols_per_clause) + # other_clause_idx = remaining_other_entries[[roe_idx]] + # meta_idx_other = available_inverse[[other_clause_idx]] + # not_subset_count[[roe_idx]] = sum(is_not_subset_of[[meta_idx_other]][meta_idx, ]) + # } + repeat { + # we do HLA by looking for a clause that is a subset of the current clause w/r/t all except one symbol. + # We also only consider every clause at most once, since it won't have anything else to add a second time. + # No need to check for == 0 here: if it was the case before, then we eliminated the clause already. If it becomes the case during the loop, we check + # for it further down. + hla_clause_idx = match(TRUE, not_subset_count_current == 1L & !was_used) + if (is.na(hla_clause_idx)) break # no more clauses to consider: all are either used or have no_subset_count > 1 + clause_idx_other = remaining_other_entries[[hla_clause_idx]] + meta_idx_other = available_inverse[[clause_idx_other]] + symbol = colnames(is_not_subset_of[[meta_idx_other]])[is_not_subset_of[[meta_idx_other]][meta_idx, ]] + range_old = clause[[symbol]] + # new range of the symbol inside the clause: Union of old range and complement of that symbol's range in the other clause. + range_new = c(range_old, char_setdiff(universe[[symbol]], c(range_old, entries[[clause_idx_other]][[symbol]]))) + if (length(range_new) == length(universe[[symbol]])) { + # hidden tautology elimination + + # We still need the symbol registry (see below), so this can not be replaced by just `eliminated[[clause_idx]] = TRUE` + eliminate_clause_update_sr(clause_idx) + remaining_nonunit_entries = remaining_other_entries + break + } + # Now loop over clauses that also use the symbol, checking if they have one less `not_subset_count_current` because of that + # Note we do not need to check subsumption w/r/t units any more: All symbols are proper subsets w/r/t units at this point, + # so if adding the complement of one symbol to another made it a superset of a unit, the result was a tautology already. + for (updating_clause_meta_idx in available_inverse[symbol_registry[[symbol]]]) { + # we don't want to skip 'was_used' here, since we might still do hidden subsumption elimination with them. + if (is_not_subset_of[[updating_clause_meta_idx]][meta_idx, symbol] && + all(entries[[available[[updating_clause_meta_idx]]]][[symbol]] %in% range_new)) { + is_not_subset_of[[updating_clause_meta_idx]][meta_idx, symbol] = FALSE + roe_idx = match(available[[updating_clause_meta_idx]], remaining_other_entries) # I wished I didn't have to do this + not_subset_count_current[[roe_idx]] = not_subset_count_current[[roe_idx]] - 1L + if (not_subset_count_current[[roe_idx]] == 0L) { + # hidden subsumption elimination + eliminate_clause_update_sr(clause_idx) + remaining_nonunit_entries = remaining_other_entries + break + } + } } + if (eliminated[[clause_idx]]) break # the break inside the for-loop above will not break the repeat loop + was_used[[hla_clause_idx]] = TRUE + clause[[symbol]] = range_new + } + } + + # We now do the same thing as above, only for units. + # Units are different, because they don't have the `is_not_subset_of` matrices. These are trivially constructed from + # The symbol registry: "is_not_subset_of" for unit relating to symbol `s` is TRUE for all symbols in a clause that are not `s`. + # We deliberately make use of `remaining_nonunit_entries` here, which has been updated in the loop above as nonunit-clauses were eliminated + delayedAssign("roe_inverse", match(seq_along(entries), remaining_nonunit_entries)) # only do this match()-call if it is actually needed + for (clause_idx in remaining_unit_entries) { + clause = entries[[clause_idx]] + unitsymbol = names(clause) + was_used = logical(length(remaining_nonunit_entries)) + # every clause that is not yet eliminated is a proper subset of the current unit. + # If it is length N and contains the unit symbol, then N - 1 of its symbols are not subsets; + # otherwise (if it does not contain the unit symbol), all N symbols are not subsets. + not_subset_count = lengths(entries[remaining_nonunit_entries]) - (remaining_nonunit_entries %in% symbol_registry[[unitsymbol]]) + + # corresponding to `is_not_subset_of` matrix; only construct this for entries where it is needed. + is_not_subset_of_unit = vector("list", length(remaining_nonunit_entries)) + # The following loop is mostly identical to the loop above, only for units. + repeat { + hla_clause_idx = match(TRUE, not_subset_count == 1L & !was_used) + if (is.na(hla_clause_idx)) break # no more clauses to consider: all are either used or have no_subset_count > 1 + clause_idx_other = remaining_nonunit_entries[[hla_clause_idx]] + clause_other = entries[[clause_idx_other]] + if (is.null(is_not_subset_of_unit[[hla_clause_idx]])) { + is_not_subset_of_unit[[hla_clause_idx]] = structure(names(clause_other) != unitsymbol, names = names(clause_other)) + } + is_not_subset_entry = is_not_subset_of_unit[[hla_clause_idx]] + symbol = names(is_not_subset_entry)[is_not_subset_entry] + range_old = clause[[symbol]] + range_new = c(range_old, char_setdiff(universe[[symbol]], c(range_old, clause_other[[symbol]]))) + if (length(range_new) == length(universe[[symbol]])) { + # hidden tautology elimination + # no more need to update the unit registry + eliminated[[clause_idx]] = TRUE + break + } + # Now loop over clauses that also use the symbol, checking if they have one less `not_subset_count` because of that + for (updating_clause_idx in symbol_registry[[symbol]]) { + updating_hla_clause_idx = roe_inverse[[updating_clause_idx]] + if (is.null(is_not_subset_of_unit[[updating_hla_clause_idx]])) { + # Dynamically construct this entry if it is not set yet. + # We could delay this further, but that would make things even more complicated + updating_clause = entries[[updating_clause_idx]] + is_not_subset_of_unit[[updating_hla_clause_idx]] = structure(names(updating_clause) != unitsymbol, names = names(updating_clause)) + } + if (is_not_subset_of_unit[[updating_hla_clause_idx]][[symbol]] && + all(entries[[updating_clause_idx]][[symbol]] %in% range_new)) { + is_not_subset_of_unit[[updating_hla_clause_idx]][[symbol]] = FALSE + not_subset_count[[updating_hla_clause_idx]] = not_subset_count[[updating_hla_clause_idx]] - 1L + if (not_subset_count[[updating_hla_clause_idx]] == 0) { + # hidden subsumption elimination + eliminated[[clause_idx]] = TRUE + break + } + } + } + if (eliminated[[clause_idx]]) break # the break inside the for-loop above will not break the repeat loop + was_used[[hla_clause_idx]] = TRUE + clause[[symbol]] = range_new } - entries = entries[!eliminated] } - structure( - if (!length(entries)) TRUE else entries, - universe = universe, - class = "CnfFormula" - ) -} + return_entries(entries[!eliminated]) +} diff --git a/R/CnfFormula_simplify1.R b/R/CnfFormula_simplify1.R deleted file mode 100644 index 7d7239d1c..000000000 --- a/R/CnfFormula_simplify1.R +++ /dev/null @@ -1,782 +0,0 @@ - - -simplify_cnf = function(entries, universe) { - ################################# - # Some vocabulary: - # - `entries` is a list of `clauses`, which are named lists. - # - `clauses`' names are `symbols`, the values are the `ranges` of the symbols within that clause - # - `unit`: clause with single symbol - # Glossary of operations: - # - `unit propagation`: ranges of a symbol within a unit constitute the entire possible range of that symbol, - # so all clauses with that symbol are restricted to those values - # - `subsumption elimination`: if all ranges of all symbols within one clause are subsets of those ranges in another clause, - # then the other clause can be removed - # - `self-subsumption elimination`: if the ranges of all except one symbol within one clause are a subset of those ranges - # in another clause, then the remaining symbol in the latter clause can be intersected with the remaining symbol. - # - `hidden literal addition` (HLA): if the ranges of all except one symbol within one clause are a subset of those ranges - # in another clause, then the *complement* of the remaining symbol in the former clause can be added to the latter clause. - # This is basically the reverse of self-subsumption elimination. We do not use this to change clauses directly; - # the point here is that the resulting clause, even if applied repeatedly, is logically equivalent to the original clause within the formula: - # - `hidden subsumption elimination`: if applying HLA results in a clause that can be subsumed, the original clause can be removed. - # - `hidden tautology elimination`: if applying HLA results in a clause that is a tautology, the original clause can be removed. - # Note: 'Clause Elimination Procedures for CNF Formulas' by Marijn Heule et al. calls this "Asymmetric Hidden Literal Addition". - ################################# - - ######################## - ## Helper functions ## - ######################## - - # faster intersect, setdiff etc. that rely on x, y being characters with no duplicates - char_intersect = function(x, y) x[x %in% y] - char_setdiff = function(x, y) x[!x %in% y] - char_union = function(x, y) c(x, y[!y %in% x]) - # construct the CnfFormula return object - return_entries = function(entries) { - structure( - if (!length(entries)) TRUE else entries, - universe = universe, - class = "CnfFormula" - ) - } - - if (is.logical(entries)) return(return_entries(entries)) - - ######################## - ## Variable setup ## - ######################## - - entries = entries[order(lengths(entries))] - - is_unit = lengths(entries) == 1L - eliminated = logical(length(entries)) - - # maps symbol name -> the index of unit clauses - unit_registry = new.env(parent = emptyenv()) - - # maps symbol name -> their current domain - unit_domains = new.env(parent = emptyenv()) - - # maps symbol name -> the index of all non-unit clauses that refer to it - symbol_registry = new.env(parent = emptyenv()) - - is_not_subset_of = NULL # see further down - - ################################## - ## Event-driven clause handling ## - ################################## - # The following functions process the CNF clauses in various ways, - # depending on the current state of the entries. - # The state of the entries is updated in-place. - # The functions are then called in a loop, but they may also call each other. - # It is therefore important that they make the global state consistent before - # calling other functions, and that they are aware of how the global state *can* - # have changed upon their return. - # - entries[[clause_idx]] should be updated if necessary before other fns are called - # - symbol_registry[[symbol]] could have been updated - # - eliminated[[clause_idx]] could have been set to TRUE - # Since functions can call each other in different ways, `eliminated` could have changed even for clauses - # for which the other functions were not called. - - # Register a clause as a unit: - # - check if there is already a unit for this symbol - # - if not, add it to the unit registry - # - otherwise, intersect unit domains (and exit on contradiction) - # - apply unit propagation - # - We do *not* update the sybmol registry here; if the clause is registered for a given symbol, - # it has to be removed from there *before* calling this function. - register_unit = function(unit_idx) { - unit = entries[[unit_idx]] - nu = names(unit) - ur = unit_registry[[nu]] - if (is.null(ur)) { - unit_registry[[nu]] = unit_idx # environment assignment - unit_domains[[nu]] = unit[[1L]] # environment assignment - # this is init'd TRUE for those w/ length 1 at the start, we set it to TRUE for clauses where symbols were eliminated - is_unit[[unit_idx]] <<- TRUE - } else { - # two units refer to the same symbol - # -> we keep the one we saw before but update it to the intersection. - # the current one is eliminated - prev_unit = unit_domains[[nu]] - unit_isct = prev_unit[prev_unit %in% unit[[1L]]] - if (!length(unit_isct)) return(TRUE) # signal that we have a contradiction and can exit - entries[[ur]][[1L]] <<- (unit_domains[[nu]] = unit_isct) # update the *old* unit and unit_domains in one go. unit_domains is updated by-reference (environment) - eliminated[[unit_idx]] <<- TRUE - } - # The symbol registry is empty at the start; the following happens when new units are added later - use_inso = FALSE - if (!is.null(is_not_subset_of)) { - # if we have the is_not_subset_of matrix, we can use it to skip some checks - unit_idx_meta = available_inverse[[unit_idx]] - use_inso = unit_idx_meta <= meta_idx_outer # .. but only if we have built the matrix up to the current index - if (use_inso) { - # if the unit is a subset of the other clause, we will never skip. - inso_column = is_not_subset_of[[unit_idx_meta]][, nu] - } - } - for (s_clause_idx in symbol_registry[[nu]]) { - # could have been eliminated by subsumption elimination during unit propagation of another clause - # (we are not afraid of is_unit here, since we are the unit for the symbol here -- everything else that has the - # symbol gets eliminated) - if (eliminated[[s_clause_idx]]) next - if (use_inso) { - # if we already know that s_clause_idx[[nu]] is a subset of unit_idx, we can skip this - # exception: unit_idx is *also* a subset, implying equality, in which case we will do subsumption elimination. - s_clause_idx_meta = available_inverse[[s_clause_idx]] - if (s_clause_idx_meta <= meta_idx_outer && inso_column[[s_clause_idx_meta]] && !is_not_subset_of[[s_clause_idx_meta]][unit_idx_meta, nu]) next - } - adr = apply_domain_restriction(s_clause_idx, nu, unit_domains[[nu]], TRUE) - if (identical(adr, TRUE)) return(TRUE) # forward contradiction signal - } - FALSE # no contradiction - } - - # restrict the symbol in the clause to a given domain, e.g. a unit - # - clause_idx: index in entries - # - symbol: name of symbol to restrict - # - restringent: domain to restrict to - # returns TRUE if a contradiction was detected, NULL if the clause was eliminated - apply_domain_restriction = function(clause_idx, symbol, restringent, is_unit_propagation) { - clause = entries[[clause_idx]] - symbol_idx = match(symbol, names(clause)) - if (is.na(symbol_idx)) return(FALSE) - - clause_symbol_length_before = length(clause[[symbol_idx]]) - clause[[symbol_idx]] = char_intersect(clause[[symbol_idx]], restringent) - if (length(clause[[symbol_idx]]) == length(restringent)) { - # If the lengths match, then the clause is a superset of the unit (since the intersections are equal) - # the clause is therefore subsumed by the unit - eliminate_clause_update_sr(clause_idx) - return(NULL) - } - # clause was not changed - if (length(clause[[symbol_idx]]) == clause_symbol_length_before) return(FALSE) - if (!length(clause[[symbol_idx]])) { - # the symbol is not in the clause anymore - return(eliminate_symbol_from_clause(clause_idx, symbol)) - } - # clause was changed. - # We don't need to do this when we go the eliminate_symbol_from_clause route, since that will update the clause in any case. - entries[[clause_idx]] <<- clause - - # We need to update the subset relations matrix, if it exists - if (is.null(is_not_subset_of)) return(FALSE) - - meta_idx = available_inverse[[clause_idx]] - # meta_idx_outer is the index up to which we have built is_not_subset_of; if meta_idx > meta_idx_outer, then we haven't seen the clause yet. - # we are not relying on the fact that as soon as is_not_subset_of is non-null, we will only get here for clauses for which - # is_not_subset_of was built, because unit-propagation could be cascading from a unit elimination. - if (meta_idx > meta_idx_outer) return(FALSE) - - if (!is_unit_propagation) { - # we are not propagating units, so we need to update the subset relations in the other direction. - # we do this first, in case on_updated_subset_relations gets too eager later - # No need to compare against meta_idx_outer, since not_subset_count will be NA for larger indices.. - idx_to_check = which(!is.na(not_subset_count[, meta_idx]) & available %in% symbol_registry[[symbol]]) - for (other_meta_idx in idx_to_check) { - # was the other a subset of us before? that could have changed now. - if (!is_not_subset_of[[other_meta_idx]][meta_idx, symbol] && !all(entries[[available[[other_meta_idx]]]][[symbol]] %in% entries[[clause_idx]][[symbol]])) { - is_not_subset_of[[other_meta_idx]][meta_idx, symbol] <<- TRUE - # no need to call on_updated_subset_relations, since we are increasing rowsums, not decreasing them - not_subset_count[other_meta_idx, meta_idx] <<- not_subset_count[other_meta_idx, meta_idx] + 1L - # no need to call the higher order self subsumption elimination handler here, since we need to do this anyways further down. - } - } - } - - is_not_subset_of_col = match(symbol, colnames(is_not_subset_of[[meta_idx]])) - # * We could now be a subset of things that we were not a subset of before, so we only need to check the TRUE entries and may be setting them to FALSE. - # --> hence `is_not_subset_of[meta_idx][is_not_subset_of[meta_idx]` - # Note: we cannot address is_not_subset_of by symbol_idx, since clauses may get shorter but is_not_subset_of stays the same! - # * If this is unit propagation, we do not need to check other entries, since apply_domain_restriction happens to all clauses in a row, so the counter-side is updated in time. - # In particular, we do not need to worry that some other clause that was formerly our subset ceases to be our subset, since that other clause - # will also be restricted by the unit. - # * We can only ever set those entries to FALSE for which the other clause is in the symbol registry for the current symbol - # --> hence `available %in% symbol_registry[[symbol]]` - # * We only need to check up to the point where we have built is_not_subset_of - # --> hence the is.na() - rows_to_check = which(!is.na(not_subset_count[meta_idx, ]) & is_not_subset_of[[meta_idx]][, is_not_subset_of_col] & available %in% symbol_registry[[symbol]]) - for (other_meta_idx in rows_to_check) { - clause_idx_other = available[[other_meta_idx]] - # while we only get here for rows that are in the symbol_registry and therefore not eliminated / units, we need to check again since on_updated_subset_relations() - # can change this during the loop. - if (eliminated[[clause_idx_other]] || is_unit[[clause_idx_other]]) next - - # when we get here, that means that the symbol exists both in clause_idx and in other_ref_this symbol, *and* we have seen both clauses - # in the is_not_subset_of building process. - # If this were not the case, then we would not need to change anything. - other_clause_range = entries[[available[[other_meta_idx]]]][[symbol]] - if (!all(entries[[clause_idx]][[symbol]] %in% other_clause_range)) next - - # we are now a subset (and most likely were not before) - # ("most likely" because it could probably happen that we re-enter this part through some cascading elimination / propagation) - if (!is_not_subset_of[[meta_idx]][other_meta_idx, is_not_subset_of_col]) next - is_not_subset_of[[meta_idx]][other_meta_idx, is_not_subset_of_col] <<- FALSE - not_subset_count[meta_idx, other_meta_idx] <<- (rowsum = not_subset_count[meta_idx, other_meta_idx] - 1L) - if (rowsum > 1L + second_order_enabled) next - ousr = on_updated_subset_relations(meta_idx, other_meta_idx, FALSE) - if (identical(ousr, TRUE)) return(TRUE) # forward contradiction signal. We don't care if other_meta_idx was eliminated. - if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) return(NULL) # need to check more directly if things escalated somehow and clause_idx was eliminated indirectly - } - # call on_domain_changed_handle_2nd_order_sse - # it is not a waste w/r/t the 'on_updated_subset_relations' call, since that one only deals with clauses for which the symbol is set to FALSE now, - # i.e. precisely the other clauses. - if (second_order_enabled) on_update_range(meta_idx, symbol) else FALSE - } - - # eliminate `symbol` from `clause_idx` - # returns 'NULL' for turned into a unit or eliminated, 'TRUE' for contradiction, 'FALSE' for nothing happened - eliminate_symbol_from_clause = function(clause_idx, symbol) { - clause = entries[[clause_idx]] - clause[[symbol]] = NULL - if (!length(clause)) return(TRUE) # signal that we have a contradiction and can exit - # remove from symbol registry of the symbol that went to 0 - sr = symbol_registry[[symbol]] - symbol_registry[[symbol]] = sr[sr != clause_idx] - - entries[[clause_idx]] <<- clause - if (length(clause) == 1) { - # new unit ahoy - # remove from symbol registry of the symbol that remains in the clause - # (since it is now a unit) - sr = symbol_registry[[names(clause)]] - symbol_registry[[names(clause)]] = sr[sr != clause_idx] - if (register_unit(clause_idx)) return(TRUE) # forward signal from register_unit: contradiction - return(NULL) # clause was turned into a unit - } - # clause was not turned into a unit, so we need to fill in is_not_subset_of - if (is.null(is_not_subset_of)) return(FALSE) # we have not started filling this one in - - meta_idx = available_inverse[[clause_idx]] - # meta_idx_outer is the index up to which we have built is_not_subset_of; if meta_idx > meta_idx_outer, then we haven't seen the clause yet. - # we are not relying on the fact that as soon as is_not_subset_of is non-null, we will only get here for clauses for which - # this was built, because it could be cascading from a unit elimination. - if (meta_idx > meta_idx_outer) return(FALSE) - - is_not_subset_of_col = match(symbol, colnames(is_not_subset_of[[meta_idx]])) - rows_changed = which(is_not_subset_of[[meta_idx]][, is_not_subset_of_col] & !is.na(not_subset_count[meta_idx, ])) - is_not_subset_of[[meta_idx]][, is_not_subset_of_col] <<- FALSE - not_subset_count[meta_idx, rows_changed] <<- not_subset_count[meta_idx, rows_changed] - 1L - others_ref_this_symbol = available_inverse[sr] - # only where we have already set up is_not_subset_of - for (meta_idx_other in others_ref_this_symbol[!is.na(not_subset_count[others_ref_this_symbol, meta_idx])]) { - if (!is_not_subset_of[[meta_idx_other]][meta_idx, symbol]) { - is_not_subset_of[[meta_idx_other]][meta_idx, symbol] <<- TRUE - not_subset_count[meta_idx_other, meta_idx] <<- not_subset_count[meta_idx_other, meta_idx] + 1L - } - } - # we could have some leftover TRUEs from eliminated or unit-ed clauses - rows_changed_ids = available[rows_changed] - for (meta_idx_other in rows_changed[!eliminated[rows_changed_ids] & !is_unit[rows_changed_ids] & rows_changed <= meta_idx_outer]) { - # We have to do this *after* we set the corresponding values to TRUE for others_ref_this_symbol, - # since calling this could realistically change the symbol registry (e.g. if it leads to a symbol - # being eliminated from other clauses). - clause_idx_other = available[[meta_idx_other]] - # while we *do* restrict meta_idx_other in the for loop already, eliminated and is_unit can still change during the loop, so check here again - if (eliminated[[clause_idx_other]] || is_unit[[clause_idx_other]]) next - if (not_subset_count[meta_idx, meta_idx_other] > 1L + second_order_enabled) next - ousr = on_updated_subset_relations(meta_idx, meta_idx_other, FALSE) - if (identical(ousr, TRUE)) return(TRUE) - # on_updated_subset_relations could cascade down to eliminating meta_idx (i.e. clause_idx) - if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) return(NULL) - } - FALSE - } - - # returns 'NULL' when meta_idx_other was eliminated (or possibly turned into a unit), - # 'TRUE' for contradiction, 'FALSE' for nothing changed - on_updated_subset_relations = function(meta_idx, meta_idx_other, second_order_only) { - # the row `meta_idx_other` of `is_not_subset_of[[meta_idx]]` has been updated. - # we now check whether we can apply subsumption elimination, or at least self-subsumption elimination, on `meta_idx`. - rowsum = not_subset_count[meta_idx, meta_idx_other] - if (rowsum > 1L + second_order_enabled) return(FALSE) # nothing to do - if (rowsum == 2L) { - # we usually don't get here when we are second_order_only; however, it may be possible that a oneend clause - # gets turned into a twoend clause during 2nd order triggering before it gets triggered itself. - hs2oo = handle_sse_2nd_order_twoend(meta_idx, meta_idx_other, NULL) - if (identical(hs2oo, TRUE)) return(TRUE) - clause_other = available[[meta_idx_other]] - if (eliminated[[clause_other]] || is_unit[[clause_other]]) return(NULL) - return(FALSE) - } - if (rowsum == 0) { - eliminate_clause_update_sr(available[[meta_idx_other]]) - return(NULL) - } - # rowsum == 1 - symbol_to_restrict = colnames(is_not_subset_of[[meta_idx]])[is_not_subset_of[[meta_idx]][meta_idx_other, ]] - # update clause and sc! - - if (!second_order_only) { - # note we update meta_idx_other: we are currently subset of that other clause w/r/t all except one symbol. - # we can therefore intersect that last symbol in the other clause with the range of that symbol in the current clause. - # apply_domain_restriction will take care of eliminating the symbol if the range becomes empty. - # It could in theory even do subsumption, but we have already taken care of that above. - adr = apply_domain_restriction(available[[meta_idx_other]], symbol_to_restrict, entries[[available[[meta_idx]]]][[symbol_to_restrict]], FALSE) - if (is.null(adr)) return(NULL) - if (adr) return(TRUE) - if (!second_order_enabled) return(FALSE) - } - if (!second_order_enabled_matrix[meta_idx, meta_idx_other]) return(FALSE) - clause_idx = available[[meta_idx]] - if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) return(FALSE) - hs2oo = handle_sse_2nd_order_oneend(meta_idx, meta_idx_other, symbol_to_restrict) - if (identical(hs2oo, TRUE)) return(TRUE) - clause_other = available[[meta_idx_other]] - if (eliminated[[clause_other]] || is_unit[[clause_other]]) return(NULL) - FALSE - } - - # second order self-subsumption elimination - # this is called whenever the range of symbol in meta_idx shrinks, opening up the possibility for 2nd order self-subsumption. - # meta_idx is the clause that will remove symbol range from other clauses. - # returns NULL if meta_idx was eliminated, FALSE if no contradiction, TRUE if contradiction - on_update_range = function(meta_idx, symbol) { - ## assuming the symbol exists in meta_idx - # availability of symbol in the other clause is not necessary here! - # units don't need to be treated separately: - # - since they only work with 2 length-2-clauses that have both the same symbol: the one of the unit, and another one; in the other one they must be disjoint. - # - because of this, they will HS-eliminate the unit. - - inso_symbol_col = match(symbol, colnames(is_not_subset_of[[meta_idx]])) - potential_targets = which(is_not_subset_of[[meta_idx]][, inso_symbol_col] & !eliminated[available] & !is_unit[available] & !is.na(not_subset_count[meta_idx, ])) - - targets_while_oneend = potential_targets[not_subset_count[meta_idx, potential_targets] == 1L] - - for (meta_idx_target in targets_while_oneend) { - if (!second_order_enabled_matrix[meta_idx, meta_idx_target]) next - hs2oo = handle_sse_2nd_order_oneend(meta_idx, meta_idx_target, symbol) - if (is.null(hs2oo)) return(NULL) # meta_idx eliminated - if (hs2oo) return(TRUE) - } - targets_while_twoend = potential_targets[not_subset_count[meta_idx, potential_targets] == 2L] - for (meta_idx_target in targets_while_twoend) { - if (!second_order_enabled_matrix[meta_idx, meta_idx_target]) next - hs2oo = handle_sse_2nd_order_twoend(meta_idx, meta_idx_target, symbol) - if (is.null(hs2oo)) return(NULL) # meta_idx eliminated - if (hs2oo) return(TRUE) - } - FALSE - } - - # meta_idx is not subset of meta_idx_target over 'symbol'. - # check if there are other clauses that are non-subsets of meta_idx_target for two symbols, one of which is 'symbol' as well. - # return NULL if clause_idx is eliminated. - handle_sse_2nd_order_oneend = function(meta_idx, meta_idx_target, symbol) { - # we don't need to check whether symbol is in meta_idx, since then it will automatically not be a non-subset of target - inso_symbol_col = match(symbol, colnames(is_not_subset_of[[meta_idx]])) - clause_idx = available[[meta_idx]] - symbol_clauses = symbol_registry[[symbol]] - symbol_clauses_meta = available_inverse[symbol_clauses] - - clause_idx_target = available[[meta_idx_target]] - # intersect on symbol with some other clause that has not_subset_count == 2, and where the target symbol is present in the garget - if (eliminated[[clause_idx_target]] || is_unit[[clause_idx_target]]) return(FALSE) - twoends = symbol_clauses_meta[not_subset_count[symbol_clauses_meta, meta_idx_target] == 2L] - for (meta_idx_twoend in twoends[!is.na(twoends)]) { # twoends is NA for clauses that have not been processed yet - # in every loop iteration, check our conditions again, since anything can happen when we do sse: - # target exists, is not a unit (these are checked outside the for loop as well as with `ts2o`), and exactly one symbol ("symbol") of meta_idx does not cover it. - if (not_subset_count[meta_idx, meta_idx_target] != 1L || !is_not_subset_of[[meta_idx]][meta_idx_target, inso_symbol_col]) break - clause_idx_twoend = available[[meta_idx_twoend]] - # now check that the meta_idx_twoend is still valid: - # exists, not a unit, it does not cover the target with exactly two symbols, one of which is `symbol` - if (eliminated[[clause_idx_twoend]] || is_unit[[clause_idx_twoend]] || - not_subset_count[meta_idx_twoend, meta_idx_target] != 2L) { - next - } - symbol_target = colnames(is_not_subset_of[[meta_idx_twoend]])[is_not_subset_of[[meta_idx_twoend]][meta_idx_target, ]] - symbol_target = symbol_target[symbol_target != symbol] - if (length(symbol_target) != 1L) next # this can happen if a previous loop changed the clause in some way - if (!symbol_target %in% names(entries[[clause_idx_target]])) next - # `symbol_target` is two symbols here: target and intersect - ts2o = try_sse_2nd_order(meta_idx, meta_idx_twoend, meta_idx_target, symbol, symbol_target) - if (identical(ts2o, TRUE)) return(TRUE) - if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) return(NULL) - if (is.null(ts2o)) return(FALSE) # target was eliminated - } - FALSE - } - - handle_sse_2nd_order_twoend = function(meta_idx, meta_idx_target, symbol) { - clause_idx = available[[meta_idx]] - - clause_idx_target = available[[meta_idx_target]] - # check that meta_idx_target is still valid: not eliminated, not a unit, not_subset_count 2 w/r/t the target, one of which is still the symbol itself. - if (eliminated[[clause_idx_target]] || is_unit[[clause_idx_target]] || not_subset_count[meta_idx, meta_idx_target] != 2) return(FALSE) - inso_symbols_cols = which(is_not_subset_of[[meta_idx]][meta_idx_target, ]) - symbols_twoend = colnames(is_not_subset_of[[meta_idx]])[inso_symbols_cols] - if (!is.null(symbol) && !symbol %in% symbols_twoend) return(FALSE) - for (symbol_inner_idx in 1:2) { - symbol_inner = symbols_twoend[[symbol_inner_idx]] # the intersection symbol - symbol_other = symbols_twoend[[3 - symbol_inner_idx]] - # symbol_other must be present in the target clause, otherwise we can skip. - if (!symbol_other %in% names(entries[[clause_idx_target]])) next - symbol_inner_clauses_meta = available_inverse[symbol_registry[[symbol_inner]]] - # 'oneends' may either have 1 or 2 non-subset symbols, with both symbols equal in the latter case. - # We do this in both inner loops, since we switch on which one of them is the target. - oneends = symbol_inner_clauses_meta[not_subset_count[symbol_inner_clauses_meta, meta_idx_target] <= 2L] - for (meta_idx_oneend in oneends[!is.na(oneends)]) { # oneends is NA for clauses that have not been processed yet - # check if the twoend-bit broke - if (not_subset_count[meta_idx, meta_idx_target] != 2 || !all(is_not_subset_of[[meta_idx]][meta_idx_target, inso_symbols_cols])) break - - # check if theoneend-bit broke - clause_idx_oneend = available[[meta_idx_oneend]] - if (eliminated[[clause_idx_oneend]] || is_unit[[clause_idx_oneend]]) next - # so the 'oneend' thing may also overlap with 'twoend' on the other symbol. - # The trouble is that we cannot rely on both symbols being in is_not_subset_of[[meta_idx_oneend]]. - # We therefore get the columns, with '0' if one of the symbols is not there, and then check whether the two columns are the only - # two that are TRUE (where the sum may be either 1 or 2). - symbols_twoend_idx = match(symbols_twoend, colnames(is_not_subset_of[[meta_idx_oneend]]), nomatch = 0L) - if (not_subset_count[meta_idx_oneend, meta_idx_target] != sum(is_not_subset_of[[meta_idx_oneend]][meta_idx_target, symbols_twoend_idx])) { - next - } - if (!symbol_other %in% names(entries[[clause_idx_target]])) next - ts2o = try_sse_2nd_order(meta_idx_oneend, meta_idx, meta_idx_target, symbol_inner, symbol_other) - if (identical(ts2o, TRUE)) return(TRUE) - if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) return(NULL) - if (is.null(ts2o)) return(FALSE) # target was eliminated - } - } - FALSE - } - - try_sse_2nd_order = function(meta_idx_oneend, meta_idx_twoends, meta_idx_target, symbol_intersect, symbol_target) { - ## assuming that symbol_target exists in meta_idx_target - ## assuming that meta_idx_oneend and meta_idx_twoends both have symbol_intersect, and that at least meta_idx_twoends has symbol_target - if (!all(is_not_subset_of[[meta_idx_target]][c(meta_idx_oneend, meta_idx_twoends), symbol_target])) return(FALSE) - idx_oneend = available[[meta_idx_oneend]] - idx_twoends = available[[meta_idx_twoends]] - idx_target = available[[meta_idx_target]] - # if (any(eliminated[c(idx_oneend, idx_twoends, idx_target)]) || any(is_unit[c(idx_oneend, idx_twoends, idx_target)])) return(FALSE) - clause_oneend = entries[[idx_oneend]] - clause_twoends = entries[[idx_twoends]] - - # only proceed if clause_oneend and clause_twoends are disjoint outside of clause_target, with respect to symbol_intersect - clause_oneend_symbol_intersect = clause_oneend[[symbol_intersect]] - if (any(clause_oneend_symbol_intersect %in% clause_twoends[[symbol_intersect]] & - !clause_oneend_symbol_intersect %in% entries[[idx_target]][[symbol_intersect]])) { - return(FALSE) - } - apply_domain_restriction(idx_target, symbol_target, char_union(clause_oneend[[symbol_target]], clause_twoends[[symbol_target]]), FALSE) - } - - # mark a clause as eliminated and update symbol registry - # This is relatively safe to call, since it does not modify any other clauses and does not create new units or subset relationships. - eliminate_clause_update_sr = function(clause_idx) { - if (is_unit[[clause_idx]]) stop("Bug in the code, this should never happen.") - eliminated[[clause_idx]] <<- TRUE - for (s in names(entries[[clause_idx]])) { - sr = symbol_registry[[s]] - symbol_registry[[s]] = sr[sr != clause_idx] - } - } - - # process units: - # - populate unit_domains - # - start populating symbol_registry; it gets finished later down with non-units - # - also reduce duplicate units and replace them with their intersection - unit_queue = which(is_unit) - for (unit_idx in unit_queue) { - if (register_unit(unit_idx)) return(return_entries(FALSE)) - } - - # if there were only units, we are done - if (length(unit_queue) == length(entries)) return(return_entries(entries[!eliminated])) - - # process non-units: - # - eliminate entries subsumed by units - # - populate symbol_registry - # we sorted clauses by length, so we can skip ahead by length(unit_queue) - # At this point, everything after the unit_queue is not (yet) a unit. - # The seq.int here is "dangerous" and only allowed because we checked for length(unit_queue) == length(entries) above. - for (clause_idx in seq.int(length(unit_queue) + 1L, length(entries))) { - - # intersect with units and eliminate subsumed clauses - clause_symbol_isct = char_intersect(names(entries[[clause_idx]]), names(unit_domains)) - # apply unit-propagation early, since we otherwise run the risk of adding the clause - # to lots of symbol registry entries, only to remove it again right away - for (symbol in clause_symbol_isct) { - adr = apply_domain_restriction(clause_idx, symbol, unit_domains[[symbol]], TRUE) - if (is.null(adr)) break - if (adr) return(return_entries(FALSE)) - } - - if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) next # could happen from unit propagation - - # do cache `clause = entries[[clause_idx]]` and refer to names(clause) here, - # since apply_domain_restriction might have removed symbols from the clause - for (symbol in names(entries[[clause_idx]])) { - sr_entry = symbol_registry[[symbol]] - if (is.null(sr_entry)) { - symbol_registry[[symbol]] = clause_idx - } else { - symbol_registry[[symbol]][[length(sr_entry) + 1L]] = clause_idx - } - } - } - - - # let's start with (self)-subsumption. - # this can also create new units etc. - - # we don't need to check for units, upon registration they are automatically removed, and they cannot help with self-subsumption or HLA - available = which(!(eliminated | is_unit)) - available_inverse = match(seq_along(entries), available) - - # record for each clause whether it is a subset of another clause. - # we record this for each symbol separately, so when a symbol gets self-subsumed, we can re-check others more quickly. - # Default is FALSE (not not a subset, i.e. it is a subset), this aligns with absent columns (which are subsets of everything) - # - # note that as soon as is_not_subset_of is non-null, some other functions assume that meta_idx_outer is also defined. - is_not_subset_of = vector("list", length(available)) - # not_subset_count[i, j]: how many symbols of clause i are not subset of clause j? - # if this is 1, we can do self-subsumption elimination and HLA. - # if this is 2, we can do self-subsumption with resolution. - # This is the same as sum(is_not_subset_of[[i]][j, ]) - not_subset_count = matrix(NA_integer_, nrow = length(available), ncol = length(available)) - - # whether second-order subsumption is enabled for the pair - # We only enable it after the initial first-order checks are done, to reduce 2nd order calls as much as possible. - second_order_enabled = FALSE - second_order_enabled_matrix = matrix(FALSE, nrow = length(available), ncol = length(available)) - - - for (meta_idx_outer in seq_along(available)) { - clause_idx = available[[meta_idx_outer]] - if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) next # may happen if we somehow turn something into a unit that eliminates a later clause - clause = entries[[clause_idx]] - - # is_not_subset_of[[i]][j, k] records whether for symbol k, clause i is not a subset of clause j - # If k is not in clause i, then var(i, k) is trivially a subset of var(j, k), so this is interpreted as FALSE. - # If k is not in clause j but is in clause i, then var(i, k) is not a subset of var(j, k), so this is interpreted as TRUE. - # We initialize with TRUE and then search for instances where a symbol k is in both clauses i and j, and where var(i, k) *is* a subset of var(j, k). - # In that case, we set the entry to FALSE. - is_not_subset_of[[meta_idx_outer]] = matrix( - TRUE, - nrow = length(available), # indexed by meta_idx! - ncol = length(clause), - dimnames = list(NULL, names(clause)) - ) - # we are not a subset of ourselves - # (this prevents us from checking this later in on_updated_subset_relations; if we do check it there, we would eliminate the clause from itself) - is_not_subset_of[[meta_idx_outer]][meta_idx_outer, ] = FALSE - - for (meta_idx_inner in seq_len(meta_idx_outer - 1L)) { - ## need to refresh clause here, since it might have been shortened by unit propagation in an earlier iteration - clause = entries[[clause_idx]] - clause_idx_inner = available[[meta_idx_inner]] - if (eliminated[[clause_idx_inner]] || is_unit[[clause_idx_inner]]) next - clause_inner = entries[[clause_idx_inner]] - # note that even though we sort entries at the beginning, we can *not* rely on clause_inner to have smaller or equal length than clause, - # since unit elimination can change the length of clauses - - sci = names(clause_inner) - sci_sc_map = match(sci, names(clause), nomatch = 0L) - sci_names_in_common = which(sci_sc_map != 0L) - - # symbols that are not in common trivially get the matrix entry TRUE - # (they are not subsets of their counterpart in the other clause, since the other ones are empty) - - for (symbol_idx_inner in sci_names_in_common) { - symbol_idx_outer = sci_sc_map[[symbol_idx_inner]] - symbol = sci[[symbol_idx_inner]] - - range_inner = clause_inner[[symbol_idx_inner]] - range_outer = clause[[symbol_idx_outer]] - - inner_subset_of_outer = all(range_inner %in% range_outer) - outer_subset_of_inner = (inner_subset_of_outer && length(range_outer) == length(range_inner)) || all(range_outer %in% range_inner) - if (inner_subset_of_outer) { - # Avoid assigning TRUE to matrix that is initialized with TRUE. - # We index by column name here, since it is possible that clauses were shortened by - # unit propagation or self subsumption elimination somewhere on the way here - is_not_subset_of[[meta_idx_inner]][meta_idx_outer, symbol] = FALSE - } - if (outer_subset_of_inner) { - is_not_subset_of[[meta_idx_outer]][meta_idx_inner, symbol] = FALSE - } - } - # prefer to eliminate the outer loopo clause first, since we have already - # done more work for the inner loop clause (which comes earlier in 'entries') - not_subset_count[meta_idx_outer, meta_idx_inner] = sum(is_not_subset_of[[meta_idx_outer]][meta_idx_inner, ]) - rowsum = sum(is_not_subset_of[[meta_idx_inner]][meta_idx_outer, ]) - not_subset_count[meta_idx_inner, meta_idx_outer] = rowsum - if (rowsum <= 1) { - ousr = on_updated_subset_relations(meta_idx_inner, meta_idx_outer, FALSE) - if (is.null(ousr)) break - if (ousr) return(return_entries(FALSE)) - if (eliminated[[clause_idx_inner]] || is_unit[[clause_idx_inner]]) next # yes this can happen. - } - # need to get rowsum back again, since the call above could have changed something! - rowsum = not_subset_count[meta_idx_outer, meta_idx_inner] - if (rowsum <= 1) { - ousr = on_updated_subset_relations(meta_idx_outer, meta_idx_inner, FALSE) - if (identical(ousr, TRUE)) return(return_entries(FALSE)) - if (eliminated[[clause_idx]] || is_unit[[clause_idx]]) break # probably this can happen if things cascade onwards when updating clause_inner - if (is.null(ousr)) next - } - } - } - - second_order_enabled = TRUE - second_order_enabled_matrix = not_subset_count != 2L # allow cascading of indirect SSE, except for the combinations where we trigger it manually (otherwise we'd be running them twice) - # We only trigger twoend-clauses, because every twoend clauses looks for all available oneend-clauses by itself. - # We can not do oneend-clauses-only, since twoend-clauses also look for other twoend-clauses that have common overlap. - # we need to make sure we don't trigger for eliminated / unit clauses, so we set them to TRUE here. - # This means all remaining entries of the second_order_enabled_matrix are exactly the ones for which we trigger on_updated_subset_relations() manually. - meta_disabled = eliminated[available] | is_unit[available] - second_order_enabled_matrix[meta_disabled, ] = TRUE - second_order_enabled_matrix[, meta_disabled] = TRUE - # alternatively, we could also enable none of the cascading in the beginning and have a nested loop in the following, where we 'repeat' until there are no more rowsum <= 2L - # That would probably give uns less cascading, but we'd have to run 'which()' on a N^2 matrix potentially many times. - - sse_to_trigger = which(!second_order_enabled_matrix, arr.ind = TRUE) - for (sse_idx in seq_len(nrow(sse_to_trigger))) { - meta_idx = sse_to_trigger[sse_idx, 1L] - meta_idx_other = sse_to_trigger[sse_idx, 2L] - if (eliminated[[available[[meta_idx]]]] || is_unit[[available[[meta_idx]]]] || eliminated[[available[[meta_idx_other]]]] || is_unit[[available[[meta_idx_other]]]]) next - second_order_enabled_matrix[meta_idx, meta_idx_other] = TRUE - if (identical(on_updated_subset_relations(meta_idx, meta_idx_other, TRUE), TRUE)) return(return_entries(FALSE)) - } - - - # Now for the big one: Asymmetric Hidden Literal Addition (Marijn et al.) - - # First, we do non-units, then we do units separately. - # We go big to small, since eliminating one clause could prevent us from eliminating other clauses, and all things being equal, we prefer eliminating long ones. - - # We only loop over the entries that have not been eliminated yet. - # We update `remaining_nonunit_entries` inside the loop whenever a clause is eliminated. - remaining_entries = which(!eliminated)[order(lengths(entries[!eliminated]), decreasing = TRUE)] - remaining_nonunit_entries = remaining_entries[seq_len(length(remaining_entries) - length(unit_domains))] - remaining_unit_entries = if (length(unit_domains)) remaining_entries[seq.int(length(remaining_entries) - length(unit_domains) + 1L, length(remaining_entries))] - - # iterating from large to small entries - for (clause_idx in remaining_nonunit_entries) { - clause = entries[[clause_idx]] - - # index inside `is_not_subset_of` - meta_idx = available_inverse[[clause_idx]] - remaining_other_entries = remaining_nonunit_entries[remaining_nonunit_entries != clause_idx] - - # we keep track of which clauses were used for HLA, since every other clause can only do that once. - was_used = logical(length(remaining_other_entries)) - - # for each of the other clauses, how many of their symbols are not a subset of the current clause? - not_subset_count_current = not_subset_count[available_inverse[remaining_other_entries], meta_idx] - # for (roe_idx in seq_along(remaining_other_entries)) { - # # if we had set up is_not_subset_of as a 3-dim array, then the following could just have been a colSums over is_not_subset_of[, meta_idx, ] - # # However, that array would take a lot of memory: N_clauses^2 x N_all_symbols; The current setup has N_clauses^2 x max(N_symbols_per_clause) - # other_clause_idx = remaining_other_entries[[roe_idx]] - # meta_idx_other = available_inverse[[other_clause_idx]] - # not_subset_count[[roe_idx]] = sum(is_not_subset_of[[meta_idx_other]][meta_idx, ]) - # } - repeat { - # we do HLA by looking for a clause that is a subset of the current clause w/r/t all except one symbol. - # We also only consider every clause at most once, since it won't have anything else to add a second time. - # No need to check for == 0 here: if it was the case before, then we eliminated the clause already. If it becomes the case during the loop, we check - # for it further down. - hla_clause_idx = match(TRUE, not_subset_count_current == 1L & !was_used) - if (is.na(hla_clause_idx)) break # no more clauses to consider: all are either used or have no_subset_count > 1 - clause_idx_other = remaining_other_entries[[hla_clause_idx]] - meta_idx_other = available_inverse[[clause_idx_other]] - symbol = colnames(is_not_subset_of[[meta_idx_other]])[is_not_subset_of[[meta_idx_other]][meta_idx, ]] - range_old = clause[[symbol]] - # new range of the symbol inside the clause: Union of old range and complement of that symbol's range in the other clause. - range_new = c(range_old, char_setdiff(universe[[symbol]], c(range_old, entries[[clause_idx_other]][[symbol]]))) - if (length(range_new) == length(universe[[symbol]])) { - # hidden tautology elimination - - # We still need the symbol registry (see below), so this can not be replaced by just `eliminated[[clause_idx]] = TRUE` - eliminate_clause_update_sr(clause_idx) - remaining_nonunit_entries = remaining_other_entries - break - } - # Now loop over clauses that also use the symbol, checking if they have one less `not_subset_count_current` because of that - # Note we do not need to check subsumption w/r/t units any more: All symbols are proper subsets w/r/t units at this point, - # so if adding the complement of one symbol to another made it a superset of a unit, the result was a tautology already. - for (updating_clause_meta_idx in available_inverse[symbol_registry[[symbol]]]) { - # we don't want to skip 'was_used' here, since we might still do hidden subsumption elimination with them. - if (is_not_subset_of[[updating_clause_meta_idx]][meta_idx, symbol] && - all(entries[[available[[updating_clause_meta_idx]]]][[symbol]] %in% range_new)) { - is_not_subset_of[[updating_clause_meta_idx]][meta_idx, symbol] = FALSE - roe_idx = match(available[[updating_clause_meta_idx]], remaining_other_entries) # I wished I didn't have to do this - not_subset_count_current[[roe_idx]] = not_subset_count_current[[roe_idx]] - 1L - if (not_subset_count_current[[roe_idx]] == 0L) { - # hidden subsumption elimination - eliminate_clause_update_sr(clause_idx) - remaining_nonunit_entries = remaining_other_entries - break - } - } - } - if (eliminated[[clause_idx]]) break # the break inside the for-loop above will not break the repeat loop - was_used[[hla_clause_idx]] = TRUE - clause[[symbol]] = range_new - } - } - - # We now do the same thing as above, only for units. - # Units are different, because they don't have the `is_not_subset_of` matrices. These are trivially constructed from - # The symbol registry: "is_not_subset_of" for unit relating to symbol `s` is TRUE for all symbols in a clause that are not `s`. - # We deliberately make use of `remaining_nonunit_entries` here, which has been updated in the loop above as nonunit-clauses were eliminated - delayedAssign("roe_inverse", match(seq_along(entries), remaining_nonunit_entries)) # only do this match()-call if it is actually needed - for (clause_idx in remaining_unit_entries) { - clause = entries[[clause_idx]] - unitsymbol = names(clause) - was_used = logical(length(remaining_nonunit_entries)) - # every clause that is not yet eliminated is a proper subset of the current unit. - # If it is length N and contains the unit symbol, then N - 1 of its symbols are not subsets; - # otherwise (if it does not contain the unit symbol), all N symbols are not subsets. - not_subset_count = lengths(entries[remaining_nonunit_entries]) - (remaining_nonunit_entries %in% symbol_registry[[unitsymbol]]) - - # corresponding to `is_not_subset_of` matrix; only construct this for entries where it is needed. - is_not_subset_of_unit = vector("list", length(remaining_nonunit_entries)) - - # The following loop is mostly identical to the loop above, only for units. - repeat { - hla_clause_idx = match(TRUE, not_subset_count == 1L & !was_used) - if (is.na(hla_clause_idx)) break # no more clauses to consider: all are either used or have no_subset_count > 1 - clause_idx_other = remaining_nonunit_entries[[hla_clause_idx]] - clause_other = entries[[clause_idx_other]] - if (is.null(is_not_subset_of_unit[[hla_clause_idx]])) { - is_not_subset_of_unit[[hla_clause_idx]] = structure(names(clause_other) != unitsymbol, names = names(clause_other)) - } - is_not_subset_entry = is_not_subset_of_unit[[hla_clause_idx]] - symbol = names(is_not_subset_entry)[is_not_subset_entry] - range_old = clause[[symbol]] - range_new = c(range_old, char_setdiff(universe[[symbol]], c(range_old, clause_other[[symbol]]))) - if (length(range_new) == length(universe[[symbol]])) { - # hidden tautology elimination - # no more need to update the unit registry - eliminated[[clause_idx]] = TRUE - break - } - # Now loop over clauses that also use the symbol, checking if they have one less `not_subset_count` because of that - for (updating_clause_idx in symbol_registry[[symbol]]) { - updating_hla_clause_idx = roe_inverse[[updating_clause_idx]] - if (is.null(is_not_subset_of_unit[[updating_hla_clause_idx]])) { - # Dynamically construct this entry if it is not set yet. - # We could delay this further, but that would make things even more complicated - updating_clause = entries[[updating_clause_idx]] - is_not_subset_of_unit[[updating_hla_clause_idx]] = structure(names(updating_clause) != unitsymbol, names = names(updating_clause)) - } - if (is_not_subset_of_unit[[updating_hla_clause_idx]][[symbol]] && - all(entries[[updating_clause_idx]][[symbol]] %in% range_new)) { - is_not_subset_of_unit[[updating_hla_clause_idx]][[symbol]] = FALSE - not_subset_count[[updating_hla_clause_idx]] = not_subset_count[[updating_hla_clause_idx]] - 1L - if (not_subset_count[[updating_hla_clause_idx]] == 0) { - # hidden subsumption elimination - eliminated[[clause_idx]] = TRUE - break - } - } - } - if (eliminated[[clause_idx]]) break # the break inside the for-loop above will not break the repeat loop - was_used[[hla_clause_idx]] = TRUE - clause[[symbol]] = range_new - } - } - - return_entries(entries[!eliminated]) -} diff --git a/attic/CnfFormula_simplify.R b/attic/CnfFormula_simplify.R new file mode 100644 index 000000000..f3661001d --- /dev/null +++ b/attic/CnfFormula_simplify.R @@ -0,0 +1,201 @@ + + + + + +simplify_cnf_1 = function(entries, universe) { + return_false = structure( + FALSE, + universe = universe, + class = "CnfFormula" + ) + + # can we do unit elimination? + # if we are already TRUE or FALSE no simplification is necessary + # this only works if there actually are units. + can_simplify = !is.logical(entries) + # likewise, if there is only one clause left, no simplification is necessary. + + units = list() + + while (can_simplify && length(entries) > 1) { + # we do the following until we are sure there are no more simplifications to be made. + # this is the case if we have not meaningfully simplified anything in the last iteration. + can_simplify = FALSE + # sort clauses by length, since (1) length-1-clauses are special, and (2) short clauses can only ever subsume longer ones + entries = entries[order(lengths(entries))] + # Let sum(A) be the symbols in clause A, and val(A, s) be the values of symbol s admitted in clause A. + if (any(lengths(entries) == 1)) { + for (i in seq_along(entries)) { + ei = entries[[i]] + # If |sym(A)| == 1, sym(A) == {s} and s is in sym(B), then val(B, s) <- intersect(val(A, s), val(B, s)) ("unit propagation") + # units is a named list of symbols in size-one-clauses, together with their values. + # We iterate over all symbols in ei that are also in units, and intersect their values. + for (unit_symbol in intersect(names(ei), names(units))) { + length_before_ei = length(ei[[unit_symbol]]) + length_before_unit = length(units[[unit_symbol]]) + intersection = intersect(units[[unit_symbol]], ei[[unit_symbol]]) + ei[[unit_symbol]] = intersection + if (length(ei) == 1 && length(intersection) != length_before_unit) { + # we made a unit shorter, this means we need to simplify the entry from which units[[unit_symbol]] came + can_simplify = TRUE + } + if (!length(ei[[unit_symbol]])) { + ei[[unit_symbol]] = NULL + } + if (!length(ei)) { + return(return_false) + } + if (length(intersection) != length_before_ei) { + # need to store changed ei entry only if its length changed; otherwise we know the intersection did not do anything. + entries[[i]] = ei + } + } + if (length(ei) == 1) { + # even if names(ei) is already in units, at this point ei[[1]] is the intersection of the values + units[[names(ei)]] = ei[[1]] + } + } + if (can_simplify) next + } + + entries = entries[order(lengths(entries))] # removing units may have changed the order + eliminated = logical(length(entries)) + for (i in seq_along(entries)) { + if (eliminated[[i]]) next # can only happen if we do the hidden subsumption elimination, which searches forward + ei = entries[[i]] + # If sym(A) is a subset of sym(B) and for each s in sym(A), val(A, s) is a subset of val(B, s), then A implies B, so B can be removed ("subsumption elimination"). + for (j in seq_along(entries)) { + if (j == i) next + if (eliminated[[j]]) next + ej = entries[[j]] + if (length(ej) > length(ei)) break # we can't just do j in 1:(i-1), since some clauses have the same length, in which case we need to check subsumption. + name_overlap = names(ej) %in% names(ei) + if (all(name_overlap) && all(sapply(names(ej), function(s) all(ej[[s]] %in% ei[[s]])))) { + # can't do entries[[i]] = NULL, since we are iterating over entries; the entries[[i]] would break. + eliminated[[i]] = TRUE + break + } + if (j >= i) next # everything that follows already checks in both directions in case of equal lengths. + # simple self subsumption and hidden subsumption elimination + # HSE: + # if s is in sym(A) and sym(B), and val(A, s) and val(B, s) are disjoint, then (A - s | B - s) is implied, + # and all superset clauses of (A - s | B - s) can be removed. + # we could also do this for higher order terms, intersection over X of val(X, s) == 0 etc., but this gets more complex. + # tbh, I am not sure if this is actually worth it + # SSE: If val(A, s) and val(B, s) are disjoint, and A - s is a subset of B - s, then A & B <=> A & (B - s) + + which_name_overlap = which(name_overlap) + # - build the union of values of overlapping symbols + # - in the innerloop we will check that most of this is a subset of any other clause + # - "most of" here means: all but the one symbol s where the values are disjoint + # - use delayedAssign to avoid computation if there is no overlap with empty intersect + delayedAssign("cnames", union(names(ei), names(ej))) + + # Putting ei[[s2]] first on purpose, since union() preserves the order of the first argument. + # If and only if ej[-s] is a subset of ei[-s], then cunion[-s] will be the same as ei[-s]. + delayedAssign("cunion", sapply(cnames, function(s2) union(ei[[s2]], ej[[s2]]), simplify = FALSE)) + + nameshift = 0 # in case we eliminate names from ej, we need to shift the indices for later loops iterations + for (no in which_name_overlap) { + s = names(ej)[[no - nameshift]] + # intersection is not 0 --> try next one + if (length(intersect(ej[[s]], ei[[s]]))) next + cnames_s = setdiff(cnames, s) + + # Let's try self subsumption elimination first + if (length(cnames) == length(ei)) { + # cnames is the union of symbols in ei and ej. + # If length(cnames) is different from max(length(ei), length(ej)), then ei and ej can not be subsets of one another. + # Since j < i, length(ej) <= length(ei). + + # ej is usually smaller than ei, so often only ej can be a subset of ei. + # They may, however, have the same number of terms, in which case the reverse is also possible. + # Use 'c()' to drop attributes from ei here. + ei_without_s = ei[cnames_s] + do_sse = identical(cunion[cnames_s], c(ei_without_s)) + # if they have the same number of terms, ei could be a subset of ej. + # However, then we can not rely on the order of values in the union being correct. + do_sse_reverse = (!do_sse && (length(ei) == length(ej)) && + all(sapply(cnames_s, function(s2) all(ei[[s2]] %in% ej[[s2]])))) + if (do_sse_reverse) { + # ei is a subset of ej + # --> eliminate s from ej + ej[[s]] = NULL + new_entry = entries[[j]] = ej + dont_eliminate = j + nameshift = nameshift + 1 + } else if (do_sse) { + # ej is a subset of ei + # --> eliminate s from ei + new_entry = entries[[i]] = ei = ei_without_s + dont_eliminate = i + } + + if (do_sse || do_sse_reverse) { + + if (length(new_entry) == 1) { + # we have a unit clause now + + # It could happen that we eliminate the entry further, in which + # case units[[]] would get stale, but then we return_false anyway. + units[[names(new_entry)]] = new_entry[[1]] + can_simplify = TRUE # do unit elimination all over again + ## TODO: we could probably make this more efficient by only unit-eliminating the terms that are new + } + + if (!length(new_entry)) { + # we have a contradiction now + # Maybe this could happen if we SS-Eliminate multiple symbols from a clause in a row. + return(return_false) + } + + # What can have happened now is that the newly created element can eliminate other elements. + # If it can eliminate the current element i, that means it is a subset of ei, which only happens if ej\s is a subset of ei\s. However, in that case, we always want to keep element i. + # We therefore only need to loop up to i - 1. + # The loop is similar to the subsumption elimination loop; only in this case, we check if we can eliminate the elements that come before i, not like above where we check if we can eliminate i. + + # loop down from large to small, since then we can break once we find a clause with insufficient entries + for (k in rev(seq_len(i - 1))) { + if (k == dont_eliminate || eliminated[[k]]) next + ek = entries[[k]] + if (length(ek) < length(new_entry)) break # once we reached entries that are shorter than the new_entry, we won't find anything longer any more and we can break + if (all(cnames_s %in% names(ek)) && all(sapply(cnames_s, function(s2) all(new_entry[[s2]] %in% ek[[s2]])))) { + eliminated[[k]] = TRUE + } + } + if (eliminated[[j]]) break # we eliminated one of the entries we are currently looking at, no more need to look at other symbols + next + } + } + # Hidden Subsumption Elimination + # + # We only do this if self subsumption elimination did not occur. + # + # We eliminate based on an implied clause (A - s | B - s) + # Since we will forget about this clause after this iteration, we have to eliminate all clauses with size larger or equal to ||A | B|| - 1 + # loop down from large to small, since then we can break once we find a clause with insufficient entries + for (k in rev(seq_along(entries))) { + if (k == i || k == j || eliminated[[k]]) next + ek = entries[[k]] + # all of cnames_s must be in ek, otherwise we can't eliminate + # since we are looping down from large to small ek, we can break once this is not the case + if (length(ek) < length(cnames) - 1) break + if (all(cnames_s %in% names(ek)) && all(sapply(cnames_s, function(s2) all(cunion[[s2]] %in% ek[[s2]])))) { + eliminated[[k]] = TRUE + } + } + } + + } + + } + entries = entries[!eliminated] + } + structure( + if (!length(entries)) TRUE else entries, + universe = universe, + class = "CnfFormula" + ) +} + diff --git a/R/CnfFormula_simplify2.R b/attic/CnfFormula_simplify2.R similarity index 100% rename from R/CnfFormula_simplify2.R rename to attic/CnfFormula_simplify2.R From 8bca904272e5f87eace14876b9810eee88ad61c9 Mon Sep 17 00:00:00 2001 From: mb706 Date: Tue, 24 Sep 2024 14:24:13 +0200 Subject: [PATCH 85/87] not going to finish this... --- R/GraphLearner.R | 18 +++++++----------- 1 file changed, 7 insertions(+), 11 deletions(-) diff --git a/R/GraphLearner.R b/R/GraphLearner.R index d3294defb..e9c05f59e 100644 --- a/R/GraphLearner.R +++ b/R/GraphLearner.R @@ -627,13 +627,13 @@ get_po_unbranch_active_input = function(graph) { # is not given or a TuneToken or something like that. if (pob_ps$class[["selection"]] == "ParamInt") { if (!test_int(selection)) { - # stopf("Cannot infer active output of PipeOpBranch %s with non-numeric 'selection'.", pipeop$id) + stopf("Cannot infer active output of PipeOpBranch %s with non-numeric 'selection'.", pipeop$id) return(pipeop$output$name) } return(pipeop$output$name[[pob_ps$values$selection]]) } else { if (!test_string(selection)) { - # stopf("Cannot infer active output of PipeOpBranch %s with non-string 'selection'.", pipeop$id) + stopf("Cannot infer active output of PipeOpBranch %s with non-string 'selection'.", pipeop$id) return(pipeop$output$name) } return(pob_ps$values$selection) @@ -697,15 +697,11 @@ get_po_unbranch_active_input = function(graph) { if (state_current && inherits(pipeop, "PipeOpBranch")) { # PipeOpBranch is only special when it is actually active active_output = get_po_branch_active_output(pipeop) - if (length(active_output) == 1) { - branch_state_info[src_id == pipeop_id, `:=`(state = src_channel == active_output, - reason = as.list(sprintf("PipeOpBranch '%s' %s output '%s'", - pipeop_id, ifelse(src_channel == active_output, "active", "inactive"), - src_channel)) - )] - } else { - - } + branch_state_info[src_id == pipeop_id, `:=`(state = src_channel == active_output, + reason = as.list(sprintf("PipeOpBranch '%s' %s output '%s'", + pipeop_id, ifelse(src_channel == active_output, "active", "inactive"), + src_channel)) + )] } else { branch_state_info[src_id == pipeop_id, `:=`(state = state_current, reason = list(reason_current))] } From 4d5695fa18a20b5c2876fc0815df6ab8a7a77108 Mon Sep 17 00:00:00 2001 From: mb706 Date: Tue, 24 Sep 2024 14:47:37 +0200 Subject: [PATCH 86/87] fix tests --- R/GraphLearner.R | 17 ++++++++++++++--- tests/testthat/test_GraphLearner.R | 6 ++++-- 2 files changed, 18 insertions(+), 5 deletions(-) diff --git a/R/GraphLearner.R b/R/GraphLearner.R index e9c05f59e..d768c7302 100644 --- a/R/GraphLearner.R +++ b/R/GraphLearner.R @@ -628,13 +628,13 @@ get_po_unbranch_active_input = function(graph) { if (pob_ps$class[["selection"]] == "ParamInt") { if (!test_int(selection)) { stopf("Cannot infer active output of PipeOpBranch %s with non-numeric 'selection'.", pipeop$id) - return(pipeop$output$name) + # return(pipeop$output$name) } return(pipeop$output$name[[pob_ps$values$selection]]) } else { if (!test_string(selection)) { stopf("Cannot infer active output of PipeOpBranch %s with non-string 'selection'.", pipeop$id) - return(pipeop$output$name) + # return(pipeop$output$name) } return(pob_ps$values$selection) } @@ -744,10 +744,21 @@ graph_base_learner = function(graph, resolve_branching = TRUE, lookup_field = "l next_pipeop = graph$edges[dst_id == current_pipeop, src_id] if (length(next_pipeop) > 1) { # more than one predecessor + if (inherits(last_pipeop, "PipeOpUnbranch") && resolve_branching) { + tryCatch({ + next_pipeop = po_unbranch_active_input[[current_pipeop]] + }, error = function(e) { + if (e$message %like% "Cannot infer active output of PipeOpBranch") { + resolve_branching <<- FALSE # give up; this happens when tuning. + } else { + stop(e) + } + }) + } if (!inherits(last_pipeop, "PipeOpUnbranch") || !resolve_branching) { return(unique(unlist(lapply(next_pipeop, search_base_learner_pipeops), recursive = FALSE, use.names = FALSE))) } - next_pipeop = po_unbranch_active_input[[current_pipeop]] + # PipeOpUnbranch inference succeeded; continue with selected branch. if (next_pipeop == "") next_pipeop = character(0) } if (length(next_pipeop) == 0) return(list()) diff --git a/tests/testthat/test_GraphLearner.R b/tests/testthat/test_GraphLearner.R index 4cc69bb44..e3fd77824 100644 --- a/tests/testthat/test_GraphLearner.R +++ b/tests/testthat/test_GraphLearner.R @@ -613,7 +613,9 @@ test_that("base_learner() works", { expect_identical(x$base_learner(), x$graph_model$pipeops$classif.debug$learner_model) x$param_set$values$branch.selection = to_tune() - expect_error(x$base_learner(), "Cannot infer active output.* PipeOpBranch branch.*non-numeric 'selection'") + # TODO: update this once something smarter happens here + # expect_error(x$base_learner(), "Cannot infer active output.* PipeOpBranch branch.*non-numeric 'selection'") + x = as_learner(ppl("branch", list(classif.rpart = lrn("classif.rpart") %>>% po("unbranch", 1, id = "poub1"), classif.debug = lrn("classif.debug") %>>% po("unbranch", 1, id = "poub2")))) expect_identical(x$base_learner(), x$graph_model$pipeops$classif.rpart$learner_model) @@ -878,7 +880,7 @@ test_that("GraphLearner hashes", { lr1 <- lrn("classif.rpart") - lr2 <- lrn("classif.rpart", fallback = lrn("classif.rpart")) + lr2 <- lrn("classif.rpart")$encapsulate("try", fallback = lrn("classif.rpart")) expect_string(all.equal(lr1$hash, lr2$hash), "mismatch") expect_string(all.equal(lr1$phash, lr2$phash), "mismatch") From bd94245e2188b7ad3e406e75804909e493671b36 Mon Sep 17 00:00:00 2001 From: mb706 Date: Tue, 24 Sep 2024 15:10:21 +0200 Subject: [PATCH 87/87] react to another renamecol problem --- tests/testthat/test_pipeop_renamecolumns.R | 1 + 1 file changed, 1 insertion(+) diff --git a/tests/testthat/test_pipeop_renamecolumns.R b/tests/testthat/test_pipeop_renamecolumns.R index 8929922e7..981507787 100644 --- a/tests/testthat/test_pipeop_renamecolumns.R +++ b/tests/testthat/test_pipeop_renamecolumns.R @@ -13,6 +13,7 @@ test_that("basic properties", { test_that("renaming works", { task = mlr_tasks$get("iris") + task$cbind(data.table(Petal.Width = as.character(1:150))) # need a char column that we can turn into the 'name'-col op = PipeOpRenameColumns$new(param_vals = list(renaming = c("Petal.Length" = "PL"))) train_out1 = op$train(list(task))[[1L]] predict_out1 = op$predict(list(task))[[1L]]