ó ¡¼™\c@ sÏdZddlmZmZddlmZddlmZmZddl m Z ddl m Z m Z ddlmZmZmZmZed„Zd „Zd efd „ƒYZd efd „ƒYZdS(s«Implementation of DPLL algorithm Features: - Clause learning - Watch literal scheme - VSIDS heuristic References: - https://en.wikipedia.org/wiki/DPLL_algorithm iÿÿÿÿ(tprint_functiontdivision(t defaultdict(theappushtheappop(trange(tdefault_sort_keytordered(t conjunctstto_cnft to_int_reprt_find_predicatescC sÔtt|ƒƒ}t|kr9|r5d„tgDƒStStt|ƒdtƒ}tdt|ƒdƒ}t||ƒ}t ||t ƒ|ƒ}|j ƒ}|r­t |ƒSyt |ƒSWntk rÏtSXdS(s˜ Check satisfiability of a propositional sentence. It returns a model rather than True when it succeeds. Returns a generator of all models if all_models is True. Examples ======== >>> from sympy.abc import A, B >>> from sympy.logic.algorithms.dpll2 import dpll_satisfiable >>> dpll_satisfiable(A & ~B) {A: True, B: False} >>> dpll_satisfiable(A & ~A) False cs s|] }|VqdS(N((t.0tf((s;lib/python2.7/site-packages/sympy/logic/algorithms/dpll2.pys )stkeyiN(RR tFalsetsortedR RRtlenR t SATSolvertsett _find_modelt _all_modelstnextt StopIteration(texprt all_modelstclausestsymbolstsymbols_int_reprtclauses_int_reprtsolvertmodels((s;lib/python2.7/site-packages/sympy/logic/algorithms/dpll2.pytdpll_satisfiables     cc sNt}y"xtr&t|ƒVt}q WWntk rI|sJtVqJnXdS(N(RtTrueRR(Rt satisfiable((s;lib/python2.7/site-packages/sympy/logic/algorithms/dpll2.pyR@s   RcB sÝeZdZddddd„Zd„Zd„Zd„Zed„ƒZ d „Z d „Z d „Z d „Z d „Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„ZRS(s‚ Class for representing a SAT solver capable of finding a model to a boolean theory in conjunctive normal form. tvsidstnoneiôcC sy||_||_t|_g|_g|_||_|dkrZtt |ƒƒ|_ n ||_ |j |ƒ|j |ƒd|krÆ|j ƒ|j|_|j|_|j|_|j|_nt‚d|kr|j|_|j|_|jj|jƒn-d|kr-d„|_d„|_nt‚tdƒg|_||j_ d|_!d|_"t#|j$ƒ|_%dS(NR#tsimpleR$cS sdS(N(tNone(tx((s;lib/python2.7/site-packages/sympy/logic/algorithms/dpll2.pytvtcS sdS(N(R&(((s;lib/python2.7/site-packages/sympy/logic/algorithms/dpll2.pyR(wR)i(&t var_settingst heuristicRtis_unsatisfiedt_unit_prop_queuetupdate_functionstINTERVALR&tlistRRt_initialize_variablest_initialize_clausest _vsids_initt_vsids_calculatetheur_calculatet_vsids_lit_assignedtheur_lit_assignedt_vsids_lit_unsettheur_lit_unsett_vsids_clause_addedtheur_clause_addedtNotImplementedErrort_simple_add_learned_clausetadd_learned_clausetsimple_compute_conflicttcompute_conflicttappendtsimple_clean_clausestLeveltlevelst_current_levelt varsettingst num_decisionstnum_learned_clausesRRtoriginal_num_clauses(tselfRt variablesR*RR+tclause_learningR/((s;lib/python2.7/site-packages/sympy/logic/algorithms/dpll2.pyt__init__Rs>                       cC s<ttƒ|_ttƒ|_tgt|ƒd|_dS(s+Set up the variable data structures needed.iN(RRt sentinelstinttoccurrence_countRRt variable_set(RJRK((s;lib/python2.7/site-packages/sympy/logic/algorithms/dpll2.pyR1„scC s÷g|_x$|D]}|jjt|ƒƒqWxÀtt|jƒƒD]©}dt|j|ƒkr†|jj|j|dƒqFn|j|j|dj|ƒ|j|j|dj|ƒx(|j|D]}|j|cd7>> from sympy.logic.algorithms.dpll2 import SATSolver >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2}, ... {3, -2}], {1, 2, 3}, set()) >>> list(l._find_model()) [{1: True, 2: False, 3: False}, {1: True, 2: True, 3: True}] >>> from sympy.abc import A, B, C >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2}, ... {3, -2}], {1, 2, 3}, set(), [A, B, C]) >>> list(l._find_model()) [{A: True, B: False, C: False}, {A: True, B: True, C: True}] Niic3 s2|](}ˆjt|ƒd|dkfVqdS(iiN(Rtabs(R RU(RJ(s;lib/python2.7/site-packages/sympy/logic/algorithms/dpll2.pys Østflipped(Rt _simplifyR,R!RGR/R.REtdecisionR5tdictR*RWt_undoRRDRARCt_assign_literalR>R@(RJtflip_vartfuncRUtflip_lit((RJs;lib/python2.7/site-packages/sympy/logic/algorithms/dpll2.pyR£sN              cC s |jdS(s£The current decision level data structure Examples ======== >>> from sympy.logic.algorithms.dpll2 import SATSolver >>> l = SATSolver([{1}, {2}], {1, 2}, set()) >>> next(l._find_model()) {1: True, 2: True} >>> l._current_level.decision 0 >>> l._current_level.flipped False >>> l._current_level.var_settings {1, 2} iÿÿÿÿ(RD(RJ((s;lib/python2.7/site-packages/sympy/logic/algorithms/dpll2.pyREscC s/x(|j|D]}||jkrtSqWtS(s¡Check if a clause is satisfied by the current variable setting. Examples ======== >>> from sympy.logic.algorithms.dpll2 import SATSolver >>> l = SATSolver([{1}, {-1}], {1}, set()) >>> try: ... next(l._find_model()) ... except StopIteration: ... pass >>> l._clause_sat(0) False >>> l._clause_sat(1) True (RR*R!R(RJRSRU((s;lib/python2.7/site-packages/sympy/logic/algorithms/dpll2.pyt _clause_satscC s||j|kS(s¨Check if a literal is a sentinel of a given clause. Examples ======== >>> from sympy.logic.algorithms.dpll2 import SATSolver >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2}, ... {3, -2}], {1, 2, 3}, set()) >>> next(l._find_model()) {1: True, 2: False, 3: False} >>> l._is_sentinel(2, 3) True >>> l._is_sentinel(-3, 1) False (RN(RJRURS((s;lib/python2.7/site-packages/sympy/logic/algorithms/dpll2.pyt _is_sentinel0scC s&|jj|ƒ|jjj|ƒt|jt|ƒ<|j|ƒt|j| ƒ}xÈ|D]À}|j |ƒs^d}x†|j |D]w}|| kr‡|j ||ƒrµ|}qþ|jt|ƒsþ|j| j |ƒ|j|j|ƒd}Pqþq‡q‡W|r|jj|ƒqq^q^WdS(sÛMake a literal assignment. The literal assignment must be recorded as part of the current decision level. Additionally, if the literal is marked as a sentinel of any clause, then a new sentinel must be chosen. If this is not possible, then unit propagation is triggered and another literal is added to the queue to be set in the future. Examples ======== >>> from sympy.logic.algorithms.dpll2 import SATSolver >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2}, ... {3, -2}], {1, 2, 3}, set()) >>> next(l._find_model()) {1: True, 2: False, 3: False} >>> l.var_settings {-3, -2, 1} >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2}, ... {3, -2}], {1, 2, 3}, set()) >>> l._assign_literal(-1) >>> try: ... next(l._find_model()) ... except StopIteration: ... pass >>> l.var_settings {-1} N(R*RRRER!RQRVR7R0RNR`R&RRatremoveR-RA(RJRUt sentinel_listRStother_sentineltnewlit((s;lib/python2.7/site-packages/sympy/logic/algorithms/dpll2.pyR\Bs&     cC sXxD|jjD]6}|jj|ƒ|j|ƒt|jt|ƒ>> from sympy.logic.algorithms.dpll2 import SATSolver >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2}, ... {3, -2}], {1, 2, 3}, set()) >>> next(l._find_model()) {1: True, 2: False, 3: False} >>> level = l._current_level >>> level.decision, level.var_settings, level.flipped (-3, {-3, -2}, False) >>> l._undo() >>> level = l._current_level >>> level.decision, level.var_settings, level.flipped (0, {1}, False) N( RER*RbR9RRQRVRDtpop(RJRU((s;lib/python2.7/site-packages/sympy/logic/algorithms/dpll2.pyR[xs  cC s=t}x0|r8t}||jƒO}||jƒO}q WdS(scIterate over the various forms of propagation to simplify the theory. Examples ======== >>> from sympy.logic.algorithms.dpll2 import SATSolver >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2}, ... {3, -2}], {1, 2, 3}, set()) >>> l.variable_set [False, False, False, False] >>> l.sentinels {-3: {0, 2}, -2: {3, 4}, 2: {0, 3}, 3: {2, 4}} >>> l._simplify() >>> l.variable_set [False, True, False, False] >>> l.sentinels {-3: {0, 2}, -2: {3, 4}, -1: set(), 2: {0, 3}, ...3: {2, 4}} N(R!Rt _unit_propt _pure_literal(RJtchanged((s;lib/python2.7/site-packages/sympy/logic/algorithms/dpll2.pyRXs  cC skt|jƒdk}xO|jrf|jjƒ}| |jkrVt|_g|_tS|j|ƒqW|S(s/Perform unit propagation on the current theory.i(RR-RfR*R!R,RR\(RJtresulttnext_lit((s;lib/python2.7/site-packages/sympy/logic/algorithms/dpll2.pyRg¹s   cC stS(s2Look for pure literals and assign them when found.(R(RJ((s;lib/python2.7/site-packages/sympy/logic/algorithms/dpll2.pyRhÇscC s­g|_i|_x”tdt|jƒƒD]z}t|j| ƒ|j|Initialize the data structures needed for the VSIDS heuristic.iN(tlit_heapt lit_scoresRRRQtfloatRPR(RJtvar((s;lib/python2.7/site-packages/sympy/logic/algorithms/dpll2.pyR3Îs  cC s1x*|jjƒD]}|j|cd>> from sympy.logic.algorithms.dpll2 import SATSolver >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2}, ... {3, -2}], {1, 2, 3}, set()) >>> l.lit_scores {-3: -2.0, -2: -2.0, -1: 0.0, 1: 0.0, 2: -2.0, 3: -2.0} >>> l._vsids_decay() >>> l.lit_scores {-3: -1.0, -2: -1.0, -1: 0.0, 1: 0.0, 2: -1.0, 3: -1.0} g@N(Rmtkeys(RJRU((s;lib/python2.7/site-packages/sympy/logic/algorithms/dpll2.pyt _vsids_decayÙscC sut|jƒdkrdSxH|jt|jddƒrct|jƒt|jƒdkrdSqWt|jƒdS(sà VSIDS Heuristic Calculation Examples ======== >>> from sympy.logic.algorithms.dpll2 import SATSolver >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2}, ... {3, -2}], {1, 2, 3}, set()) >>> l.lit_heap [(-2.0, -3), (-2.0, 2), (-2.0, -2), (0.0, 1), (-2.0, 3), (0.0, -1)] >>> l._vsids_calculate() -3 >>> l.lit_heap [(-2.0, -2), (-2.0, 2), (0.0, -1), (0.0, 1), (-2.0, 3)] ii(RRlRQRVR(RJ((s;lib/python2.7/site-packages/sympy/logic/algorithms/dpll2.pyR4ðs! cC sdS(s;Handle the assignment of a literal for the VSIDS heuristic.N((RJRU((s;lib/python2.7/site-packages/sympy/logic/algorithms/dpll2.pyR6scC sLt|ƒ}t|j|j||fƒt|j|j| | fƒdS(sHandle the unsetting of a literal for the VSIDS heuristic. Examples ======== >>> from sympy.logic.algorithms.dpll2 import SATSolver >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2}, ... {3, -2}], {1, 2, 3}, set()) >>> l.lit_heap [(-2.0, -3), (-2.0, 2), (-2.0, -2), (0.0, 1), (-2.0, 3), (0.0, -1)] >>> l._vsids_lit_unset(2) >>> l.lit_heap [(-2.0, -3), (-2.0, -2), (-2.0, -2), (-2.0, 2), (-2.0, 3), (0.0, -1), ...(-2.0, 2), (0.0, 1)] N(RVRRlRm(RJRURo((s;lib/python2.7/site-packages/sympy/logic/algorithms/dpll2.pyR8s cC s7|jd7_x!|D]}|j|cd7>> from sympy.logic.algorithms.dpll2 import SATSolver >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2}, ... {3, -2}], {1, 2, 3}, set()) >>> l.num_learned_clauses 0 >>> l.lit_scores {-3: -2.0, -2: -2.0, -1: 0.0, 1: 0.0, 2: -2.0, 3: -2.0} >>> l._vsids_clause_added({2, -3}) >>> l.num_learned_clauses 1 >>> l.lit_scores {-3: -1.0, -2: -2.0, -1: 0.0, 1: 0.0, 2: -1.0, 3: -2.0} iN(RHRm(RJRSRU((s;lib/python2.7/site-packages/sympy/logic/algorithms/dpll2.pyR:)s cC s„t|jƒ}|jj|ƒx!|D]}|j|cd7>> from sympy.logic.algorithms.dpll2 import SATSolver >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2}, ... {3, -2}], {1, 2, 3}, set()) >>> l.num_learned_clauses 0 >>> l.clauses [[2, -3], [1], [3, -3], [2, -2], [3, -2]] >>> l.sentinels {-3: {0, 2}, -2: {3, 4}, 2: {0, 3}, 3: {2, 4}} >>> l._simple_add_learned_clause([3]) >>> l.clauses [[2, -3], [1], [3, -3], [2, -2], [3, -2], [3]] >>> l.sentinels {-3: {0, 2}, -2: {3, 4}, 2: {0, 3}, 3: {2, 4, 5}} iiiÿÿÿÿN(RRRARPRNRRR;(RJRStcls_numRU((s;lib/python2.7/site-packages/sympy/logic/algorithms/dpll2.pyR=Fs cC s"g|jdD]}|j ^qS(sª Build a clause representing the fact that at least one decision made so far is wrong. Examples ======== >>> from sympy.logic.algorithms.dpll2 import SATSolver >>> l = SATSolver([{2, -3}, {1}, {3, -3}, {2, -2}, ... {3, -2}], {1, 2, 3}, set()) >>> next(l._find_model()) {1: True, 2: False, 3: False} >>> l._simple_compute_conflict() [3] i(RDRY(RJtlevel((s;lib/python2.7/site-packages/sympy/logic/algorithms/dpll2.pyt_simple_compute_conflictiscC sdS(sClean up learned clauses.N((RJ((s;lib/python2.7/site-packages/sympy/logic/algorithms/dpll2.pyt_simple_clean_clauseszsN(t__name__t __module__t__doc__R&RMR1R2RtpropertyRER`RaR\R[RXRgRhR3RqR4R6R8R:R=RtRu(((s;lib/python2.7/site-packages/sympy/logic/algorithms/dpll2.pyRKs.1   c   6 %         # RCcB seZdZed„ZRS(s‚ Represents a single level in the DPLL algorithm, and contains enough information for a sound backtracking procedure. cC s"||_tƒ|_||_dS(N(RYRR*RW(RJRYRW((s;lib/python2.7/site-packages/sympy/logic/algorithms/dpll2.pyRM…s  (RvRwRxRRM(((s;lib/python2.7/site-packages/sympy/logic/algorithms/dpll2.pyRCsN(Rxt __future__RRt collectionsRtheapqRRtsympy.core.compatibilityRtsympyRRtsympy.logic.boolalgRR R R RR RtobjectRRC(((s;lib/python2.7/site-packages/sympy/logic/algorithms/dpll2.pyt s" + ÿÿ6