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       1                 :            : /******************************************************************************
       2                 :            :  * Top contributors (to current version):
       3                 :            :  *   Tim King, Gereon Kremer, Mathias Preiner
       4                 :            :  *
       5                 :            :  * This file is part of the cvc5 project.
       6                 :            :  *
       7                 :            :  * Copyright (c) 2009-2025 by the authors listed in the file AUTHORS
       8                 :            :  * in the top-level source directory and their institutional affiliations.
       9                 :            :  * All rights reserved.  See the file COPYING in the top-level source
      10                 :            :  * directory for licensing information.
      11                 :            :  * ****************************************************************************
      12                 :            :  *
      13                 :            :  * This is an implementation of the Simplex Module for the Simplex for
      14                 :            :  * DPLL(T) decision procedure.
      15                 :            :  *
      16                 :            :  * This implements the Simplex module for the Simpelx for DPLL(T) decision
      17                 :            :  * procedure.
      18                 :            :  * See the Simplex for DPLL(T) technical report for more background.(citation?)
      19                 :            :  * This shares with the theory a Tableau, and a PartialModel that:
      20                 :            :  *  - satisfies the equalities in the Tableau, and
      21                 :            :  *  - the assignment for the non-basic variables satisfies their bounds.
      22                 :            :  * This is required to either produce a conflict or satisifying PartialModel.
      23                 :            :  * Further, we require being told when a basic variable updates its value.
      24                 :            :  *
      25                 :            :  * During the Simplex search we maintain a queue of variables.
      26                 :            :  * The queue is required to contain all of the basic variables that voilate
      27                 :            :  * their bounds.
      28                 :            :  * As elimination from the queue is more efficient to be done lazily,
      29                 :            :  * we do not maintain that the queue of variables needs to be only basic
      30                 :            :  * variables or only variables that satisfy their bounds.
      31                 :            :  *
      32                 :            :  * The simplex procedure roughly follows Alberto's thesis. (citation?)
      33                 :            :  * There is one round of selecting using a heuristic pivoting rule.
      34                 :            :  * (See PreferenceFunction Documentation for the available options.)
      35                 :            :  * The non-basic variable is the one that appears in the fewest pivots.
      36                 :            :  * (Bruno says that Leonardo invented this first.)
      37                 :            :  * After this, Bland's pivot rule is invoked.
      38                 :            :  *
      39                 :            :  * During this process, we periodically inspect the queue of variables to
      40                 :            :  * 1) remove now extraneous extries,
      41                 :            :  * 2) detect conflicts that are "waiting" on the queue but may not be detected
      42                 :            :  *    by the current queue heuristics, and
      43                 :            :  * 3) detect multiple conflicts.
      44                 :            :  *
      45                 :            :  * Conflicts are greedily slackened to use the weakest bounds that still
      46                 :            :  * produce the conflict.
      47                 :            :  *
      48                 :            :  * Extra things tracked atm: (Subject to change at Tim's whims)
      49                 :            :  * - A superset of all of the newly pivoted variables.
      50                 :            :  * - A queue of additional conflicts that were discovered by Simplex.
      51                 :            :  *   These are theory valid and are currently turned into lemmas
      52                 :            :  */
      53                 :            : 
      54                 :            : #include "cvc5_private.h"
      55                 :            : 
      56                 :            : #pragma once
      57                 :            : 
      58                 :            : #include <unordered_map>
      59                 :            : 
      60                 :            : #include "options/arith_options.h"
      61                 :            : #include "smt/env_obj.h"
      62                 :            : #include "theory/arith/linear/arithvar.h"
      63                 :            : #include "theory/arith/linear/partial_model.h"
      64                 :            : #include "util/dense_map.h"
      65                 :            : #include "util/result.h"
      66                 :            : #include "util/statistics_stats.h"
      67                 :            : 
      68                 :            : namespace cvc5::internal {
      69                 :            : namespace theory {
      70                 :            : namespace arith::linear {
      71                 :            : 
      72                 :            : class ErrorSet;
      73                 :            : class LinearEqualityModule;
      74                 :            : class Tableau;
      75                 :            : 
      76                 :            : class SimplexDecisionProcedure : protected EnvObj
      77                 :            : {
      78                 :            :  protected:
      79                 :            :   typedef std::vector< std::pair<ArithVar, int> > AVIntPairVec;
      80                 :            : 
      81                 :            :   /** Pivot count of the current round of pivoting. */
      82                 :            :   uint32_t d_pivots;
      83                 :            : 
      84                 :            :   /** The set of variables that are in conflict in this round. */
      85                 :            :   DenseSet d_conflictVariables;
      86                 :            : 
      87                 :            :   /** The rule to use for heuristic selection mode. */
      88                 :            :   options::ErrorSelectionRule d_heuristicRule;
      89                 :            : 
      90                 :            :   /** Linear equality module. */
      91                 :            :   LinearEqualityModule& d_linEq;
      92                 :            : 
      93                 :            :   /**
      94                 :            :    * Manages information about the assignment and upper and lower bounds on
      95                 :            :    * variables.
      96                 :            :    * Partial model matches that in LinearEqualityModule.
      97                 :            :    */
      98                 :            :   ArithVariables& d_variables;
      99                 :            : 
     100                 :            :   /**
     101                 :            :    * Stores the linear equalities used by Simplex.
     102                 :            :    * Tableau from the LinearEquality module.
     103                 :            :    */
     104                 :            :   Tableau& d_tableau;
     105                 :            : 
     106                 :            :   /** Contains a superset of the basic variables in violation of their bounds. */
     107                 :            :   ErrorSet& d_errorSet;
     108                 :            : 
     109                 :            :   /** Number of variables in the system. This is used for tuning heuristics. */
     110                 :            :   ArithVar d_numVariables;
     111                 :            : 
     112                 :            :   /** This is the call back channel for Simplex to report conflicts. */
     113                 :            :   RaiseConflict d_conflictChannel;
     114                 :            : 
     115                 :            :   /** This is the call back channel for Simplex to report conflicts. */
     116                 :            :   FarkasConflictBuilder* d_conflictBuilder;
     117                 :            : 
     118                 :            :   /** Used for requesting d_opt, bound and error variables for primal.*/
     119                 :            :   TempVarMalloc d_arithVarMalloc;
     120                 :            : 
     121                 :            :   /** The size of the error set. */
     122                 :            :   uint32_t d_errorSize;
     123                 :            : 
     124                 :            :   /** A local copy of 0. */
     125                 :            :   const Rational d_zero;
     126                 :            : 
     127                 :            :   /** A local copy of 1. */
     128                 :            :   const Rational d_posOne;
     129                 :            : 
     130                 :            :   /** A local copy of -1. */
     131                 :            :   const Rational d_negOne;
     132                 :            : 
     133                 :            :   /**
     134                 :            :    * Locally cached value of arithStandardCheckVarOrderPivots option. It is
     135                 :            :    * cached here to allow for single runs with a different (lower) limit.
     136                 :            :    */
     137                 :            :   int64_t d_varOrderPivotLimit = -1;
     138                 :            : 
     139                 :            :   ArithVar constructInfeasiblityFunction(TimerStat& timer);
     140                 :            :   ArithVar constructInfeasiblityFunction(TimerStat& timer, ArithVar e);
     141                 :            :   ArithVar constructInfeasiblityFunction(TimerStat& timer, const ArithVarVec& set);
     142                 :            : 
     143                 :            :   void tearDownInfeasiblityFunction(TimerStat& timer, ArithVar inf);
     144                 :            :   void adjustInfeasFunc(TimerStat& timer, ArithVar inf, const AVIntPairVec& focusChanges);
     145                 :            :   void addToInfeasFunc(TimerStat& timer, ArithVar inf, ArithVar e);
     146                 :            :   void removeFromInfeasFunc(TimerStat& timer, ArithVar inf, ArithVar e);
     147                 :            :   void shrinkInfeasFunc(TimerStat& timer, ArithVar inf, const ArithVarVec& dropped);
     148                 :            : 
     149                 :            : public:
     150                 :            :  SimplexDecisionProcedure(Env& env,
     151                 :            :                           LinearEqualityModule& linEq,
     152                 :            :                           ErrorSet& errors,
     153                 :            :                           RaiseConflict conflictChannel,
     154                 :            :                           TempVarMalloc tvmalloc);
     155                 :            :  virtual ~SimplexDecisionProcedure();
     156                 :            : 
     157                 :            :  /**
     158                 :            :   * Tries to update the assignments of variables such that all of the
     159                 :            :   * assignments are consistent with their bounds.
     160                 :            :   * This is done by a simplex search through the possible bases of the tableau.
     161                 :            :   *
     162                 :            :   * If all of the variables can be made consistent with their bounds
     163                 :            :   * SAT is returned. Otherwise UNSAT is returned, and at least 1 conflict
     164                 :            :   * was reported on the conflictCallback passed to the Module.
     165                 :            :   *
     166                 :            :   * Tableau pivoting is performed so variables may switch from being basic to
     167                 :            :   * nonbasic and vice versa.
     168                 :            :   *
     169                 :            :   * Corresponds to the "check()" procedure in [Cav06].
     170                 :            :   */
     171                 :            :  virtual Result::Status findModel(bool exactResult) = 0;
     172                 :            : 
     173                 :     358751 :  void increaseMax() { d_numVariables++; }
     174                 :            : 
     175                 :    3299948 :  uint32_t getPivots() const { return d_pivots; }
     176                 :            : 
     177                 :            :  /** Set the variable ordering pivot limit */
     178                 :          6 :  void setVarOrderPivotLimit(int64_t value) { d_varOrderPivotLimit = value; }
     179                 :            : 
     180                 :            : protected:
     181                 :            :  /** Reports a conflict to on the output channel. */
     182                 :            :  void reportConflict(ArithVar basic);
     183                 :            : 
     184                 :            :  /**
     185                 :            :   * Checks a basic variable, b, to see if it is in conflict.
     186                 :            :   * If a conflict is discovered a node summarizing the conflict is returned.
     187                 :            :   * Otherwise, Node::null() is returned.
     188                 :            :   */
     189                 :            :  bool maybeGenerateConflictForBasic(ArithVar basic) const;
     190                 :            : 
     191                 :            :  /** Returns true if a tracked basic variable has a conflict on it. */
     192                 :            :  bool checkBasicForConflict(ArithVar b) const;
     193                 :            : 
     194                 :            :  /**
     195                 :            :   * If a basic variable has a conflict on its row,
     196                 :            :   * this produces a minimized row on the conflict channel.
     197                 :            :   */
     198                 :            :  ConstraintCP generateConflictForBasic(ArithVar basic) const;
     199                 :            : 
     200                 :            :  /** Gets a fresh variable from TheoryArith. */
     201                 :       3943 :  ArithVar requestVariable() { return d_arithVarMalloc.request(); }
     202                 :            : 
     203                 :            :  /** Releases a requested variable from TheoryArith.*/
     204                 :       3943 :  void releaseVariable(ArithVar v) { d_arithVarMalloc.release(v); }
     205                 :            : 
     206                 :            :  /** Post condition: !d_queue.moreSignals() */
     207                 :            :  bool standardProcessSignals(TimerStat& timer, IntStat& conflictStat);
     208                 :            : 
     209                 :            :  struct ArithVarIntPairHashFunc
     210                 :            :  {
     211                 :          0 :    size_t operator()(const std::pair<ArithVar, int>& p) const
     212                 :            :    {
     213                 :          0 :      size_t h1 = std::hash<ArithVar>()(p.first);
     214                 :          0 :      size_t h2 = std::hash<int>()(p.second);
     215                 :          0 :      return h1 + 3389 * h2;
     216                 :            :    }
     217                 :            :   };
     218                 :            : 
     219                 :            :   typedef std::unordered_map< std::pair<ArithVar, int>, ArithVarVec, ArithVarIntPairHashFunc> sgn_table;
     220                 :            : 
     221                 :          0 :   static inline int determinizeSgn(int sgn){
     222         [ -  - ]:          0 :     return sgn < 0 ? -1 : (sgn == 0 ? 0 : 1);
     223                 :            :   }
     224                 :            : 
     225                 :            :   void addSgn(sgn_table& sgns, ArithVar col, int sgn, ArithVar basic);
     226                 :            :   void addRowSgns(sgn_table& sgns, ArithVar basic, int norm);
     227                 :            :   ArithVar find_basic_in_sgns(const sgn_table& sgns, ArithVar col, int sgn, const DenseSet& m, bool inside);
     228                 :            : 
     229                 :            :   sgn_table::const_iterator find_sgns(const sgn_table& sgns, ArithVar col, int sgn);
     230                 :            : 
     231                 :            : }; /* class SimplexDecisionProcedure */
     232                 :            : 
     233                 :            : }  // namespace arith
     234                 :            : }  // namespace theory
     235                 :            : }  // namespace cvc5::internal