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z3/src/math/polysat/solver.h

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24 KiB
C++

/*++
Copyright (c) 2021 Microsoft Corporation
Module Name:
polysat solver
Abstract:
Polynomial solver for modular arithmetic.
Author:
Nikolaj Bjorner (nbjorner) 2021-03-19
Jakob Rath 2021-04-6
--*/
#pragma once
#include "util/statistics.h"
#include "util/params.h"
#include "math/polysat/boolean.h"
#include "math/polysat/conflict.h"
#include "math/polysat/constraint.h"
#include "math/polysat/constraint_manager.h"
#include "math/polysat/clause_builder.h"
#include "math/polysat/simplify_clause.h"
#include "math/polysat/simplify.h"
#include "math/polysat/restart.h"
#include "math/polysat/ule_constraint.h"
#include "math/polysat/justification.h"
#include "math/polysat/linear_solver.h"
#include "math/polysat/search_state.h"
#include "math/polysat/assignment.h"
#include "math/polysat/trail.h"
#include "math/polysat/viable.h"
#include "math/polysat/log.h"
#include <limits>
#include <optional>
namespace polysat {
struct config {
uint64_t m_max_conflicts = std::numeric_limits<uint64_t>::max();
uint64_t m_max_decisions = std::numeric_limits<uint64_t>::max();
bool m_log_conflicts = false;
};
/**
* A metric to evaluate lemmas from conflict analysis.
* Lower is better.
*
* Comparison criterion:
* - Lowest jump level has priority, because otherwise, some of the accumulated lemmas may still be false after backjumping.
* - To break ties on jump level, choose clause with the fewest literals at its highest decision level;
* to limit case splits.
*/
class lemma_score {
unsigned m_jump_level;
unsigned m_literals_at_max_level;
public:
lemma_score(unsigned jump_level, unsigned at_max_level)
: m_jump_level(jump_level), m_literals_at_max_level(at_max_level)
{ }
unsigned jump_level() const { return m_jump_level; }
unsigned literals_at_max_level() const { return m_literals_at_max_level; }
static lemma_score max() {
return {UINT_MAX, UINT_MAX};
}
bool operator==(lemma_score const& other) const {
return m_jump_level == other.m_jump_level
&& m_literals_at_max_level == other.m_literals_at_max_level;
}
bool operator!=(lemma_score const& other) const { return !operator==(other); }
bool operator<(lemma_score const& other) const {
return m_jump_level < other.m_jump_level
|| (m_jump_level == other.m_jump_level && m_literals_at_max_level < other.m_literals_at_max_level);
}
bool operator>(lemma_score const& other) const { return other.operator<(*this); }
bool operator<=(lemma_score const& other) const { return operator==(other) || operator<(other); }
bool operator>=(lemma_score const& other) const { return operator==(other) || operator>(other); }
std::ostream& display(std::ostream& out) const {
return out << "jump_level=" << m_jump_level << " at_max_level=" << m_literals_at_max_level;
}
};
inline std::ostream& operator<<(std::ostream& out, lemma_score const& ls) { return ls.display(out); }
class solver {
struct stats {
unsigned m_num_iterations;
unsigned m_num_decisions;
unsigned m_num_propagations;
unsigned m_num_conflicts;
unsigned m_num_restarts;
unsigned m_num_viable_fallback; ///< how often did we query the univariate solver
void reset() { memset(this, 0, sizeof(*this)); }
stats() { reset(); }
};
friend class assignment;
friend class constraint;
friend class ule_constraint;
friend class umul_ovfl_constraint;
friend class smul_fl_constraint;
friend class op_constraint;
friend class signed_constraint;
friend class clause;
friend class clause_builder;
friend class conflict;
friend class conflict_explainer;
friend class simplify_clause;
friend class simplify;
friend class restart;
friend class explainer;
friend class inference_engine;
friend class file_inference_logger;
friend class forbidden_intervals;
friend class linear_solver;
friend class viable;
friend class viable_fallback;
friend class search_state;
friend class num_pp;
friend class lit_pp;
friend class assignment_pp;
friend class assignments_pp;
friend class ex_polynomial_superposition;
friend class free_variable_elimination;
friend class saturation;
friend class constraint_manager;
friend class scoped_solverv;
friend class test_polysat;
friend class test_fi;
friend struct inf_resolve_with_assignment;
reslimit& m_lim;
params_ref m_params;
mutable scoped_ptr_vector<dd::pdd_manager> m_pdd;
viable m_viable; // viable sets per variable
viable_fallback m_viable_fallback; // fallback for viable, using bitblasting over univariate constraints
linear_solver m_linear_solver;
conflict m_conflict;
simplify_clause m_simplify_clause;
simplify m_simplify;
restart m_restart;
bool_var_manager m_bvars; // Map boolean variables to constraints
var_queue m_free_pvars; // free poly vars
stats m_stats;
config m_config;
// Per constraint state
constraint_manager m_constraints;
// Per variable information
vector<rational> m_value; // assigned value
vector<justification> m_justification; // justification for variable assignment
vector<constraints> m_pwatch; // watch list datastructure into constraints.
#ifndef NDEBUG
std::optional<pvar> m_locked_wlist; // restrict watch list modification while it is being propagated
bool m_is_propagating = false; // set to true during propagation
bool m_is_solving = false; // set to true during solving
#endif
unsigned_vector m_activity;
vector<pdd> m_vars;
unsigned_vector m_size; // store size of variables (bit width)
search_state m_search;
unsigned m_qhead = 0; // next item to propagate (index into m_search)
unsigned m_level = 0;
svector<trail_instr_t> m_trail;
unsigned_vector m_qhead_trail;
constraints m_pwatch_queue;
#if 0
constraints m_pwatch_trail;
#endif
ptr_vector<clause> m_lemmas; ///< the non-asserting lemmas
unsigned m_lemmas_qhead = 0;
unsigned_vector m_base_levels; // External clients can push/pop scope.
void push_qhead() {
m_trail.push_back(trail_instr_t::qhead_i);
m_qhead_trail.push_back(m_qhead);
}
void pop_qhead() {
m_qhead = m_qhead_trail.back();
m_qhead_trail.pop_back();
}
unsigned size(pvar v) const { return m_size[v]; }
/**
* undo trail operations for backtracking.
* Each struct is a subclass of trail and implements undo().
*/
void del_var();
dd::pdd_manager& sz2pdd(unsigned sz) const;
dd::pdd_manager& var2pdd(pvar v) const;
assignment const& assignment() const { return m_search.assignment(); }
void push_level();
void pop_levels(unsigned num_levels);
void try_assign_eval(signed_constraint c);
void assign_propagate(sat::literal lit, clause& reason);
void assign_decision(sat::literal lit);
void assign_eval(sat::literal lit);
void activate_constraint(signed_constraint c);
unsigned level(sat::literal lit, clause const& cl);
void assign_propagate(pvar v, rational const& val);
void assign_verify(pvar v, rational val, justification j);
void assign_core(pvar v, rational const& val, justification const& j);
bool is_assigned(pvar v) const { return !m_justification[v].is_unassigned(); }
bool is_decision(pvar v) const { return m_justification[v].is_decision(); }
bool should_search();
void propagate(sat::literal lit);
void propagate(pvar v);
bool propagate(pvar v, constraint* c);
bool propagate(sat::literal lit, clause& cl);
void enqueue_pwatch(constraint* c);
bool should_add_pwatch() const;
void add_pwatch();
void add_pwatch(constraint* c);
void add_pwatch(constraint* c, pvar v);
void erase_pwatch(pvar v, constraint* c);
void erase_pwatch(constraint* c);
void set_conflict_at_base_level() { m_conflict.init_at_base_level(); }
void set_conflict(signed_constraint c) { m_conflict.init(c); }
void set_conflict(clause& cl) { m_conflict.init(cl); }
void set_conflict(pvar v, bool by_viable_fallback) { m_conflict.init(v, by_viable_fallback); }
bool can_decide() const;
bool can_bdecide() const;
bool can_pdecide() const;
void decide();
void bdecide();
void pdecide(pvar v);
void linear_propagate();
bool is_conflict() const { return !m_conflict.empty(); }
bool at_base_level() const;
unsigned base_level() const;
void resolve_conflict();
void revert_decision(pvar v);
void revert_bool_decision(sat::literal lit);
void backjump_and_learn(unsigned jump_level, clause& lemma);
void backjump_and_learn(unsigned max_jump_level);
std::optional<lemma_score> compute_lemma_score(clause const& lemma);
// activity of variables based on standard VSIDS
unsigned m_activity_inc = 128;
unsigned m_variable_decay = 110;
void inc_activity(pvar v);
void decay_activity();
void rescale_activity();
void report_unsat();
void learn_lemma(clause& lemma);
void backjump(unsigned new_level);
void add_clause(clause& clause);
void add_clause(signed_constraint c1, bool is_redundant);
void add_clause(signed_constraint c1, signed_constraint c2, bool is_redundant);
void add_clause(signed_constraint c1, signed_constraint c2, signed_constraint c3, bool is_redundant);
void add_clause(signed_constraint c1, signed_constraint c2, signed_constraint c3, signed_constraint c4, bool is_redundant);
void add_clause(std::initializer_list<signed_constraint> cs, bool is_redundant);
void add_clause(unsigned n, signed_constraint const* cs, bool is_redundant);
// Create a clause without adding it to the solver.
clause_ref mk_clause(signed_constraint c1, bool is_redundant);
clause_ref mk_clause(signed_constraint c1, signed_constraint c2, bool is_redundant);
clause_ref mk_clause(signed_constraint c1, signed_constraint c2, signed_constraint c3, bool is_redundant);
clause_ref mk_clause(signed_constraint c1, signed_constraint c2, signed_constraint c3, signed_constraint c4, bool is_redundant);
clause_ref mk_clause(signed_constraint c1, signed_constraint c2, signed_constraint c3, signed_constraint c4, signed_constraint c5, bool is_redundant);
clause_ref mk_clause(std::initializer_list<signed_constraint> cs, bool is_redundant);
clause_ref mk_clause(unsigned n, signed_constraint const* cs, bool is_redundant);
signed_constraint lit2cnstr(sat::literal lit) const { return m_constraints.lookup(lit); }
bool inc() { return m_lim.inc(); }
bool invariant();
static bool invariant(signed_constraints const& cs);
bool wlist_invariant();
bool assignment_invariant();
bool verify_sat();
bool can_propagate();
void propagate();
public:
/**
* to share chronology we pass an external trail stack.
* every update to the solver is going to be retractable
* by pushing an undo action on the trail stack.
*/
solver(reslimit& lim);
~solver();
/**
* End-game satisfiability checker.
*
* Returns l_undef if the search cannot proceed.
* Possible reasons:
* - Resource limits are exhausted.
*/
lbool check_sat();
/**
* retrieve unsat core dependencies
*/
void unsat_core(dependency_vector& deps);
/**
* Return value / level of v in the current model (only meaningful if check_sat() returned l_true).
*/
rational get_value(pvar v) const { SASSERT(is_assigned(v)); return m_value[v]; }
unsigned get_level(pvar v) const { SASSERT(is_assigned(v)); return m_justification[v].level(); }
/**
* Evaluate term under the current assignment.
*/
bool try_eval(pdd const& p, rational& out_value) const;
/**
* Add variable with bit-size.
*/
pvar add_var(unsigned sz);
/**
* Create polynomial terms
*/
pdd var(pvar v) { return m_vars[v]; }
/**
* Create terms for unsigned quot-rem
*
* Return tuple (quot, rem)
*
* The following properties are enforced:
* b*quot + rem = a
* ~ovfl(b*quot)
* rem < b or b = 0
*/
std::pair<pdd, pdd> quot_rem(pdd const& a, pdd const& b) { return m_constraints.quot_rem(a, b); }
/** Create expression for the logical right shift of p by q. */
pdd lshr(pdd const& p, pdd const& q) { return m_constraints.lshr(p, q); }
/** Create expression for the logical left shift of p by q. */
pdd shl(pdd const& p, pdd const& q) { return m_constraints.shl(p, q); }
/** Create expression for the bit-wise negation of p. */
pdd bnot(pdd const& p) { return m_constraints.bnot(p); }
/** Create expression for bit-wise and of p, q. */
pdd band(pdd const& p, pdd const& q) { return m_constraints.band(p, q); }
/** Create expression for bit-wise or of p, q. */
pdd bor(pdd const& p, pdd const& q) { return m_constraints.bor(p, q); }
/** Create expression for bit-wise xor of p, q. */
pdd bxor(pdd const& p, pdd const& q) { return m_constraints.bxor(p, q); }
/** Create expression for bit-wise nand of p, q. */
pdd bnand(pdd const& p, pdd const& q) { return m_constraints.bnand(p, q); }
/** Create expression for bit-wise nor of p, q. */
pdd bnor(pdd const& p, pdd const& q) { return m_constraints.bnor(p, q); }
/**
* Create polynomial constant.
*/
pdd value(rational const& v, unsigned sz);
/**
* Apply current substitution to p.
*/
pdd subst(pdd const& p) const;
/** Create constraints */
signed_constraint eq(pdd const& p) { return m_constraints.eq(p); }
signed_constraint diseq(pdd const& p) { return ~m_constraints.eq(p); }
signed_constraint eq(pdd const& p, pdd const& q) { return eq(p - q); }
signed_constraint diseq(pdd const& p, pdd const& q) { return diseq(p - q); }
signed_constraint eq(pdd const& p, rational const& q) { return eq(p - q); }
signed_constraint eq(pdd const& p, unsigned q) { return eq(p - q); }
signed_constraint odd(pdd const& p) { return ~even(p); }
signed_constraint even(pdd const& p) { return parity(p, 1); }
signed_constraint parity(pdd const& p, unsigned k) { return eq(p*rational::power_of_two(p.manager().power_of_2() - k)); }
signed_constraint diseq(pdd const& p, rational const& q) { return diseq(p - q); }
signed_constraint diseq(pdd const& p, unsigned q) { return diseq(p - q); }
signed_constraint ule(pdd const& p, pdd const& q) { return m_constraints.ule(p, q); }
signed_constraint ule(pdd const& p, rational const& q) { return ule(p, p.manager().mk_val(q)); }
signed_constraint ule(rational const& p, pdd const& q) { return ule(q.manager().mk_val(p), q); }
signed_constraint ule(pdd const& p, int n) { return ule(p, rational(n)); }
signed_constraint ule(int n, pdd const& p) { return ule(rational(n), p); }
signed_constraint uge(pdd const& p, pdd const& q) { return ule(q, p); }
signed_constraint uge(pdd const& p, rational const& q) { return ule(q, p); }
signed_constraint ult(pdd const& p, pdd const& q) { return m_constraints.ult(p, q); }
signed_constraint ult(pdd const& p, rational const& q) { return ult(p, p.manager().mk_val(q)); }
signed_constraint ult(rational const& p, pdd const& q) { return ult(q.manager().mk_val(p), q); }
signed_constraint ult(int p, pdd const& q) { return ult(rational(p), q); }
signed_constraint ult(pdd const& p, int q) { return ult(p, rational(q)); }
signed_constraint sle(pdd const& p, pdd const& q) { return m_constraints.sle(p, q); }
signed_constraint slt(pdd const& p, pdd const& q) { return m_constraints.slt(p, q); }
signed_constraint slt(pdd const& p, rational const& q) { return slt(p, p.manager().mk_val(q)); }
signed_constraint slt(rational const& p, pdd const& q) { return slt(q.manager().mk_val(p), q); }
signed_constraint slt(pdd const& p, int n) { return slt(p, rational(n)); }
signed_constraint slt(int n, pdd const& p) { return slt(rational(n), p); }
signed_constraint sgt(pdd const& p, pdd const& q) { return slt(q, p); }
signed_constraint sgt(pdd const& p, int n) { return slt(n, p); }
signed_constraint sgt(int n, pdd const& p) { return slt(p, n); }
signed_constraint umul_ovfl(pdd const& p, pdd const& q) { return m_constraints.umul_ovfl(p, q); }
signed_constraint umul_ovfl(rational const& p, pdd const& q) { return umul_ovfl(q.manager().mk_val(p), q); }
signed_constraint smul_ovfl(pdd const& p, pdd const& q) { return m_constraints.smul_ovfl(p, q); }
signed_constraint smul_udfl(pdd const& p, pdd const& q) { return m_constraints.smul_udfl(p, q); }
signed_constraint bit(pdd const& p, unsigned i) { return m_constraints.bit(p, i); }
/** Create and activate constraints */
void add_eq(pdd const& p, dependency dep = null_dependency) { assign_eh(eq(p), dep); }
void add_eq(pdd const& p, pdd const& q, dependency dep = null_dependency) { assign_eh(eq(p, q), dep); }
void add_eq(pdd const& p, rational const& q, dependency dep = null_dependency) { assign_eh(eq(p, q), dep); }
void add_eq(pdd const& p, unsigned q, dependency dep = null_dependency) { assign_eh(eq(p, q), dep); }
void add_diseq(pdd const& p, dependency dep = null_dependency) { assign_eh(diseq(p), dep); }
void add_diseq(pdd const& p, pdd const& q, dependency dep = null_dependency) { assign_eh(diseq(p, q), dep); }
void add_diseq(pdd const& p, rational const& q, dependency dep = null_dependency) { assign_eh(diseq(p, q), dep); }
void add_diseq(pdd const& p, unsigned q, dependency dep = null_dependency) { assign_eh(diseq(p, q), dep); }
void add_ule(pdd const& p, pdd const& q, dependency dep = null_dependency) { assign_eh(ule(p, q), dep); }
void add_ult(pdd const& p, pdd const& q, dependency dep = null_dependency) { assign_eh(ult(p, q), dep); }
void add_sle(pdd const& p, pdd const& q, dependency dep = null_dependency) { assign_eh(sle(p, q), dep); }
void add_slt(pdd const& p, pdd const& q, dependency dep = null_dependency) { assign_eh(slt(p, q), dep); }
void add_umul_noovfl(pdd const& p, pdd const& q, dependency dep = null_dependency) { assign_eh(~umul_ovfl(p, q), dep); }
void add_umul_ovfl(pdd const& p, pdd const& q, dependency dep = null_dependency) { assign_eh(umul_ovfl(p, q), dep); }
void add_ule(pdd const& p, rational const& q, dependency dep = null_dependency) { add_ule(p, p.manager().mk_val(q), dep); }
void add_ule(rational const& p, pdd const& q, dependency dep = null_dependency) { add_ule(q.manager().mk_val(p), q, dep); }
void add_ule(pdd const& p, unsigned q, dependency dep = null_dependency) { add_ule(p, rational(q), dep); }
void add_ule(unsigned p, pdd const& q, dependency dep = null_dependency) { add_ule(rational(p), q, dep); }
void add_ult(pdd const& p, rational const& q, dependency dep = null_dependency) { add_ult(p, p.manager().mk_val(q), dep); }
void add_ult(rational const& p, pdd const& q, dependency dep = null_dependency) { add_ult(q.manager().mk_val(p), q, dep); }
void add_ult(pdd const& p, unsigned q, dependency dep = null_dependency) { add_ult(p, rational(q), dep); }
void add_ult(unsigned p, pdd const& q, dependency dep = null_dependency) { add_ult(rational(p), q, dep); }
void add_umul_noovfl(pdd const& p, rational const& q, dependency dep = null_dependency) { add_umul_noovfl(p, p.manager().mk_val(q), dep); }
void add_umul_noovfl(rational const& p, pdd const& q, dependency dep = null_dependency) { add_umul_noovfl(q, p, dep); }
void add_umul_noovfl(pdd const& p, unsigned q, dependency dep = null_dependency) { add_umul_noovfl(p, rational(q), dep); }
void add_umul_noovfl(unsigned p, pdd const& q, dependency dep = null_dependency) { add_umul_noovfl(q, p, dep); }
/**
* Activate the constraint corresponding to the given boolean variable.
* Note: to deactivate, use push/pop.
*/
void assign_eh(signed_constraint c, dependency dep);
/**
* Unit propagation accessible over API.
*/
lbool unit_propagate();
/**
* External context managment.
* Adds so-called user-scope.
*/
void push();
void pop(unsigned num_scopes = 1);
std::ostream& display(std::ostream& out) const;
void collect_statistics(statistics& st) const;
params_ref const & params() const { return m_params; }
void updt_params(params_ref const& p);
config const& get_config() const { return m_config; }
}; // class solver
class assignments_pp { // TODO: can probably remove this now.
solver const& s;
public:
assignments_pp(solver const& s): s(s) {}
std::ostream& display(std::ostream& out) const;
};
class assignment_pp {
solver const& s;
pvar var;
rational const& val;
bool with_justification;
public:
assignment_pp(solver const& s, pvar var, rational const& val, bool with_justification = false): s(s), var(var), val(val), with_justification(with_justification) {}
std::ostream& display(std::ostream& out) const;
};
class lit_pp {
solver const& s;
sat::literal lit;
public:
lit_pp(solver const& s, signed_constraint c): s(s), lit(c ? c.blit() : sat::null_literal) {}
lit_pp(solver const& s, sat::literal lit): s(s), lit(lit) {}
std::ostream& display(std::ostream& out) const;
};
/** Format value 'val' as member of the domain of 'var' */
class num_pp {
solver const& s;
pvar var;
rational const& val;
public:
num_pp(solver const& s, pvar var, rational const& val): s(s), var(var), val(val) {}
std::ostream& display(std::ostream& out) const;
};
inline std::ostream& operator<<(std::ostream& out, solver const& s) { return s.display(out); }
inline std::ostream& operator<<(std::ostream& out, num_pp const& v) { return v.display(out); }
inline std::ostream& operator<<(std::ostream& out, lit_pp const& l) { return l.display(out); }
inline std::ostream& operator<<(std::ostream& out, assignment_pp const& p) { return p.display(out); }
inline std::ostream& operator<<(std::ostream& out, assignments_pp const& a) { return a.display(out); }
}