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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
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Nikolaj Bjorner 2025-09-27 16:59:22 +03:00
parent 88844a84aa
commit ad11e4626e
5 changed files with 120 additions and 100 deletions
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src/math/lp/nla_stellensatz.h Normal file
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/*++
Copyright (c) 2025 Microsoft Corporation
--*/
#pragma once
#include "math/lp/nla_coi.h"
#include "math/lp/int_solver.h"
#include <variant>
namespace nla {
class core;
class lar_solver;
class stellensatz : common {
class solver {
scoped_ptr<lp::lar_solver> lra_solver;
scoped_ptr<lp::int_solver> int_solver;
lbool solve_lra(lp::explanation &ex);
lbool solve_lia(lp::explanation &ex);
public:
void init();
lbool solve(lp::explanation &ex);
lp::lar_solver &lra() { return *lra_solver; }
lp::lar_solver const &lra() const { return *lra_solver; }
};
solver m_solver;
struct bound {
lpvar v = lp::null_lpvar;
lp::lconstraint_kind k;
rational rhs;
};
using bound_justification = std::variant<u_dependency*, bound>;
coi m_coi;
u_map<vector<bound_justification>> m_new_mul_constraints;
indexed_uint_set m_to_refine;
ptr_vector<u_dependency> m_ci2dep;
vector<rational> m_values;
struct eq {
bool operator()(unsigned_vector const& a, unsigned_vector const& b) const {
return a == b;
}
};
map<unsigned_vector, unsigned, svector_hash<unsigned_hash>, eq> m_vars2mon;
u_map<unsigned_vector> m_mon2vars;
// initialization
void init_solver();
void init_vars();
void init_monomial(unsigned mon_var);
bool constraint_is_true(lp::constraint_index ci);
void insert_monomials_from_constraint(lp::constraint_index ci);
// additional variables and monomials and constraints
lpvar add_monomial(svector<lp::lpvar> const& vars);
bool is_int(svector<lp::lpvar> const& vars) const;
lpvar add_var(bool is_int);
void saturate_constraints();
void saturate_constraint(lp::constraint_index con_id, lp::lpvar mi, lpvar x);
// lemmas
void add_lemma(lp::explanation const& ex);
std::ostream& display(std::ostream& out) const;
std::ostream& display_product(std::ostream& out, svector<lpvar> const& vars) const;
std::ostream& display_constraint(std::ostream& out, lp::constraint_index ci) const;
std::ostream& display_constraint(std::ostream& out, vector<std::pair<rational, lpvar>> const& lhs,
lp::lconstraint_kind k, rational const& rhs) const;
public:
stellensatz(core* core);
lbool saturate();
};
}