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https://github.com/Z3Prover/z3
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113 lines
3.8 KiB
C++
113 lines
3.8 KiB
C++
/*++
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Copyright (c) 2012 Microsoft Corporation
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Module Name:
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nlsat_explain.h
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Abstract:
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Functor that implements the "explain" procedure defined in Dejan and Leo's paper.
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Uses paper Haokun Li and Bican Xia, "Solving Satisfiability of Polynomial Formulas By Sample - Cell Projection",https://arxiv.org/abs/2003.00409,
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and code from https://github.com/hybridSMT/hybridSMT.git
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Author:
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Leonardo de Moura (leonardo) 2012-01-13.
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Revision History:
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--*/
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#pragma once
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#include "nlsat/nlsat_solver.h"
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#include "nlsat/nlsat_scoped_literal_vector.h"
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#include "math/polynomial/polynomial_cache.h"
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#include "math/polynomial/algebraic_numbers.h"
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namespace nlsat {
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class evaluator;
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class explain {
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public:
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struct imp;
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private:
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imp * m_imp;
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public:
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explain(solver & s, assignment const & x2v, polynomial::cache & u,
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atom_vector const& atoms, atom_vector const& x2eq, evaluator & ev, bool use_cell_sample_proj, bool use_lazard_proj);
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~explain();
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void reset();
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void set_simplify_cores(bool f);
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void set_full_dimensional(bool f);
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void set_minimize_cores(bool f);
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void set_factor(bool f);
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void set_add_all_coeffs(bool f);
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void set_signed_project(bool f);
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void set_lazard(bool f);
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/**
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\brief Given a set of literals ls[0], ... ls[n-1] s.t.
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- n > 0
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- all of them are arithmetic literals.
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- all of them have the same maximal variable.
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- (ls[0] and ... and ls[n-1]) is infeasible in the current interpretation.
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Let x be the maximal variable in {ls[0], ..., ls[n-1]}.
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Remark: the current interpretation assigns all variables in ls[0], ..., ls[n-1] but x.
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This procedure stores in result a set of literals: s_1, ..., s_m
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s.t.
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- (s_1 or ... or s_m or ~ls[0] or ... or ~ls[n-1]) is a valid clause
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- s_1, ..., s_m do not contain variable x.
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- s_1, ..., s_m are false in the current interpretation
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*/
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void main_operator(unsigned n, literal const * ls, scoped_literal_vector & result);
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/**
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\brief projection for a given variable.
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Given: M |= l1[x] /\ ... /\ ln[x]
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Find: M |= s1, ..., sm
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Such that: |= ~s1 \/ ... \/ ~sm \/ E x. l1[x] /\ ... /\ ln[x]
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Contrast this with with the core-based projection above:
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Given: M |= A x . l1[x] \/ ... \/ ln[x]
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Find: M |= ~s1, ..., ~sm.
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Such that: |= s1 \/ ... \/ sm \/ A x . l1[x] \/ ... \/ ln[x]
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Claim: the two compute the same solutions if the projection operators are independent of the value of x.
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Claim: A complete, convergent projection operator can be obtained from M in a way that is independent of x.
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*/
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void project(var x, unsigned n, literal const * ls, scoped_literal_vector & result);
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/**
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Maximize the value of x (locally) under the current assignment to other variables and
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while maintaining the assignment to the literals ls.
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Set unbounded to 'true' if the value of x is unbounded.
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Precondition: the set of literals are true in the current model.
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By local optimization we understand that x is increased to the largest value within
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the signs delineated by the roots of the polynomials in ls.
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*/
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void maximize(var x, unsigned n, literal const * ls, scoped_anum& val, bool& unbounded);
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/**
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Unit test routine.
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*/
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void test_root_literal(atom::kind k, var y, unsigned i, poly* p, scoped_literal_vector & result);
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};
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};
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