mirror of
https://github.com/Z3Prover/z3
synced 2025-04-28 19:35:50 +00:00
use cone of influence reduction before calling nlsat.
This commit is contained in:
Nikolaj Bjorner
parent
e2db2b864b
commit
20c54048f7
6 changed files with 323 additions and 138 deletions
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@ -19,17 +19,17 @@ typedef nla::mon_eq mon_eq;
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typedef nla::variable_map_type variable_map_type;
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struct solver::imp {
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lp::lar_solver& s;
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lp::lar_solver& lra;
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reslimit& m_limit;
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params_ref m_params;
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u_map<polynomial::var> m_lp2nl; // map from lar_solver variables to nlsat::solver variables
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indexed_uint_set m_term_set;
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indexed_uint_set m_term_set;
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scoped_ptr<nlsat::solver> m_nlsat;
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scoped_ptr<scoped_anum> m_zero;
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mutable variable_map_type m_variable_values; // current model
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nla::core& m_nla_core;
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scoped_ptr<scoped_anum_vector> m_values; // values provided by LRA solver
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nla::core& m_nla_core;
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imp(lp::lar_solver& s, reslimit& lim, params_ref const& p, nla::core& nla_core):
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s(s),
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lra(s),
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m_limit(lim),
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m_params(p),
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m_nla_core(nla_core) {}
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@ -38,6 +38,68 @@ struct solver::imp {
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return m_nla_core.m_to_refine.size() != 0;
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}
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indexed_uint_set m_mon_set, m_constraint_set;
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struct occurs {
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unsigned_vector constraints;
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unsigned_vector monics;
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};
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void init_cone_of_influence() {
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indexed_uint_set visited;
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unsigned_vector todo;
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vector<occurs> var2occurs;
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m_term_set.reset();
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m_mon_set.reset();
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m_constraint_set.reset();
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for (auto ci : lra.constraints().indices()) {
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auto const& c = lra.constraints()[ci];
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for (auto const& [coeff, v] : c.coeffs()) {
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var2occurs.reserve(v + 1);
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var2occurs[v].constraints.push_back(ci);
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}
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}
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for (auto const& m : m_nla_core.emons()) {
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for (auto v : m.vars()) {
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var2occurs.reserve(v + 1);
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var2occurs[v].monics.push_back(m.var());
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}
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}
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for (auto const& m : m_nla_core.m_to_refine)
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todo.push_back(m);
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for (unsigned i = 0; i < todo.size(); ++i) {
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auto v = todo[i];
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if (visited.contains(v))
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continue;
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visited.insert(v);
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var2occurs.reserve(v + 1);
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for (auto ci : var2occurs[v].constraints) {
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m_constraint_set.insert(ci);
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auto const& c = lra.constraints()[ci];
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for (auto const& [coeff, w] : c.coeffs())
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todo.push_back(w);
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}
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for (auto w : var2occurs[v].monics)
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todo.push_back(w);
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if (lra.column_corresponds_to_term(v)) {
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m_term_set.insert(v);
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lp::tv ti = lp::tv::raw(lra.column_to_reported_index(v));
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for (auto kv : lra.get_term(ti))
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todo.push_back(kv.column().index());
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}
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if (m_nla_core.is_monic_var(v)) {
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m_mon_set.insert(v);
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for (auto w : m_nla_core.emons()[v])
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todo.push_back(w);
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}
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}
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}
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/**
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\brief one-shot nlsat check.
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@ -52,24 +114,25 @@ struct solver::imp {
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*/
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lbool check() {
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SASSERT(need_check());
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m_zero = nullptr;
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m_values = nullptr;
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m_nlsat = alloc(nlsat::solver, m_limit, m_params, false);
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m_zero = alloc(scoped_anum, am());
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m_values = alloc(scoped_anum_vector, am());
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m_term_set.reset();
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m_lp2nl.reset();
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vector<nlsat::assumption, false> core;
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init_cone_of_influence();
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// add linear inequalities from lra_solver
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for (lp::constraint_index ci : s.constraints().indices()) {
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for (auto ci : m_constraint_set)
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add_constraint(ci);
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}
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// add polynomial definitions.
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for (auto const& m : m_nla_core.emons())
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add_monic_eq(m);
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for (auto const& m : m_mon_set)
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add_monic_eq(m_nla_core.emons()[m]);
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// add term definitions.
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for (unsigned i : m_term_set)
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add_term(i);
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// TBD: add variable bounds?
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lbool r = l_undef;
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try {
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@ -86,12 +149,27 @@ struct solver::imp {
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TRACE("nra",
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m_nlsat->display(tout << r << "\n");
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display(tout);
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for (auto kv : m_lp2nl)
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tout << "j" << kv.m_key << " := x" << kv.m_value << "\n";
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for (auto [j, x] : m_lp2nl) tout << "j" << j << " := x" << x << "\n";
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);
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switch (r) {
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case l_true:
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m_nla_core.set_use_nra_model(true);
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lra.init_model();
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for (lp::constraint_index ci : lra.constraints().indices())
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if (!check_constraint(ci)) {
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IF_VERBOSE(0, verbose_stream() << "constraint " << ci << " violated\n";
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lra.constraints().display(verbose_stream()));
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UNREACHABLE();
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return l_undef;
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}
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for (auto const& m : m_nla_core.emons()) {
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if (!check_monic(m)) {
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IF_VERBOSE(0, verbose_stream() << "monic " << m << " violated\n";
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lra.constraints().display(verbose_stream()));
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UNREACHABLE();
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return l_undef;
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}
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}
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break;
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case l_false: {
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lp::explanation ex;
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@ -112,12 +190,31 @@ struct solver::imp {
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return r;
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}
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void add_monic_eq_bound(mon_eq const& m) {
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if (!lra.column_has_lower_bound(m.var()) &&
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!lra.column_has_upper_bound(m.var()))
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return;
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polynomial::manager& pm = m_nlsat->pm();
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svector<polynomial::var> vars;
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for (auto v : m.vars())
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vars.push_back(lp2nl(v));
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auto v = m.var();
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polynomial::monomial_ref m1(pm.mk_monomial(vars.size(), vars.data()), pm);
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polynomial::monomial * mls[1] = { m1 };
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polynomial::scoped_numeral_vector coeffs(pm.m());
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coeffs.push_back(mpz(1));
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polynomial::polynomial_ref p(pm.mk_polynomial(1, coeffs.data(), mls), pm);
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if (lra.column_has_lower_bound(v))
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add_lb(lra.get_lower_bound(v), p, lra.get_column_lower_bound_witness(v));
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if (lra.column_has_upper_bound(v))
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add_ub(lra.get_upper_bound(v), p, lra.get_column_upper_bound_witness(v));
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}
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void add_monic_eq(mon_eq const& m) {
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polynomial::manager& pm = m_nlsat->pm();
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svector<polynomial::var> vars;
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for (auto v : m.vars()) {
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for (auto v : m.vars())
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vars.push_back(lp2nl(v));
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}
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polynomial::monomial_ref m1(pm.mk_monomial(vars.size(), vars.data()), pm);
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polynomial::monomial_ref m2(pm.mk_monomial(lp2nl(m.var()), 1), pm);
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polynomial::monomial * mls[2] = { m1, m2 };
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@ -132,7 +229,7 @@ struct solver::imp {
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}
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void add_constraint(unsigned idx) {
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auto& c = s.constraints()[idx];
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auto& c = lra.constraints()[idx];
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auto& pm = m_nlsat->pm();
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auto k = c.kind();
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auto rhs = c.rhs();
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@ -140,9 +237,9 @@ struct solver::imp {
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auto sz = lhs.size();
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svector<polynomial::var> vars;
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rational den = denominator(rhs);
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for (auto kv : lhs) {
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vars.push_back(lp2nl(kv.second));
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den = lcm(den, denominator(kv.first));
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for (auto [coeff, v] : lhs) {
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vars.push_back(lp2nl(v));
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den = lcm(den, denominator(coeff));
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}
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vector<rational> coeffs;
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for (auto kv : lhs) {
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@ -176,21 +273,128 @@ struct solver::imp {
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m_nlsat->mk_clause(1, &lit, a);
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}
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bool check_monic(mon_eq const& m) {
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scoped_anum val1(am()), val2(am());
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am().set(val1, value(m.var()));
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am().set(val2, rational::one().to_mpq());
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for (auto v : m.vars())
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am().mul(val2, value(v), val2);
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return am().eq(val1, val2);
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}
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bool check_constraint(unsigned idx) {
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auto& c = lra.constraints()[idx];
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auto& pm = m_nlsat->pm();
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auto k = c.kind();
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auto offset = -c.rhs();
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auto lhs = c.coeffs();
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auto sz = lhs.size();
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scoped_anum val(am()), mon(am());
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am().set(val, offset.to_mpq());
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for (auto [coeff, v] : lhs) {
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am().set(mon, coeff.to_mpq());
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am().mul(mon, value(v), mon);
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am().add(val, mon, val);
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}
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am().set(mon, rational::zero().to_mpq());
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switch (k) {
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case lp::lconstraint_kind::LE:
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return am().le(val, mon);
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case lp::lconstraint_kind::GE:
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return am().ge(val, mon);
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case lp::lconstraint_kind::LT:
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return am().lt(val, mon);
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case lp::lconstraint_kind::GT:
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return am().gt(val, mon);
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case lp::lconstraint_kind::EQ:
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return am().eq(val, mon);
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default:
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UNREACHABLE();
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}
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return false;
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}
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lbool check(dd::solver::equation_vector const& eqs) {
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m_values = nullptr;
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m_nlsat = alloc(nlsat::solver, m_limit, m_params, false);
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m_values = alloc(scoped_anum_vector, am());
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m_lp2nl.reset();
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m_term_set.reset();
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for (auto const& eq : eqs)
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add_eq(*eq);
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for (auto const& m : m_nla_core.emons())
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if (any_of(m.vars(), [&](lp::lpvar v) { return m_lp2nl.contains(v); }))
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add_monic_eq_bound(m);
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for (unsigned i : m_term_set)
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add_term(i);
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for (auto const& [v, w] : m_lp2nl) {
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if (lra.column_has_lower_bound(v))
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add_lb(lra.get_lower_bound(v), w, lra.get_column_lower_bound_witness(v));
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if (lra.column_has_upper_bound(v))
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add_ub(lra.get_upper_bound(v), w, lra.get_column_upper_bound_witness(v));
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}
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lbool r = l_undef;
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try {
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r = m_nlsat->check();
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}
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catch (z3_exception&) {
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if (m_limit.is_canceled()) {
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r = l_undef;
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}
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else {
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throw;
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}
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}
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switch (r) {
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case l_true:
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m_nla_core.set_use_nra_model(true);
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lra.init_model();
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for (lp::constraint_index ci : lra.constraints().indices())
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if (!check_constraint(ci))
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return l_undef;
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for (auto const& m : m_nla_core.emons()) {
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if (!check_monic(m))
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return l_undef;
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break;
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case l_false: {
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lp::explanation ex;
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vector<nlsat::assumption, false> core;
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m_nlsat->get_core(core);
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u_dependency_manager dm;
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vector<unsigned, false> lv;
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for (auto c : core)
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dm.linearize(static_cast<u_dependency*>(c), lv);
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for (auto ci : lv)
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ex.push_back(ci);
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nla::new_lemma lemma(m_nla_core, __FUNCTION__);
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lemma &= ex;
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break;
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}
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case l_undef:
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break;
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}
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return r;
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}
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lbool check(vector<dd::pdd> const& eqs) {
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m_zero = nullptr;
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m_values = nullptr;
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m_nlsat = alloc(nlsat::solver, m_limit, m_params, false);
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m_zero = alloc(scoped_anum, am());
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m_values = alloc(scoped_anum_vector, am());
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m_lp2nl.reset();
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m_term_set.reset();
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for (auto const& eq : eqs)
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add_eq(eq);
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for (auto const& m : m_nla_core.emons())
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add_monic_eq(m);
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for (auto const& [v, w] : m_lp2nl) {
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auto& ls = m_nla_core.lra;
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if (ls.column_has_lower_bound(v))
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add_lb(ls.get_lower_bound(v), w);
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if (ls.column_has_upper_bound(v))
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add_ub(ls.get_upper_bound(v), w);
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if (lra.column_has_lower_bound(v))
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add_lb(lra.get_lower_bound(v), w);
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if (lra.column_has_upper_bound(v))
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add_ub(lra.get_upper_bound(v), w);
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}
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lbool r = l_undef;
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@ -212,63 +416,21 @@ struct solver::imp {
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IF_VERBOSE(0, verbose_stream() << "check-nra " << r << "\n";
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m_nlsat->display(verbose_stream());
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for (auto const& [v, w] : m_lp2nl) {
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auto& ls = m_nla_core.lra;
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if (ls.column_has_lower_bound(v))
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verbose_stream() << "x" << w << " >= " << ls.get_lower_bound(v) << "\n";
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if (ls.column_has_upper_bound(v))
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verbose_stream() << "x" << w << " <= " << ls.get_upper_bound(v) << "\n";
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if (lra.column_has_lower_bound(v))
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verbose_stream() << "x" << w << " >= " << lra.get_lower_bound(v) << "\n";
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if (lra.column_has_upper_bound(v))
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verbose_stream() << "x" << w << " <= " << lra.get_upper_bound(v) << "\n";
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});
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return r;
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}
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lbool check_tight(dd::pdd const& eq) {
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m_zero = nullptr;
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m_nlsat = alloc(nlsat::solver, m_limit, m_params, false);
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m_zero = alloc(scoped_anum, am());
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m_lp2nl.reset();
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m_term_set.reset();
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add_eq(eq);
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for (auto const& [v, w] : m_lp2nl) {
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auto& ls = m_nla_core.lra;
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if (ls.column_has_lower_bound(v))
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add_strict_lb(ls.get_lower_bound(v), w);
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if (ls.column_has_upper_bound(v))
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add_strict_ub(ls.get_upper_bound(v), w);
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}
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lbool r = l_undef;
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try {
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r = m_nlsat->check();
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}
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catch (z3_exception&) {
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if (m_limit.is_canceled()) {
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r = l_undef;
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}
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else {
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throw;
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}
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}
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if (r == l_true)
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return r;
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IF_VERBOSE(0, verbose_stream() << "check-nra tight " << r << "\n";
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m_nlsat->display(verbose_stream());
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for (auto const& [v, w] : m_lp2nl) {
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auto& ls = m_nla_core.lra;
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if (ls.column_has_lower_bound(v))
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verbose_stream() << "x" << w << " >= " << ls.get_lower_bound(v) << "\n";
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if (ls.column_has_upper_bound(v))
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verbose_stream() << "x" << w << " <= " << ls.get_upper_bound(v) << "\n";
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});
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return r;
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void add_eq(dd::solver::equation const& eq) {
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add_eq(eq.poly(), eq.dep());
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}
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void add_eq(dd::pdd const& eq) {
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void add_eq(dd::pdd const& eq, nlsat::assumption a = nullptr) {
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dd::pdd normeq = eq;
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rational lc(1);
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for (auto const& [c, m] : eq)
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@ -280,28 +442,35 @@ struct solver::imp {
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bool is_even[1] = { false };
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polynomial::polynomial* ps[1] = { p };
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nlsat::literal lit = m_nlsat->mk_ineq_literal(nlsat::atom::kind::EQ, 1, ps, is_even);
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m_nlsat->mk_clause(1, &lit, nullptr);
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m_nlsat->mk_clause(1, &lit, a);
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}
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void add_strict_lb(lp::impq const& b, unsigned w) {
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add_bound(b.x, w, false, nlsat::atom::kind::GT);
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}
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void add_strict_ub(lp::impq const& b, unsigned w) {
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add_bound(b.x, w, false, nlsat::atom::kind::LT);
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void add_lb(lp::impq const& b, unsigned w, nlsat::assumption a = nullptr) {
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polynomial::manager& pm = m_nlsat->pm();
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polynomial::polynomial_ref p(pm.mk_polynomial(w), pm);
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add_lb(b, p, a);
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}
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void add_lb(lp::impq const& b, unsigned w) {
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add_bound(b.x, w, b.y <= 0, b.y > 0 ? nlsat::atom::kind::GT : nlsat::atom::kind::LT);
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void add_ub(lp::impq const& b, unsigned w, nlsat::assumption a = nullptr) {
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polynomial::manager& pm = m_nlsat->pm();
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polynomial::polynomial_ref p(pm.mk_polynomial(w), pm);
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add_ub(b, p, a);
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}
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void add_ub(lp::impq const& b, unsigned w) {
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add_bound(b.x, w, b.y >= 0, b.y < 0 ? nlsat::atom::kind::LT : nlsat::atom::kind::GT);
|
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|
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void add_lb(lp::impq const& b, polynomial::polynomial* p, nlsat::assumption a = nullptr) {
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add_bound(b.x, p, b.y <= 0, b.y > 0 ? nlsat::atom::kind::GT : nlsat::atom::kind::LT, a);
|
||||
}
|
||||
|
||||
void add_ub(lp::impq const& b, polynomial::polynomial* p, nlsat::assumption a = nullptr) {
|
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add_bound(b.x, p, b.y >= 0, b.y < 0 ? nlsat::atom::kind::LT : nlsat::atom::kind::GT, a);
|
||||
}
|
||||
|
||||
// w - bound < 0
|
||||
// w - bound > 0
|
||||
void add_bound(lp::mpq const& bound, unsigned w, bool neg, nlsat::atom::kind k) {
|
||||
|
||||
void add_bound(lp::mpq const& bound, polynomial::polynomial* p1, bool neg, nlsat::atom::kind k, nlsat::assumption a = nullptr) {
|
||||
polynomial::manager& pm = m_nlsat->pm();
|
||||
polynomial::polynomial_ref p1(pm.mk_polynomial(w), pm);
|
||||
polynomial::polynomial_ref p2(pm.mk_const(bound), pm);
|
||||
polynomial::polynomial_ref p(pm.sub(p1, p2), pm);
|
||||
polynomial::polynomial* ps[1] = { p };
|
||||
|
|
@ -309,7 +478,13 @@ struct solver::imp {
|
|||
nlsat::literal lit = m_nlsat->mk_ineq_literal(k, 1, ps, is_even);
|
||||
if (neg)
|
||||
lit.neg();
|
||||
m_nlsat->mk_clause(1, &lit, nullptr);
|
||||
m_nlsat->mk_clause(1, &lit, a);
|
||||
}
|
||||
|
||||
void add_bound(lp::mpq const& bound, unsigned w, bool neg, nlsat::atom::kind k, nlsat::assumption a = nullptr) {
|
||||
polynomial::manager& pm = m_nlsat->pm();
|
||||
polynomial::polynomial_ref p1(pm.mk_polynomial(w), pm);
|
||||
add_bound(bound, p1, neg, k, a);
|
||||
}
|
||||
|
||||
polynomial::polynomial* pdd2polynomial(dd::pdd const& p) {
|
||||
|
|
@ -320,7 +495,7 @@ struct solver::imp {
|
|||
polynomial::polynomial_ref hi(pdd2polynomial(p.hi()), pm);
|
||||
unsigned w, v = p.var();
|
||||
if (!m_lp2nl.find(v, w)) {
|
||||
w = m_nlsat->mk_var(false);
|
||||
w = m_nlsat->mk_var(is_int(v));
|
||||
m_lp2nl.insert(v, w);
|
||||
}
|
||||
polynomial::polynomial_ref vp(pm.mk_polynomial(w, 1), pm);
|
||||
|
|
@ -329,16 +504,15 @@ struct solver::imp {
|
|||
}
|
||||
|
||||
bool is_int(lp::var_index v) {
|
||||
return s.var_is_int(v);
|
||||
return lra.var_is_int(v);
|
||||
}
|
||||
|
||||
|
||||
polynomial::var lp2nl(lp::var_index v) {
|
||||
polynomial::var r;
|
||||
if (!m_lp2nl.find(v, r)) {
|
||||
r = m_nlsat->mk_var(is_int(v));
|
||||
m_lp2nl.insert(v, r);
|
||||
if (!m_term_set.contains(v) && s.column_corresponds_to_term(v)) {
|
||||
if (!m_term_set.contains(v) && lra.column_corresponds_to_term(v)) {
|
||||
m_term_set.insert(v);
|
||||
}
|
||||
}
|
||||
|
|
@ -346,9 +520,9 @@ struct solver::imp {
|
|||
}
|
||||
//
|
||||
void add_term(unsigned term_column) {
|
||||
lp::tv ti = lp::tv::raw(s.column_to_reported_index(term_column));
|
||||
const lp::lar_term& t = s.get_term(ti);
|
||||
// code that creates a polynomial equality between the linear coefficients and
|
||||
lp::tv ti = lp::tv::raw(lra.column_to_reported_index(term_column));
|
||||
const lp::lar_term& t = lra.get_term(ti);
|
||||
// code that creates a polynomial equality between the linear coefficients and
|
||||
// variable representing the term.
|
||||
svector<polynomial::var> vars;
|
||||
rational den(1);
|
||||
|
|
@ -367,16 +541,22 @@ struct solver::imp {
|
|||
polynomial::polynomial_ref p(pm.mk_linear(coeffs.size(), coeffs.data(), vars.data(), rational(0)), pm);
|
||||
polynomial::polynomial* ps[1] = { p };
|
||||
bool is_even[1] = { false };
|
||||
nlsat::literal lit = m_nlsat->mk_ineq_literal(nlsat::atom::kind::EQ, 1, ps, is_even);
|
||||
nlsat::literal lit = m_nlsat->mk_ineq_literal(nlsat::atom::kind::EQ, 1, ps, is_even);
|
||||
m_nlsat->mk_clause(1, &lit, nullptr);
|
||||
}
|
||||
|
||||
nlsat::anum const& value(lp::var_index v) const {
|
||||
nlsat::anum const& value(lp::var_index v) {
|
||||
polynomial::var pv;
|
||||
if (m_lp2nl.find(v, pv))
|
||||
return m_nlsat->value(pv);
|
||||
else
|
||||
return *m_zero;
|
||||
else {
|
||||
for (unsigned w = m_values->size(); w <= v; ++w) {
|
||||
scoped_anum a(am());
|
||||
am().set(a, m_nla_core.val(w).to_mpq());
|
||||
m_values->push_back(a);
|
||||
}
|
||||
return (*m_values)[v];
|
||||
}
|
||||
}
|
||||
|
||||
nlsat::anum_manager& am() {
|
||||
|
|
@ -417,8 +597,8 @@ lbool solver::check(vector<dd::pdd> const& eqs) {
|
|||
return m_imp->check(eqs);
|
||||
}
|
||||
|
||||
lbool solver::check_tight(dd::pdd const& eq) {
|
||||
return m_imp->check_tight(eq);
|
||||
lbool solver::check(dd::solver::equation_vector const& eqs) {
|
||||
return m_imp->check(eqs);
|
||||
}
|
||||
|
||||
bool solver::need_check() {
|
||||
|
|
@ -429,7 +609,7 @@ std::ostream& solver::display(std::ostream& out) const {
|
|||
return m_imp->display(out);
|
||||
}
|
||||
|
||||
nlsat::anum const& solver::value(lp::var_index v) const {
|
||||
nlsat::anum const& solver::value(lp::var_index v) {
|
||||
return m_imp->value(v);
|
||||
}
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue