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https://github.com/Z3Prover/z3
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do not use conflicts with fresh vars to create branches
Signed-off-by: Lev Nachmanson <levnach@hotmail.com>
This commit is contained in:
Lev Nachmanson
Lev Nachmanson
parent
eaf2f7f165
commit
9e8b17b5f8
2 changed files with 64 additions and 95 deletions
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@ -4,7 +4,7 @@
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#include "math/lp/lp_utils.h"
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#include <list>
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#include <queue>
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#include <util/heap.h>
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namespace lp {
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// This class represents a term with an added constant number c, in form sum {x_i*a_i} + c.
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class dioph_eq::imp {
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@ -136,7 +136,7 @@ namespace lp {
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std::list<unsigned> m_f; // F = {λ(t):t in m_f}
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// set S
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std::list<unsigned> m_s; // S = {λ(t): t in m_s}
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vector<std::pair<unsigned, unsigned>> m_k2s; // k is substituted by using equation in m_eprime[m_k2s[k].first] and m_k2s[k].second
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vector<unsigned> m_k2s; // k is substituted by using equation in m_eprime[m_k2s[k].first] and m_k2s[k].second
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// gives the order of substitution
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unsigned m_conflict_index = -1; // m_eprime[m_conflict_index] gives the conflict
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@ -159,7 +159,7 @@ namespace lp {
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m_report_branch = false;
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unsigned n_of_rows = lra.A_r().row_count();
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m_k2s.clear();
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m_k2s.resize(lra.column_count(), std::make_pair(-1,-1));
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m_k2s.resize(lra.column_count(), -1);
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m_conflict_index = -1;
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m_infeas_explanation.clear();
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lia.get_term().clear();
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@ -226,69 +226,60 @@ namespace lp {
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std::string var_str(unsigned j) {
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return std::string(is_fresh_var(j)? "~":"") + std::to_string(j);
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}
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bool has_fresh_var(const term_o & t) const {
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for (const auto & p: t) {
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if (is_fresh_var(p.j()))
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return true;
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}
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return false;
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}
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void prepare_lia_branch_report(const term_o & e, const mpq& g, const mpq new_c) {
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/* We have ep.m_e/g = 0, or sum((coff_i/g)*x_i) + new_c = 0,
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or sum((coeff_i/g)*x_i) = -new_c, where new_c is not an integer
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Then sum((coeff_i/g)*x_i) <= floor(-new_c) or sum((coeff_i/g)*x_i) >= ceil(-new_c)
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*/
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lar_term& t = lia.get_term();
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for (const auto& p: e) {
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t.add_monomial(p.coeff()/g, p.j());
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}
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lia.offset() = floor(-new_c);
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lia.is_upper() = true;
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m_report_branch = true;
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TRACE("dioph_eq", tout << "prepare branch:"; print_lar_term_L(t, tout) << " <= " << lia.offset() << std::endl;);
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}
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// returns true if no conflict is found and false otherwise
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// this function devides all cooficients, and the free constant, of the ep.m_e by the gcd of all coefficients,
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// this function devides all cooficients, and the free constant, of the ep.m_e by the gcd of all coefficients,
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// it is needed by the next steps
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// the conflict can be used to report "cuts from proofs"
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bool normalize_e_by_gcd(eprime_pair& ep) {
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TRACE("dioph_eq", print_term_o(ep.m_e, tout << "m_e:") << std::endl;
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print_dep(tout << "m_l:", ep.m_l) << std::endl;
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);
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TRACE("dioph_eq", print_eprime_entry(ep, tout) << std::endl;);
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mpq g = gcd_of_coeffs(ep.m_e);
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if (g.is_zero()) {
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SASSERT(ep.m_e.c().is_zero());
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if (g.is_zero() || g.is_one()) {
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SASSERT(g.is_one() || ep.m_e.c().is_zero());
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return true;
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}
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if (g.is_one())
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return true;
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TRACE("dioph_eq", tout << "g:" << g << std::endl;);
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mpq new_c = ep.m_e.c() / g;
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if (!new_c.is_int()) {
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TRACE("dioph_eq",
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print_term_o(ep.m_e, tout << "conflict m_e:") << std::endl;
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tout << "g:" << g << std::endl;
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print_dep(tout << "m_l:", ep.m_l) << std::endl;
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tout << "S:\n";
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for (const auto& t : m_sigma) {
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tout << "x" << var_str(t.m_key) << " -> ";
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print_term_o(t.m_value, tout) << std::endl;
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}
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);
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/* We have ep.m_e/g = 0, or sum((coff_i/g)*x_i) + new_c = 0,
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or sum((coeff_i/g)*x_i) = -new_c, where new_c is not an integer
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Then sum((coeff_i/g)*x_i) <= floor(-new_c) or sum((coeff_i/g)*x_i) >= ceil(-new_c)
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*/
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if (lra.settings().stats().m_dio_conflicts % lra.settings().dio_cut_from_proof_period() == 0) {
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bool has_fresh = false;
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for (const auto& p : ep.m_e)
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if ((has_fresh = is_fresh_var(p.j())))
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break;
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if (!has_fresh) { // consider remove all fresh variables in a copy of m_e and report the conflict
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// prepare int_solver for reporting
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lar_term& t = lia.get_term();
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for (const auto& p: ep.m_e) {
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t.add_monomial(p.coeff()/g, p.j());
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}
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lia.offset() = floor(-new_c);
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lia.is_upper() = true;
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m_report_branch = true;
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TRACE("dioph_eq", tout << "prepare branch:"; print_lar_term_L(t, tout) << " <= " << lia.offset() << std::endl;);
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}
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}
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return false;
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} else {
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mpq c_g = ep.m_e.c() / g;
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if (c_g.is_int()) {
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for (auto& p: ep.m_e.coeffs()) {
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p.m_value /= g;
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}
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ep.m_e.c() = new_c;
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ep.m_e.c() = c_g;
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// ep.m_l *= (1/g);
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TRACE("dioph_eq",
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tout << "ep_m_e:"; print_term_o(ep.m_e, tout) << std::endl;
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tout << "ep.ml:";
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print_dep(tout, ep.m_l) << std::endl;);
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TRACE("dioph_eq", tout << "ep_m_e:"; print_eprime_entry(ep, tout) << std::endl;);
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return true;
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}
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return true;
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// c_g is not integral
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if (lra.settings().stats().m_dio_conflicts % lra.settings().dio_cut_from_proof_period() == 0 &&
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!has_fresh_var(ep.m_e))
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prepare_lia_branch_report(ep.m_e, g, c_g);
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return false;
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}
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// returns true if no conflict is found and false otherwise
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bool normalize_by_gcd() {
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for (unsigned l: m_f) {
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@ -330,18 +321,18 @@ namespace lp {
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if (is_fresh_var(p.j())) {
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continue;
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}
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if (m_k2s[p.j()].first != null_lpvar)
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if (m_k2s[p.j()] != null_lpvar)
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q.push(p.j());
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}
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}
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const eprime_pair& k_th_entry(unsigned k) const {
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return m_eprime[m_k2s[k].first];
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return m_eprime[m_k2s[k]];
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}
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const unsigned sub_index(unsigned k) const {
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return m_k2s[k].first;
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return m_k2s[k];
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}
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void substitude_term_on_q_with_S_for_tightening(std::queue<unsigned> &q, term_o& t, u_dependency* &dep) {
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@ -387,13 +378,15 @@ namespace lp {
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}
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return lia_move::undef;
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}
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void print_queue(std::queue<unsigned> q, std::ostream& out) {
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std::ostream& print_queue(std::queue<unsigned> q, std::ostream& out) {
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out << "qu: ";
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while (!q.empty()) {
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out << q.front() << " ";
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q.pop();
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}
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out<< std::endl;
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return out;
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}
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// j is the index of the column representing a term
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// return true if there is a change
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@ -512,7 +505,7 @@ namespace lp {
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tout << "bound_dep:\n";print_dep(tout, dep) << std::endl;);
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}
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lia_move check() {
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lia_move check() {
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init();
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while(m_f.size()) {
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if (!normalize_by_gcd()) {
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@ -624,7 +617,7 @@ namespace lp {
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auto & eh = e_pair.m_e;
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// xt is the fresh variable
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unsigned xt = m_last_fresh_x_var++;
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TRACE("dioph_eq", tout << "introduce fresh xt:" << "~x"<< fresh_index(xt) << std::endl;
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TRACE("dioph_eq", tout << "introduce fresh xt:" << "x"<< var_str(xt) << std::endl;
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tout << "eh:"; print_term_o(eh,tout) << std::endl;);
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/* Let eh = sum (a_i*x_i) + c
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For each i != k, let a_i = a_qi*ahk + a_ri, and let c = c_q * ahk + c_r
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@ -665,14 +658,19 @@ namespace lp {
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// the term to eliminate the fresh variable
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term_o xt_subs = xt_term.clone();
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xt_subs.add_monomial(mpq(1), xt);
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TRACE("dioph_eq", tout << "xt_subs: x~"<< fresh_index(xt) << " -> "; print_term_o(xt_subs, tout) << std::endl;);
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TRACE("dioph_eq", tout << "xt_subs: x"<< var_str(xt) << " -> "; print_term_o(xt_subs, tout) << std::endl;);
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m_sigma.insert(xt, xt_subs);
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}
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std::ostream& print_eprime_entry(unsigned i, std::ostream& out) {
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out << "m_eprime[" << i << "]:{\n";
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print_term_o(m_eprime[i].m_e, out << "\tm_e:") << "," << std::endl;
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// print_dep(out<< "\tm_l:", m_eprime[i].m_l) << "\n"
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out << "m_eprime[" << i << "]:";
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return print_eprime_entry(m_eprime[i], out);
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}
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std::ostream& print_eprime_entry(const eprime_pair& e, std::ostream& out) {
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out << "{\n";
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print_term_o(e.m_e, out << "\tm_e:") << "," << std::endl;
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print_dep(out<< "\tm_l:", e.m_l) << "\n";
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out << "}"<< std::endl;
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return out;
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}
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@ -680,11 +678,11 @@ namespace lp {
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// k is the index of the index of the variable with the coefficient +-1 that is being substituted
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void move_entry_from_f_to_s(unsigned k, std::list<unsigned>::iterator it) {
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if (k >= m_k2s.size()) { // k is a fresh variable
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m_k2s.resize(k+1, std::make_pair(-1,-1));
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m_k2s.resize(k+1, -1 );
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}
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m_s.push_back(*it);
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TRACE("dioph_eq", tout << "removed " << *it << "th entry from F" << std::endl;);
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m_k2s[k] = std::make_pair(*it, static_cast<unsigned>(m_s.size()));
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m_k2s[k] = *it;
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m_f.erase(it);
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}
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@ -731,36 +729,6 @@ namespace lp {
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TRACE("dioph_eq", lra.print_expl(tout, ex););
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}
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unsigned fresh_index(unsigned j) const {return UINT_MAX - j;}
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struct subs_lt {
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const vector<std::pair<unsigned, unsigned>> & m_order;
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subs_lt(const vector<std::pair<unsigned, unsigned>>& order) : m_order(order){}
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bool operator()(unsigned v1, unsigned v2) const {
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return m_order[v1].second < m_order[v2].second;
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}
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};
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void remove_fresh_variables(term_o& t) {
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heap<subs_lt> q(static_cast<int>(lra.column_count()), subs_lt(m_k2s));
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for (auto p : t) {
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if (is_fresh_var(p.j())) {
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q.insert(p.j());
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}
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}
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CTRACE("dioph_eq_fresh", q.empty() == false, print_term_o(t, tout)<< std::endl);
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while (!q.empty()) {
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unsigned j = q.erase_min();
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const term_o& sub_t = m_sigma.find(j);
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TRACE("dioph_eq_fresh", tout << "x~" << fresh_index(j) << "; sub_t:"; print_term_o(sub_t, tout) << std::endl;);
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t.substitute_var_with_term(sub_t, j);
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TRACE("dioph_eq_fresh", tout << "sub_t:"; print_term_o(sub_t, tout) << std::endl;
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tout << "after sub:";print_term_o(t, tout) << std::endl;);
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for (auto p : sub_t)
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if (is_fresh_var(p.j()))
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q.insert(p.j());
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}
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}
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bool is_fresh_var(unsigned j) const {
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return j >= lra.column_count();
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}
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@ -161,6 +161,7 @@ struct statistics {
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st.update("arith-nla-lemmas", m_nla_lemmas);
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st.update("arith-nra-calls", m_nra_calls);
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st.update("arith-bounds-improvements", m_nla_bounds_improvements);
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st.update("arith-lp-dio-conflicts", m_dio_conflicts);
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st.copy(m_st);
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}
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};
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