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https://github.com/Z3Prover/z3
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simpler order lemma
Signed-off-by: Lev Nachmanson <levnach@hotmail.com>
This commit is contained in:
Lev Nachmanson
parent
1959710a5b
commit
cbe920756b
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@ -172,9 +172,9 @@ struct solver::imp {
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lp::impq vv(lpvar j) const { return m_lar_solver.get_column_value(j); }
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lpvar var(const rooted_mon& rm) const {return m_monomials[rm.orig().m_i].var(); }
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lpvar var(const rooted_mon& rm) const {return m_monomials[rm.orig_index()].var(); }
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rational vvr(const rooted_mon& rm) const { return vvr(m_monomials[rm.orig().m_i].var()) * rm.orig().m_sign; }
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rational vvr(const rooted_mon& rm) const { return vvr(m_monomials[rm.orig_index()].var()) * rm.orig_sign(); }
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rational vvr(const factor& f) const { return vvr(var(f)); }
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@ -196,9 +196,15 @@ struct solver::imp {
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// by the flip_sign
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rational flip_sign(const factor& f) const {
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return f.is_var()?
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rational(1) : m_rm_table.vec()[f.index()].orig().sign();
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flip_sign_of_var(f.index()) : m_rm_table.vec()[f.index()].orig_sign();
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}
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rational flip_sign_of_var(lpvar j) const {
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rational sign(1);
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m_vars_equivalence.map_to_root(j, sign);
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return sign;
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}
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// the value of the rooted monomias is equal to the value of the variable multiplied
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// by the flip_sign
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rational flip_sign(const rooted_mon& m) const {
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@ -648,60 +654,6 @@ struct solver::imp {
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explain(n, current_expl());
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TRACE("nla_solver", print_lemma(tout););
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}
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// the value of the i-th monomial has to be equal to the value of the k-th monomial modulo sign
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// but it is not the case in the model
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// abs_vars_key is formed by m_vars_equivalence.get_abs_root_for_var(k), where
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// k runs over m.
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void generate_sign_lemma_model_based(const monomial& m, const monomial& n, const rational& sign) {
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TRACE("nla_solver",);
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if (sign.is_zero()) {
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// either m or n has to be equal zero, but it is not the case
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SASSERT(!vvr(m).is_zero() || !vvr(n).is_zero());
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if (!vvr(m).is_zero())
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generate_zero_lemmas(m);
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if (!vvr(n).is_zero())
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generate_zero_lemmas(n);
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return;
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}
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add_empty_lemma();
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unsigned_vector mvars(m.vars());
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unsigned_vector nvars(n.vars());
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divide_by_common_factor(mvars, nvars);
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TRACE("nla_solver",
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tout << "m = "; print_monomial_with_vars(m, tout);
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tout << "n = "; print_monomial_with_vars(n, tout);
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tout << "mvars = "; print_product(mvars, tout);
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tout << "\nnvars = "; print_product(nvars, tout); tout << "\n";
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);
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std::unordered_map<unsigned, unsigned_vector> map;
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const unsigned_vector key = get_abs_key(mvars);
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// create and fill the map from "abs root vars" to lists,
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// all elementl of map[j] have the same abs vvr() as vvr(j)
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for (lpvar j : key) {
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map[j] = unsigned_vector();
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}
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for (unsigned j : mvars) {
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lpvar k = m_vars_equivalence.get_abs_root_for_var(abs(vvr(j)));
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map.find(k)->second.push_back(j);
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}
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for (unsigned j : nvars) {
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lpvar k = m_vars_equivalence.get_abs_root_for_var(abs(vvr(j)));
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auto it = map.find(k);
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lpvar jj = it->second.back();
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rational s = vvr(jj) == vvr(j)? rational(1) : rational(-1);
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// todo : check that each pair is processed only once
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mk_ineq(j, -s, jj, llc::NE);
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it->second.pop_back();
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}
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mk_ineq(m.var(), -sign, n.var(), llc::EQ);
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TRACE("nla_solver", print_lemma(tout););
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}
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lemma& current_lemma() { return m_lemma_vec->back(); }
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vector<ineq>& current_ineqs() { return current_lemma().ineqs(); }
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lp::explanation& current_expl() { return current_lemma().expl(); }
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@ -1053,7 +1005,7 @@ struct solver::imp {
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std::ostream & print_ineqs(const lemma& l, std::ostream & out) const {
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std::unordered_set<lpvar> vars;
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out << "lemma: ";
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out << "ineqs: ";
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for (unsigned i = 0; i < l.ineqs().size(); i++) {
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auto & in = l.ineqs()[i];
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print_ineq(in, out);
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@ -1074,8 +1026,11 @@ struct solver::imp {
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if (f[k].is_var())
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print_var(f[k].index(), out);
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else {
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out << "(";
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print_product(m_rm_table.vec()[f[k].index()].vars(), out);
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out << ")";
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}
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if (k < f.size() - 1)
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out << "*";
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}
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@ -1909,81 +1864,6 @@ struct solver::imp {
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);
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}
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bool divide(const rooted_mon& bc, const factor& c, factor & b) const {
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svector<lpvar> c_vars = sorted_vars(c);
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TRACE("nla_solver_div",
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tout << "c_vars = ";
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print_product(c_vars, tout);
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tout << "\nbc_vars = ";
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print_product(bc.vars(), tout););
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if (!lp::is_proper_factor(c_vars, bc.vars()))
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return false;
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auto b_vars = lp::vector_div(bc.vars(), c_vars);
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TRACE("nla_solver_div", tout << "b_vars = "; print_product(b_vars, tout););
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SASSERT(b_vars.size() > 0);
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if (b_vars.size() == 1) {
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b = factor(b_vars[0]);
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return true;
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}
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auto it = m_rm_table.map().find(b_vars);
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if (it == m_rm_table.map().end()) {
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TRACE("nla_solver_div", tout << "not in rooted";);
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return false;
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}
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b = factor(it->second, factor_type::RM);
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TRACE("nla_solver_div", tout << "success div:"; print_factor(b, tout););
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return true;
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}
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void negate_factor_equality(const factor& c,
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const factor& d) {
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if (c == d)
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return;
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lpvar i = var(c);
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lpvar j = var(d);
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auto iv = vvr(i), jv = vvr(j);
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SASSERT(abs(iv) == abs(jv));
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if (iv == jv) {
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mk_ineq(i, -rational(1), j, llc::NE);
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} else { // iv == -jv
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mk_ineq(i, j, llc::NE, current_lemma());
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}
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}
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void negate_factor_relation(const rational& a_sign, const factor& a, const rational& b_sign, const factor& b) {
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rational a_fs = flip_sign(a);
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rational b_fs = flip_sign(b);
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llc cmp = a_sign*vvr(a) < b_sign*vvr(b)? llc::GE : llc::LE;
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mk_ineq(a_fs*a_sign, var(a), - b_fs*b_sign, var(b), cmp);
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}
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// |c_sign| = |d_sign| = 1, and c*c_sign = d*d_sign > 0
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// a*c_sign > b*d_sign => ac > bd.
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// The sign ">" above is replaced by ab_cmp
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void generate_ol(const rooted_mon& ac,
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const factor& a,
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int c_sign,
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const factor& c,
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const rooted_mon& bd,
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const factor& b,
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int d_sign,
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const factor& d,
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llc ab_cmp) {
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add_empty_lemma();
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mk_ineq(rational(c_sign) * flip_sign(c), var(c), llc::LE);
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negate_factor_equality(c, d);
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negate_factor_relation(rational(c_sign), a, rational(d_sign), b);
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mk_ineq(flip_sign(ac), var(ac), -flip_sign(bd), var(bd), ab_cmp);
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explain(ac, current_expl());
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explain(a, current_expl());
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explain(bd, current_expl());
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explain(b, current_expl());
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explain(c, current_expl());
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explain(d, current_expl());
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TRACE("nla_solver", print_lemma(tout););
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}
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std::unordered_set<lpvar> collect_vars( const lemma& l) {
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std::unordered_set<lpvar> vars;
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for (const auto& i : current_lemma().ineqs()) {
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@ -2013,6 +1893,8 @@ struct solver::imp {
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}
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void print_lemma(std::ostream& out) {
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static int n = 0;
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out << "lemma:" << ++n << " ";
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print_ineqs(current_lemma(), out);
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print_explanation(current_expl(), out);
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std::unordered_set<lpvar> vars = collect_vars(current_lemma());
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@ -2022,203 +1904,119 @@ struct solver::imp {
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}
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}
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bool get_cd_signs_for_ol(const rational& c, const rational& d, int& c_sign, int & d_sign) const {
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if (c.is_zero() || d.is_zero())
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return false;
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if (c == d) {
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if (c.is_pos()) {
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c_sign = d_sign = 1;
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}
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else {
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c_sign = d_sign = -1;
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}
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return true;
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} else if (c == -d){
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if (c.is_pos()) {
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c_sign = 1;
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d_sign = -1;
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}
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else {
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c_sign = -1;
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d_sign = 1;
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}
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return true;
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}
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return false;
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}
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bool order_lemma_on_ac_and_bd_and_factors(const rooted_mon& ac,
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const factor& a,
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const factor& c,
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const rooted_mon& bd,
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const factor& b,
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const factor& d) {
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SASSERT(abs(vvr(c)) == abs(vvr(d)));
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auto cv = vvr(c); auto dv = vvr(d);
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int c_sign, d_sign;
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if (!get_cd_signs_for_ol(cv, dv, c_sign, d_sign))
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return false;
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SASSERT(cv*c_sign == dv*d_sign && (dv*d_sign).is_pos() && abs(c_sign) == 1 &&
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abs(d_sign) == 1);
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auto av = vvr(a)*rational(c_sign); auto bv = vvr(b)*rational(d_sign);
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auto acv = vvr(ac); auto bdv = vvr(bd);
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// ab is a factorization of rm.vars()
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// if, say, ab = -3, when a = -2, and b = 2
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// then we create a lemma
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// b <= 0 or a > -2 or ab <= -2b
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void order_lemma_on_factorization(const rooted_mon& rm, const factorization& ab) {
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const monomial& m = m_monomials[rm.orig_index()];
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rational sign = rm.orig_sign();
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for(factor f: ab)
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sign *= flip_sign(f);
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const rational & fv = vvr(ab[0]) * vvr(ab[1]);
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const rational mv = sign * vvr(m);
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TRACE("nla_solver",
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tout << "ac = ";
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print_rooted_monomial_with_vars(ac, tout);
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tout << "\nbd = ";
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print_rooted_monomial_with_vars(bd, tout);
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tout << "\na = ";
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print_factor_with_vars(a, tout);
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tout << ", \nb = ";
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print_factor_with_vars(b, tout);
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tout << "\nc = ";
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print_factor_with_vars(c, tout);
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tout << ", \nd = ";
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print_factor_with_vars(d, tout);
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);
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if (av < bv){
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if(!(acv < bdv)) {
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generate_ol(ac, a, c_sign, c, bd, b, d_sign, d, llc::LT);
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return true;
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}
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} else if (av > bv){
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if(!(acv > bdv)) {
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generate_ol(ac, a, c_sign, c, bd, b, d_sign, d, llc::GT);
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return true;
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}
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}
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return false;
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}
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// a > b && c > 0 && d = c => ac > bd
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// ac is a factorization of m_monomials[i_mon]
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// ac[k] plays the role of c
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bool order_lemma_on_ac_and_bd(const rooted_mon& rm_ac,
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const factorization& ac_f,
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unsigned k,
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const rooted_mon& rm_bd,
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const factor& d) {
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TRACE("nla_solver", tout << "rm_ac = ";
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print_rooted_monomial(rm_ac, tout);
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tout << "\nrm_bd = ";
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print_rooted_monomial(rm_bd, tout);
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tout << "\nac_f[k] = ";
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print_factor_with_vars(ac_f[k], tout);
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tout << "\nd = ";
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print_factor_with_vars(d, tout););
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SASSERT(abs(vvr(ac_f[k])) == abs(vvr(d)));
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factor b;
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if (!divide(rm_bd, d, b)){
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return false;
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}
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return order_lemma_on_ac_and_bd_and_factors(rm_ac, ac_f[(k + 1) % 2], ac_f[k], rm_bd, b, d);
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}
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void maybe_add_a_factor(lpvar i,
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const factor& c,
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std::unordered_set<lpvar>& found_vars,
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std::unordered_set<unsigned>& found_rm,
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vector<factor> & r) const {
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SASSERT(abs(vvr(i)) == abs(vvr(c)));
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auto it = m_var_to_its_monomial.find(i);
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if (it == m_var_to_its_monomial.end()) {
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i = m_vars_equivalence.map_to_root(i);
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if (try_insert(i, found_vars)) {
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r.push_back(factor(i, factor_type::VAR));
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}
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} else {
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SASSERT(m_monomials[it->second].var() == i && abs(vvr(m_monomials[it->second])) == abs(vvr(c)));
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const index_with_sign & i_s = m_rm_table.get_rooted_mon(it->second);
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unsigned rm_i = i_s.index();
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// SASSERT(abs(vvr(m_rm_table.vec()[i])) == abs(vvr(c)));
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if (try_insert(rm_i, found_rm)) {
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r.push_back(factor(rm_i, factor_type::RM));
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TRACE("nla_solver", tout << "inserting factor = "; print_factor_with_vars(factor(rm_i, factor_type::RM), tout); );
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}
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tout << "ab.size()=" << ab.size() << "\n";
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tout << "we should have sign*vvr(m):" << mv << "=(" << sign << ")*(" << vvr(m) <<") to be equal to " << " vvr(ab[0])*vvr(ab[1]):" << fv << "\n";);
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if (mv == fv)
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return;
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bool gt = mv > fv;
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TRACE("nla_solver_f", tout << "m="; print_monomial_with_vars(m, tout); tout << "\nfactorization="; print_factorization(ab, tout););
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for (unsigned j = 0, k = 1; j < 2; j++, k--) {
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order_lemma_on_ab(m, sign, var(ab[k]), var(ab[j]), gt);
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explain(ab, current_expl()); explain(m, current_expl());
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}
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}
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// collect all vars and rooted monomials with the same absolute
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// value as the absolute value af c and return them as factors
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vector<factor> factors_with_the_same_abs_val(const factor& c) const {
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vector<factor> r;
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std::unordered_set<lpvar> found_vars;
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std::unordered_set<unsigned> found_rm;
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TRACE("nla_solver", tout << "c = "; print_factor_with_vars(c, tout););
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for (lpvar i : m_vars_equivalence.get_vars_with_the_same_abs_val(vvr(c))) {
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maybe_add_a_factor(i, c, found_vars, found_rm, r);
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}
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return r;
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}
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bool order_lemma_on_ad(const rooted_mon& rm, const factorization& ac, unsigned k, const factor & d) {
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TRACE("nla_solver", tout << "d = "; print_factor_with_vars(d, tout); );
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SASSERT(abs(vvr(d)) == abs(vvr(ac[k])));
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if (d.is_var()) {
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TRACE("nla_solver", tout << "var(d) = " << var(d););
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for (unsigned rm_bd : m_rm_table.var_map()[d.index()]) {
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TRACE("nla_solver", );
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if (order_lemma_on_ac_and_bd(rm ,ac, k, m_rm_table.vec()[rm_bd], d)) {
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return true;
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}
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}
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// if gt is true we need to deduce ab <= vvr(b)*a
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void order_lemma_on_ab_gt(const monomial& m, const rational& sign, lpvar a, lpvar b) {
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SASSERT(sign * vvr(m) > vvr(a) * vvr(b));
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add_empty_lemma();
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if (vvr(a).is_pos()) {
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TRACE("nla_solver", tout << "a is pos\n";);
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//negate a > 0
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mk_ineq(a, llc::LE);
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// negate b <= vvr(b)
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mk_ineq(b, llc::GT, vvr(b));
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// ab <= vvr(b)a
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mk_ineq(sign, m.var(), -vvr(b), a, llc::LE);
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} else {
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for (unsigned rm_b : m_rm_table.proper_factors()[d.index()]) {
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if (order_lemma_on_ac_and_bd(rm , ac, k, m_rm_table.vec()[rm_b], d)) {
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return true;
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}
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}
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TRACE("nla_solver", tout << "a is neg\n";);
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SASSERT(vvr(a).is_neg());
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//negate a < 0
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mk_ineq(a, llc::GE);
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// negate b >= vvr(b)
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mk_ineq(b, llc::LT, vvr(b));
|
||||
// ab <= vvr(b)a
|
||||
mk_ineq(sign, m.var(), -vvr(b), a, llc::LE);
|
||||
}
|
||||
return false;
|
||||
TRACE("nla_solver", print_lemma(tout););
|
||||
}
|
||||
// we need to deduce ab >= vvr(b)*a
|
||||
void order_lemma_on_ab_lt(const monomial& m, const rational& sign, lpvar a, lpvar b) {
|
||||
SASSERT(sign * vvr(m) < vvr(a) * vvr(b));
|
||||
add_empty_lemma();
|
||||
if (vvr(a).is_pos()) {
|
||||
//negate a > 0
|
||||
mk_ineq(a, llc::LE);
|
||||
// negate b >= vvr(b)
|
||||
mk_ineq(b, llc::LT, vvr(b));
|
||||
// ab <= vvr(b)a
|
||||
mk_ineq(sign, m.var(), -vvr(b), a, llc::GE);
|
||||
} else {
|
||||
SASSERT(vvr(a).is_neg());
|
||||
//negate a < 0
|
||||
mk_ineq(a, llc::GE);
|
||||
// negate b <= vvr(b)
|
||||
mk_ineq(b, llc::GT, vvr(b));
|
||||
// ab >= vvr(b)a
|
||||
mk_ineq(sign, m.var(), -vvr(b), a, llc::GE);
|
||||
}
|
||||
TRACE("nla_solver", print_lemma(tout););
|
||||
}
|
||||
|
||||
|
||||
void order_lemma_on_ab(const monomial& m, const rational& sign, lpvar a, lpvar b, bool gt) {
|
||||
if (gt)
|
||||
order_lemma_on_ab_gt(m, sign, a, b);
|
||||
else
|
||||
order_lemma_on_ab_lt(m, sign, a, b);
|
||||
}
|
||||
|
||||
// void order_lemma_on_ab(const monomial& m, const rational& sign, lpvar a, lpvar b, bool gt) {
|
||||
// add_empty_lemma();
|
||||
// if (gt) {
|
||||
// if (vvr(a).is_pos()) {
|
||||
// //negate a > 0
|
||||
// mk_ineq(a, llc::LE);
|
||||
// // negate b >= vvr(b)
|
||||
// mk_ineq(b, llc::LT, vvr(b));
|
||||
// // ab <= vvr(b)a
|
||||
// mk_ineq(sign, m.var(), -vvr(b), a, llc::LE);
|
||||
// } else {
|
||||
// SASSERT(vvr(a).is_neg());
|
||||
// //negate a < 0
|
||||
// mk_ineq(a, llc::GE);
|
||||
// // negate b <= vvr(b)
|
||||
// mk_ineq(b, llc::GT, vvr(b));
|
||||
// // ab < vvr(b)a
|
||||
// mk_ineq(sign, m.var(), -vvr(b), a, llc::LE); }
|
||||
// }
|
||||
// }
|
||||
|
||||
// a > b && c > 0 => ac > bc
|
||||
// ac is a factorization of rm.vars()
|
||||
// ac[k] plays the role of c
|
||||
bool order_lemma_on_factor(const rooted_mon& rm, const factorization& ac, unsigned k) {
|
||||
auto c = ac[k];
|
||||
TRACE("nla_solver", tout << "k = " << k << ", c = "; print_factor_with_vars(c, tout); );
|
||||
|
||||
for (const factor & d : factors_with_the_same_abs_val(c)) {
|
||||
if (order_lemma_on_ad(rm, ac, k, d))
|
||||
return true;
|
||||
}
|
||||
return false;
|
||||
}
|
||||
|
||||
// a > b && c == d => ac > bd
|
||||
// ac is a factorization of rm.vars()
|
||||
bool order_lemma_on_factorization(const rooted_mon& rm, const factorization& ac) {
|
||||
SASSERT(ac.size() == 2);
|
||||
TRACE("nla_solver", tout << "rm = "; print_rooted_monomial(rm, tout);
|
||||
tout << ", factorization = "; print_factorization(ac, tout););
|
||||
for (unsigned k = 0; k < ac.size(); k++) {
|
||||
const rational & v = vvr(ac[k]);
|
||||
if (v.is_zero())
|
||||
continue;
|
||||
|
||||
if (order_lemma_on_factor(rm, ac, k)) {
|
||||
TRACE("nla_solver", print_lemma(tout););
|
||||
return true;
|
||||
}
|
||||
}
|
||||
return false;
|
||||
}
|
||||
|
||||
// a > b && c > 0 => ac > bc
|
||||
bool order_lemma_on_monomial(const rooted_mon& rm) {
|
||||
void order_lemma_on_monomial(const rooted_mon& rm) {
|
||||
TRACE("nla_solver_details",
|
||||
tout << "rm = "; print_product(rm, tout);
|
||||
tout << ", orig = "; print_monomial(m_monomials[rm.orig_index()], tout);
|
||||
);
|
||||
for (auto ac : factorization_factory_imp(rm.vars(), *this)) {
|
||||
if (ac.size() == 2 && order_lemma_on_factorization(rm, ac))
|
||||
return true;
|
||||
if (ac.size() != 2)
|
||||
continue;
|
||||
order_lemma_on_factorization(rm, ac);
|
||||
if (done())
|
||||
break;
|
||||
}
|
||||
return false;
|
||||
}
|
||||
|
||||
void order_lemma() {
|
||||
|
|
|
|||
Loading…
Reference in a new issue