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https://github.com/Z3Prover/z3
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Polysat: add two more prototype rules (#5355)
* Add try_div to PDDs * x>y is false when x==y * First version of the other two prototype rules * More band-aid fixes...
This commit is contained in:
Jakob Rath
GitHub
parent
3e1cfcd538
commit
c4963f4381
7 changed files with 239 additions and 17 deletions
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@ -40,6 +40,9 @@ namespace polysat {
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LOG("New constraint: " << show_deref(c));
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}
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}
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else {
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LOG("No lemma");
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}
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m_var = null_var;
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m_cjust_v.reset();
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@ -72,7 +75,7 @@ namespace polysat {
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/// [x] zx > yx ==> ...
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clause_ref conflict_explainer::by_ugt_x() {
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LOG_H3("Try zx > yx");
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LOG_H3("Try zx > yx where x := v" << m_var);
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for (auto* c : m_conflict.units())
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LOG("Constraint: " << show_deref(c));
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for (auto* c : m_conflict.clauses())
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@ -82,8 +85,8 @@ namespace polysat {
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for (auto* c : m_conflict.units()) {
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if (!c->is_ule())
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continue;
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pdd lhs = c->to_ule().lhs();
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pdd rhs = c->to_ule().rhs();
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pdd const& lhs = c->to_ule().lhs();
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pdd const& rhs = c->to_ule().rhs();
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if (lhs.degree(m_var) != 1)
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continue;
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if (rhs.degree(m_var) != 1)
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@ -127,13 +130,179 @@ namespace polysat {
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return nullptr;
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}
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/// [y] y >= z' /\ zx > yx ==> ...
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/// [y] z' <= y /\ zx > yx ==> ...
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clause_ref conflict_explainer::by_ugt_y() {
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LOG_H3("Try z' <= y && zx > yx where y := v" << m_var);
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for (auto* c : m_conflict.units())
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LOG("Constraint: " << show_deref(c));
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for (auto* c : m_conflict.clauses())
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LOG("Clause: " << show_deref(c));
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pdd const y = m_solver.var(m_var);
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// Collect constraints of shape "_ <= y"
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ptr_vector<constraint> ds;
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for (auto* d : m_conflict.units()) {
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if (!d->is_ule())
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continue;
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if (!d->is_positive())
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continue;
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pdd const& rhs = d->to_ule().rhs();
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// TODO: a*y where 'a' divides 'x' should also be easy to handle (assuming for now they're numbers)
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// TODO: also z' < y should follow the same pattern.
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if (rhs != y)
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continue;
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LOG("z' <= y candidate: " << show_deref(d));
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ds.push_back(d);
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}
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if (ds.empty())
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return nullptr;
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// Find constraint of shape: zx > yx
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for (auto* c : m_conflict.units()) {
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if (!c->is_ule())
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continue;
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pdd const& lhs = c->to_ule().lhs();
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pdd const& rhs = c->to_ule().rhs();
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if (rhs.degree(m_var) != 1)
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continue;
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pdd x = lhs;
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pdd rest = lhs;
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rhs.factor(m_var, 1, x, rest);
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if (!rest.is_zero())
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continue;
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// TODO: in principle, 'x' could be any polynomial. However, we need to divide the lhs by x, and we don't have general polynomial division yet.
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// so for now we just allow the form 'value*variable'.
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// (extension to arbitrary monomials for 'x' should be fairly easy too)
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if (!x.is_unary())
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continue;
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unsigned x_var = x.var();
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rational x_coeff = x.hi().val();
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pdd xz = lhs;
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if (!lhs.try_div(x_coeff, xz))
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continue;
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pdd z = lhs;
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xz.factor(x_var, 1, z, rest);
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if (!rest.is_zero())
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continue;
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unsigned const lvl = c->level();
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if (c->is_positive()) {
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// zx <= yx
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NOT_IMPLEMENTED_YET();
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}
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else {
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SASSERT(c->is_negative());
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// zx > yx
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LOG("zx > yx: " << show_deref(c));
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// TODO: for now, we just choose the first of the other constraints
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constraint* d = ds[0];
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SASSERT(d->is_ule() && d->is_positive());
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pdd const& z_prime = d->to_ule().lhs();
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unsigned const p = m_solver.size(m_var);
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clause_builder clause(m_solver);
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// Omega^*(x, y)
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push_omega_mul(clause, lvl, p, x, y);
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// zx > z'x
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constraint_ref zx_gt_zpx = m_solver.m_constraints.ult(lvl, pos_t, z*x, z_prime*x, null_dep());
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LOG("zx>z'x: " << show_deref(zx_gt_zpx));
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clause.push_new_constraint(std::move(zx_gt_zpx));
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return clause.build(lvl, {c->dep(), m_solver.m_dm});
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}
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}
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return nullptr;
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}
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/// [z] y' >= z /\ zx > yx ==> ...
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/// [z] z <= y' /\ zx > yx ==> ...
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clause_ref conflict_explainer::by_ugt_z() {
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LOG_H3("Try z <= y' && zx > yx where z := v" << m_var);
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for (auto* c : m_conflict.units())
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LOG("Constraint: " << show_deref(c));
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for (auto* c : m_conflict.clauses())
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LOG("Clause: " << show_deref(c));
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pdd const z = m_solver.var(m_var);
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// Collect constraints of shape "z <= _"
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ptr_vector<constraint> ds;
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for (auto* d : m_conflict.units()) {
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if (!d->is_ule())
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continue;
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if (!d->is_positive())
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continue;
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pdd const& lhs = d->to_ule().lhs();
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// TODO: a*y where 'a' divides 'x' should also be easy to handle (assuming for now they're numbers)
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// TODO: also z < y' should follow the same pattern.
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if (lhs != z)
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continue;
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LOG("z <= y' candidate: " << show_deref(d));
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ds.push_back(d);
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}
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if (ds.empty())
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return nullptr;
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// Find constraint of shape: zx > yx
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for (auto* c : m_conflict.units()) {
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if (!c->is_ule())
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continue;
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pdd const& lhs = c->to_ule().lhs();
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pdd const& rhs = c->to_ule().rhs();
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if (lhs.degree(m_var) != 1)
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continue;
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pdd x = lhs;
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pdd rest = lhs;
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lhs.factor(m_var, 1, x, rest);
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if (!rest.is_zero())
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continue;
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// TODO: in principle, 'x' could be any polynomial. However, we need to divide the lhs by x, and we don't have general polynomial division yet.
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// so for now we just allow the form 'value*variable'.
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// (extension to arbitrary monomials for 'x' should be fairly easy too)
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if (!x.is_unary())
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continue;
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unsigned x_var = x.var();
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rational x_coeff = x.hi().val();
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pdd xy = lhs;
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if (!rhs.try_div(x_coeff, xy))
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continue;
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pdd y = lhs;
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xy.factor(x_var, 1, y, rest);
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if (!rest.is_zero())
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continue;
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unsigned const lvl = c->level();
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if (c->is_positive()) {
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// zx <= yx
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NOT_IMPLEMENTED_YET();
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}
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else {
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SASSERT(c->is_negative());
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// zx > yx
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LOG("zx > yx: " << show_deref(c));
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// TODO: for now, we just choose the first of the other constraints
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constraint* d = ds[0];
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SASSERT(d->is_ule() && d->is_positive());
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pdd const& y_prime = d->to_ule().rhs();
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unsigned const p = m_solver.size(m_var);
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clause_builder clause(m_solver);
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// Omega^*(x, y')
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push_omega_mul(clause, lvl, p, x, y_prime);
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// y'x > yx
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constraint_ref ypx_gt_yx = m_solver.m_constraints.ult(lvl, pos_t, y_prime*x, y*x, null_dep());
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LOG("y'x>yx: " << show_deref(ypx_gt_yx));
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clause.push_new_constraint(std::move(ypx_gt_yx));
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return clause.build(lvl, {c->dep(), m_solver.m_dm});
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}
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}
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return nullptr;
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}
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