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filter pseudo-linear monomials

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This commit is contained in:
Nikolaj Bjorner 2025-09-03 17:51:01 -07:00
parent 449704ef64
commit e0c315bc3e
3 changed files with 77 additions and 2 deletions
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71
src/math/lp/nla_grobner.cpp
View file

@ -32,6 +32,7 @@ namespace nla {
smt_params_helper ph(p);
m_config.m_propagate_quotients = ph.arith_nl_grobner_propagate_quotients();
m_config.m_gcd_test = ph.arith_nl_grobner_gcd_test();
m_config.m_expand_terms = ph.arith_nl_grobner_expand_terms();
}
lp::lp_settings& grobner::lp_settings() {
@ -63,6 +64,7 @@ namespace nla {
if (!configure())
return;
m_solver.saturate();
TRACE(grobner, m_solver.display(tout));
if (m_delay_base > 0)
--m_delay_base;
@ -359,6 +361,11 @@ namespace nla {
auto v_value = val(v);
auto r_value = eval(r);
auto lc_value = eval(lc);
TRACE(grobner, tout << "nl-var: " << v << " " << v_value << "\n"
<< "lc: " << lc << " " << lc_value << "\n"
<< "r: " << r << " " << r_value << "\n";
);
SASSERT(v_value.is_int());
SASSERT(r_value.is_int());
SASSERT(lc_value.is_int());
@ -447,6 +454,44 @@ namespace nla {
found_lemma = true;
continue;
}
if (abs(lc_value) > 1 && abs(v_value) > 1 && abs(v_value) >= abs(r_value)) {
// v*c + t = 0 & |c| > 1, |v| > 1 => |v| < |t|
lemma_builder lemma(c(), "grobner-bounds");
auto [tr, offset_t] = linear_to_term(r);
auto [tc, offset_c] = linear_to_term(lc);
add_dependencies(lemma, eq);
if (lc_value > 1) // c <= 1
lemma |= ineq(tc, llc::LE, rational(1) - offset_c); // lc <= 1
else // c >= -1
lemma |= ineq(tc, llc::GE, rational(-1) - offset_c); // lc >= -1
if (v_value > 1)
lemma |= ineq(v, llc::LE, rational(1)); // v <= 1
else
lemma |= ineq(v, llc::GE, rational(-1)); // v >= -1
if (v_value > 0 && r_value > 0) {
// t >= v + 1
tr.add_monomial(rational(-1), v);
lemma |= ineq(tr, llc::GE, rational(1) - offset_t);
}
else if (v_value > 0 && r_value < 0) {
// t + v <= -1
tr.add_monomial(rational(1), v);
lemma |= ineq(tr, llc::LE, rational(-1) - offset_t);
}
else if (v_value < 0 && r_value > 0) {
// t + v >= 1
tr.add_monomial(rational(1), v);
lemma |= ineq(tr, llc::GE, rational(1) - offset_t);
}
else if (v_value < 0 && r_value < 0) {
// t - v <= -1
tr.add_monomial(rational(-1), v);
lemma |= ineq(tr, llc::LE, rational(-1) - offset_t);
}
found_lemma = true;
TRACE(grobner, lemma.display(tout << "quotient5\n"));
continue;
}
// other division lemmas are possible.
// also extend to non-linear r, non-linear lc
}
@ -693,6 +738,13 @@ namespace nla {
return lra.column_lower_bound(j).x;
}
dd::pdd grobner::pdd_expr(lp::lar_term const& t, u_dependency*& dep) {
dd::pdd r = m_pdd_manager.mk_val(0);
for (auto const& ti : t)
r += pdd_expr(ti.coeff(), ti.j(), dep);
return r;
}
dd::pdd grobner::pdd_expr(const rational& coeff, lpvar j, u_dependency*& dep) {
dd::pdd r = m_pdd_manager.mk_val(coeff);
sbuffer<lpvar> vars;
@ -709,6 +761,8 @@ namespace nla {
}
if (c().params().arith_nl_grobner_subs_fixed() == 1 && c().var_is_fixed(j))
r *= val_of_fixed_var_with_deps(j, dep);
else if (m_config.m_expand_terms && c().lra.column_has_term(j))
r *= pdd_expr(c().lra.get_term(j), dep);
else if (!c().is_monic_var(j))
r *= m_pdd_manager.mk_var(j);
else
@ -787,6 +841,22 @@ namespace nla {
m_solver.add(p, dep);
}
bool grobner::is_pseudo_linear(unsigned_vector const& vars) const {
bool has_unbounded = false;
for (auto v : vars) {
if (c().lra.column_is_bounded(v) && c().lra.var_is_int(v)) {
auto lb = c().lra.get_lower_bound(v);
auto ub = c().lra.get_upper_bound(v);
if (ub - lb <= rational(4))
continue;
}
if (has_unbounded)
return false;
has_unbounded = true;
}
return true;
}
void grobner::add_fixed_monic(unsigned j) {
u_dependency* dep = nullptr;
dd::pdd r = m_pdd_manager.mk_val(rational(1));
@ -812,6 +882,7 @@ namespace nla {
TRACE(grobner, for (lpvar j : c().m_to_refine) print_monic(c().emons()[j], tout) << "\n";);
for (lpvar j : c().m_to_refine)
if (!is_pseudo_linear(c().emons()[j].vars()))
q.push_back(j);
while (!q.empty()) {

3
src/math/lp/nla_grobner.h
View file

@ -22,6 +22,7 @@ namespace nla {
struct config {
bool m_propagate_quotients = false;
bool m_gcd_test = false;
bool m_expand_terms = false;
};
dd::pdd_manager m_pdd_manager;
dd::solver m_solver;
@ -78,8 +79,10 @@ namespace nla {
void add_fixed_monic(unsigned j);
bool is_solved(dd::pdd const& p, unsigned& v, dd::pdd& r);
void add_eq(dd::pdd& p, u_dependency* dep);
bool is_pseudo_linear(unsigned_vector const& vars) const;
const rational& val_of_fixed_var_with_deps(lpvar j, u_dependency*& dep);
dd::pdd pdd_expr(const rational& c, lpvar j, u_dependency*& dep);
dd::pdd pdd_expr(lp::lar_term const& t, u_dependency*& dep);
void display_matrix_of_m_rows(std::ostream& out) const;
std::ostream& diagnose_pdd_miss(std::ostream& out);

1
src/params/smt_params_helper.pyg
View file

@ -82,6 +82,7 @@ def_module_params(module_name='smt',
('arith.nl.grobner_gcd_test', BOOL, False, 'detect gcd conflicts for polynomial powers x^k - y = 0'),
('arith.nl.gr_q', UINT, 10, 'grobner\'s quota'),
('arith.nl.grobner_subs_fixed', UINT, 1, '0 - no subs, 1 - substitute, 2 - substitute fixed zeros only'),
('arith.nl.grobner_expand_terms', BOOL, False, 'expand terms before computing grobner basis'),
('arith.nl.delay', UINT, 10, 'number of calls to final check before invoking bounded nlsat check'),
('arith.nl.propagate_linear_monomials', BOOL, True, 'propagate linear monomials'),
('arith.nl.optimize_bounds', BOOL, True, 'enable bounds optimization'),