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fix bug with saturation of monotonicity, and add more general case for downward saturation

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2025-09-28 14:36:53 +03:00
parent e684537b01
commit c621f59740
2 changed files with 62 additions and 24 deletions
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78
src/math/lp/nla_stellensatz.cpp
View file

@ -46,6 +46,7 @@ namespace nla {
init_solver();
saturate_constraints();
saturate_basic_linearize();
TRACE(arith, display(tout << "stellensatz after saturation\n"));
lbool r = m_solver.solve(ex);
if (r == l_false)
add_lemma(ex);
@ -137,7 +138,7 @@ namespace nla {
}
//
// a constraint can be explained by a set of bounds used as assumptions for the constraint
// a constraint can be explained by a set of bounds used as assumptions
// and by an original constraint.
//
void stellensatz::explain_constraint(lemma_builder& new_lemma, lp::constraint_index ci, lp::explanation& ex) {
@ -156,7 +157,13 @@ namespace nla {
if (std::holds_alternative<u_dependency *>(b)) {
auto dep = *std::get_if<u_dependency *>(&b);
m_solver.lra().push_explanation(dep, ex);
} else {
}
else {
//
// the inequality was posted as an assumption
// negate it to add to the lemma
// recall that lemmas are represented in the form: /\ Assumptions => \/ C
//
auto [v, k, rhs] = *std::get_if<bound>(&b);
k = negate(k);
if (m_solver.lra().var_is_int(v)) {
@ -296,13 +303,13 @@ namespace nla {
auto valx = m_values[x];
auto valy = m_values[y];
if (valx > 1 && valy > 0 && val_j <= valy)
saturate_monotonicity(j, val_j, x, false, y, false);
saturate_monotonicity(j, val_j, x, 1, y, 1);
else if (valx > 1 && valy < 0 && -val_j <= -valy)
saturate_monotonicity(j, val_j, x, false, y, true);
saturate_monotonicity(j, val_j, x, 1, y, -1);
else if (valx < -1 && valy > 0 && -val_j <= valy)
saturate_monotonicity(j, val_j, x, true, y, false);
saturate_monotonicity(j, val_j, x, -1, y, 1);
else if (valx < -1 && valy < 0 && val_j <= -valy)
saturate_monotonicity(j, val_j, x, true, y, true);
saturate_monotonicity(j, val_j, x, -1, y, -1);
}
// x > 1, y > 0 => xy > y
@ -349,6 +356,7 @@ namespace nla {
lp::constraint_index stellensatz::add_ineq(bound_justifications const& bounds,
lp::lar_term const& t, lp::lconstraint_kind k,
rational const& rhs) {
SASSERT(!t.coeffs_as_vector().empty());
auto ti = m_solver.lra().add_term(t.coeffs_as_vector(), m_solver.lra().number_of_vars());
m_values.push_back(value(t));
auto new_ci = m_solver.lra().add_var_bound(ti, k, rhs);
@ -369,7 +377,8 @@ namespace nla {
// record new monomials that are created and recursively down-saturate with respect to these.
// this is a simplistic pass
void stellensatz::saturate_constraints() {
vector<svector<lp::constraint_index>> var2cs;
vector<svector<lp::constraint_index>> var2cs; // cs contain a term using v
vector<svector<lp::constraint_index>> vars2cs; // cs contain a term with a monomial using v
// current approach: only resolve against var2cs, which is initialized
// with monomials in the input.
@ -380,25 +389,55 @@ namespace nla {
if (v >= var2cs.size())
var2cs.resize(v + 1);
var2cs[v].push_back(ci);
if (m_mon2vars.contains(v)) {
for (auto w : m_mon2vars[v]) {
if (w >= vars2cs.size())
vars2cs.resize(w + 1);
vars2cs[w].push_back(ci);
}
}
}
// insert monomials to be refined
insert_monomials_from_constraint(ci);
}
auto is_subset = [&](svector<lpvar> const &a, svector<lpvar> const& b) {
if (a.size() >= b.size())
return false;
// check if a is a subset of b, counting multiplicies, assume a, b are sorted
unsigned i = 0, j = 0;
while (i < a.size() && j < b.size()) {
if (a[i] == b[j])
++i;
++j;
}
return i == a.size();
};
for (unsigned it = 0; it < m_to_refine.size(); ++it) {
auto j = m_to_refine[it];
auto vars = m_mon2vars[j];
for (auto v : vars) {
if (v >= var2cs.size())
continue;
auto cs = var2cs[v];
for (auto ci : cs) {
svector<lpvar> _vars;
_vars.push_back(v);
for (auto ci : var2cs[v]) {
for (auto [coeff, u] : m_solver.lra().constraints()[ci].coeffs()) {
if (u == v)
saturate_constraint(ci, j, v);
saturate_constraint(ci, j, _vars);
}
}
}
for (auto v : vars) {
if (v >= vars2cs.size())
continue;
for (auto ci : vars2cs[v]) {
for (auto [coeff, u] : m_solver.lra().constraints()[ci].coeffs())
if (m_mon2vars.contains(u) && is_subset(m_mon2vars[u], vars))
saturate_constraint(ci, j, m_mon2vars[u]);
}
}
}
IF_VERBOSE(5,
c().lra_solver().display(verbose_stream() << "original\n");
@ -407,8 +446,8 @@ namespace nla {
}
// multiply by remaining vars
void stellensatz::saturate_constraint(lp::constraint_index old_ci, lpvar mi, lpvar x) {
resolvent r = {old_ci, mi, x};
void stellensatz::saturate_constraint(lp::constraint_index old_ci, lpvar mi, svector<lpvar> const& xs) {
resolvent r = {old_ci, mi, xs};
if (m_resolvents.contains(r))
return;
m_resolvents.insert(r);
@ -419,15 +458,14 @@ namespace nla {
if (k == lp::lconstraint_kind::NE || k == lp::lconstraint_kind::EQ)
return; // not supported
svector<lpvar> vars;
bool first = true;
for (auto v : m_mon2vars[mi]) {
if (v != x || !first)
vars.push_back(v);
else
first = false;
// xs is a proper subset of vars in mi
svector<lpvar> vars(m_mon2vars[mi]);
for (auto x : xs) {
SASSERT(vars.contains(x));
vars.erase(x);
}
SASSERT(!first); // v was a member and was removed
SASSERT(!vars.empty());
bound_justifications bounds;
// compute bounds constraints and sign of vars

8
src/math/lp/nla_stellensatz.h
View file

@ -58,15 +58,15 @@ namespace nla {
struct resolvent {
lp::constraint_index old_ci;
lpvar mi;
lpvar x;
svector<lpvar> xs;
struct eq {
bool operator()(resolvent const& a, resolvent const& b) const {
return a.old_ci == b.old_ci && a.mi == b.mi && a.x == b.x;
return a.old_ci == b.old_ci && a.mi == b.mi && a.xs == b.xs;
}
};
struct hash {
unsigned operator()(resolvent const& a) const {
return hash_u_u(a.old_ci, hash_u_u(a.mi, a.x));
return hash_u_u(a.old_ci, hash_u_u(a.mi, svector_hash<unsigned_hash>()(a.xs)));
}
};
};
@ -92,7 +92,7 @@ namespace nla {
lpvar add_var(bool is_int);
lbool add_bounds(svector<lpvar> const &vars, bound_justifications &bounds);
void saturate_constraints();
void saturate_constraint(lp::constraint_index con_id, lp::lpvar mi, lpvar x);
void saturate_constraint(lp::constraint_index con_id, lp::lpvar mi, svector<lpvar> const & xs);
void saturate_basic_linearize();
void saturate_basic_linearize(lpvar j, rational const &val_j, svector<lpvar> const &vars,
rational const &val_vars);