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Tune Grobner equations

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\brief convert p == 0 into a solved form v == r, such that
   v has bounds [lo, oo) iff r has bounds [lo', oo)
   v has bounds (oo,hi]  iff r has bounds (oo,hi']

   The solved form allows the Grobner solver identify more bounds conflicts.
   A bad leading term can miss bounds conflicts.
   For example for x + y + z == 0 where x, y : [0, oo) and z : (oo,0]
   we prefer to solve z == -x - y instead of x == -z - y
   because the solution -z - y has neither an upper, nor a lower bound.

The Grobner solver is augmented with a notion of a substitution that is applied before the solver is run.
This commit is contained in:
Nikolaj Bjorner 2022-07-11 16:14:26 -07:00
parent f33c933241
commit 316ed778e0
5 changed files with 127 additions and 13 deletions
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55
src/math/grobner/pdd_solver.cpp
View file

@ -342,6 +342,7 @@ namespace dd {
for (equation* e : m_solved) dealloc(e);
for (equation* e : m_to_simplify) dealloc(e);
for (equation* e : m_processed) dealloc(e);
m_subst.reset();
m_solved.reset();
m_processed.reset();
m_to_simplify.reset();
@ -354,16 +355,39 @@ namespace dd {
void solver::add(pdd const& p, u_dependency * dep) {
if (p.is_zero()) return;
equation * eq = alloc(equation, p, dep);
if (check_conflict(*eq)) {
if (check_conflict(*eq))
return;
}
push_equation(to_simplify, eq);
if (!m_var2level.empty()) {
if (!m_var2level.empty())
m_levelp1 = std::max(m_var2level[p.var()]+1, m_levelp1);
}
update_stats_max_degree_and_size(*eq);
}
}
void solver::add_subst(unsigned v, pdd const& p, u_dependency* dep) {
SASSERT(m_processed.empty());
SASSERT(m_solved.empty());
m_subst.push_back({v, p, dep});
for (auto* e : m_to_simplify) {
auto r = e->poly().subst_pdd(v, p);
if (r == e->poly())
continue;
*e = m_dep_manager.mk_join(dep, e->dep());
*e = r;
}
}
void solver::simplify(pdd& p, u_dependency*& d) {
for (auto const& [v, q, d2] : m_subst) {
pdd r = p.subst_pdd(v, q);
if (r != p) {
p = r;
d = m_dep_manager.mk_join(d, d2);
}
}
}
bool solver::canceled() {
return m_limit.is_canceled();
@ -446,9 +470,24 @@ namespace dd {
}
std::ostream& solver::display(std::ostream& out) const {
out << "solved\n"; for (auto e : m_solved) display(out, *e);
out << "processed\n"; for (auto e : m_processed) display(out, *e);
out << "to_simplify\n"; for (auto e : m_to_simplify) display(out, *e);
if (!m_solved.empty()) {
out << "solved\n"; for (auto e : m_solved) display(out, *e);
}
if (!m_processed.empty()) {
out << "processed\n"; for (auto e : m_processed) display(out, *e);
}
if (!m_to_simplify.empty()) {
out << "to_simplify\n"; for (auto e : m_to_simplify) display(out, *e);
}
if (!m_subst.empty()) {
out << "subst\n";
for (auto const& [v, p, d] : m_subst) {
out << "v" << v << " := " << p;
if (m_print_dep)
m_print_dep(d, out);
out << "\n";
}
}
return display_statistics(out);
}

4
src/math/grobner/pdd_solver.h
View file

@ -118,6 +118,7 @@ private:
equation_vector m_solved; // equations with solved variables, triangular
equation_vector m_processed;
equation_vector m_to_simplify;
vector<std::tuple<unsigned, pdd, u_dependency*>> m_subst;
mutable u_dependency_manager m_dep_manager;
equation_vector m_all_eqs;
equation* m_conflict;
@ -136,6 +137,9 @@ public:
void add(pdd const& p) { add(p, nullptr); }
void add(pdd const& p, u_dependency * dep);
void simplify(pdd& p, u_dependency*& dep);
void add_subst(unsigned v, pdd const& p, u_dependency* dep);
void simplify();
void saturate();