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outline for adding monomials

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This commit is contained in:
Nikolaj Bjorner 2025-09-26 12:03:26 +03:00
parent a6ea667776
commit 6adb234673
14 changed files with 242 additions and 140 deletions
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6
src/math/lp/explanation.h
View file

@ -23,11 +23,11 @@ Revision History:
#include "util/hashtable.h"
namespace lp {
class explanation {
typedef vector<std::pair<unsigned, mpq>> pair_vec;
typedef vector<std::pair<constraint_index, mpq>> pair_vec;
typedef hashtable<unsigned, u_hash, u_eq> ci_set;
// Only one of the fields below is used. The first call adding an entry decides which one it is.
vector<std::pair<constraint_index, mpq>> m_vector;
ci_set m_set;
pair_vec m_vector;
ci_set m_set;
public:
explanation() = default;

25
src/math/lp/lp_types.h
View file

@ -19,8 +19,8 @@ Revision History:
--*/
#pragma once
#include <sstream>
#include <limits.h>
#include <sstream>
#include "util/debug.h"
#include "util/dependency.h"
@ -30,12 +30,17 @@ namespace nla {
namespace lp {
typedef unsigned constraint_index;
typedef unsigned row_index;
enum lconstraint_kind { LE = -2, LT = -1 , GE = 2, GT = 1, EQ = 0, NE = 3 };
typedef unsigned lpvar;
const lpvar null_lpvar = UINT_MAX;
const constraint_index null_ci = UINT_MAX;
}
typedef unsigned constraint_index;
typedef unsigned row_index;
enum lconstraint_kind {
LE = -2,
LT = -1,
GE = 2,
GT = 1,
EQ = 0,
NE = 3
};
typedef unsigned lpvar;
const lpvar null_lpvar = UINT_MAX;
const constraint_index null_ci = UINT_MAX;
} // namespace lp

20
src/math/lp/mon_eq.cpp
View file

@ -9,28 +9,20 @@ namespace nla {
template <typename T>
bool check_assignment(T const& m, variable_map_type & vars) {
rational r1 = vars[m.var()];
if (r1.is_zero()) {
for (auto w : m.vars()) {
if (vars[w].is_zero())
return true;
}
return false;
}
if (r1.is_zero())
return any_of(m.vars(), [&](auto w) { return vars[w].is_zero(); });
rational r2(1);
for (auto w : m.vars()) {
r2 *= vars[w];
}
for (auto w : m.vars())
r2 *= vars[w];
return r1 == r2;
}
template <typename K>
bool check_assignments(const K & monomials,
const lp::lar_solver& s,
variable_map_type & vars) {
s.get_model(vars);
for (auto const& m : monomials) {
if (!check_assignment(m, vars)) return false;
}
return true;
return all_of(monomials, [&](auto const& m) { return check_assignment(m, vars); });
}
template bool check_assignments<vector<mon_eq>>(const vector<mon_eq>&,

6
src/math/lp/nla_basics_lemmas.cpp
View file

@ -245,11 +245,7 @@ bool basics::basic_lemma(bool derived) {
if (derived)
return false;
const auto& mon_inds_to_ref = c().m_to_refine;
TRACE(nla_solver, tout << "mon_inds_to_ref = "; print_vector(mon_inds_to_ref, tout) << "\n";);
unsigned start = c().random();
unsigned sz = mon_inds_to_ref.size();
for (unsigned j = 0; j < sz; ++j) {
lpvar v = mon_inds_to_ref[(j + start) % mon_inds_to_ref.size()];
for (auto v : mon_inds_to_ref) {
const monic& r = c().emons()[v];
SASSERT (!c().check_monic(c().emons()[v]));
basic_lemma_for_mon(r, derived);

5
src/math/lp/nla_core.cpp
View file

@ -35,6 +35,7 @@ core::core(lp::lar_solver& s, params_ref const& p, reslimit & lim) :
m_divisions(*this),
m_intervals(this, lim),
m_monomial_bounds(this),
m_mul_saturate(this),
m_horner(this),
m_grobner(this),
m_emons(m_evars),
@ -1331,7 +1332,6 @@ lbool core::check() {
if (!m_lemmas.empty() || !m_literals.empty() || m_check_feasible)
return l_false;
}
if (no_effect() && should_run_bounded_nlsat())
ret = bounded_nlsat();
@ -1348,6 +1348,9 @@ lbool core::check() {
if (no_effect())
m_order.order_lemma();
if (false && no_effect())
ret = m_mul_saturate.saturate();
if (no_effect()) {
unsigned num_calls = lp_settings().stats().m_nla_calls;
if (!conflict_found() && params().arith_nl_nra() && num_calls % 50 == 0 && num_calls > 500)

11
src/math/lp/nla_core.h
View file

@ -21,6 +21,7 @@
#include "math/lp/nla_grobner.h"
#include "math/lp/nla_powers.h"
#include "math/lp/nla_divisions.h"
#include "math/lp/nla_mul_saturate.h"
#include "math/lp/emonics.h"
#include "math/lp/nex.h"
#include "math/lp/horner.h"
@ -90,6 +91,7 @@ class core {
divisions m_divisions;
intervals m_intervals;
monomial_bounds m_monomial_bounds;
mul_saturate m_mul_saturate;
unsigned m_conflicts;
bool m_check_feasible = false;
horner m_horner;
@ -221,8 +223,8 @@ public:
void set_relevant(std::function<bool(lpvar)>& is_relevant) { m_relevant = is_relevant; }
bool is_relevant(lpvar v) const { return !m_relevant || m_relevant(v); }
void push();
void push();
void pop(unsigned n);
trail_stack& trail() { return m_emons.get_trail_stack(); }
@ -237,11 +239,16 @@ public:
std::ostream & display_row(std::ostream& out, lp::row_strip<lp::mpq> const& row) const;
std::ostream & display(std::ostream& out);
std::ostream& display_smt(std::ostream& out);
std::ostream& display_coeff(std::ostream& out, bool first, lp::mpq const& p) const;
std::ostream& display_constraint(std::ostream& out, lp::constraint_index ci) const;
std::ostream& display_constraint(std::ostream& out, lp::lar_term const& lhs, lp::lconstraint_kind k, lp::mpq const& rhs) const;
std::ostream& display_constraint(std::ostream& out, vector<std::pair<rational, lpvar>> const& lhs, lp::lconstraint_kind k, lp::mpq const& rhs) const;
std::ostream & print_ineq(const ineq & in, std::ostream & out) const;
std::ostream & print_var(lpvar j, std::ostream & out) const;
std::ostream & print_monics(std::ostream & out) const;
std::ostream & print_ineqs(const lemma& l, std::ostream & out) const;
std::ostream & print_factorization(const factorization& f, std::ostream& out) const;
template <typename T>
std::ostream& print_product(const T & m, std::ostream& out) const;
template <typename T>

180
src/math/lp/nla_mul_saturate.cpp
View file

@ -10,7 +10,11 @@
Check if the system with new constraints is LP feasible.
If it is not, then produce a lemma that explains the infeasibility.
The lemma is in terms of the original constraints and bounds.
Strategy 1: The lemma is in terms of the original constraints and bounds.
Strategy 2: Attempt to eliminate new monomials from the lemma by relying on Farkas multipliers.
If it succeeds to eliminate new monomials we have a lemma that is a linear
combination of existing variables.
Strategy 3: The lemma uses the new constraints.
--*/
@ -21,78 +25,144 @@
namespace nla {
mul_saturate::mul_saturate(core* core) :
common(core),
lra(m_core.lra) {}
common(core) {}
lbool mul_saturate::saturate() {
lra.push();
for (auto j : c().m_to_refine) {
auto& m = c().emons()[j];
for (auto& con : lra.constraints().active()) {
for (auto v : m.vars()) {
for (auto [coeff, u] : con.coeffs()) {
if (u == v)
// multiply by remaining vars
multiply_constraint(con, m, v);
// add new constraint
}
}
}
}
// record new monomials that are created and recursively down-saturate with respect to these.
auto st = lra.solve();
lbool r = l_undef;
if (st == lp::lp_status::INFEASIBLE) {
// now we need to filter new constraints into bounds and old constraints.
r = l_false;
}
if (st == lp::lp_status::OPTIMAL || st == lp::lp_status::FEASIBLE) {
// TODO: check model just in case it got lucky.
}
lra.pop(1);
lp::explanation ex;
init_solver();
add_multiply_constraints();
lbool r = solve(ex);
if (r == l_false)
add_lemma(ex);
return r;
}
void mul_saturate::init_solver() {
local_solver = alloc(lp::lar_solver);
}
void mul_saturate::add_lemma(lp::explanation const& ex1) {
lp::explanation ex2;
for (auto p : ex1) {
lp::constraint_index src_ci;
if (m_new_mul_constraints.find(p.ci(), src_ci))
ex2.add_pair(src_ci, mpq(1));
else
ex2.add_pair(p.ci(), p.coeff());
}
lemma_builder new_lemma(c(), "stellensatz");
new_lemma &= ex2;
for (auto [v, sign] : m_var_signs) {
if (sign)
new_lemma.explain_existing_upper_bound(v);
else
new_lemma.explain_existing_lower_bound(v);
}
IF_VERBOSE(1, verbose_stream() << "unsat \n" << new_lemma << "\n");
}
lbool mul_saturate::solve(lp::explanation& ex) {
for (auto const& [new_ci, old_ci] : m_new_mul_constraints)
local_solver->activate(new_ci);
auto st = local_solver->solve();
lbool r = l_undef;
if (st == lp::lp_status::INFEASIBLE) {
local_solver->get_infeasibility_explanation(ex);
IF_VERBOSE(0, c().print_explanation(ex, verbose_stream()) << "\n";);
r = l_false;
}
if (st == lp::lp_status::OPTIMAL || st == lp::lp_status::FEASIBLE) {
// TODO: check model just in case it got lucky.
IF_VERBOSE(1, verbose_stream() << "saturation is LP feasible, maybe it is a model of the NLA problem\n");
}
IF_VERBOSE(0, local_solver->display(verbose_stream()); c().display(verbose_stream()));
return r;
}
// record new monomials that are created and recursively down-saturate with respect to these.
void mul_saturate::add_multiply_constraints() {
m_new_mul_constraints.reset();
m_seen_vars.reset();
m_var_signs.reset();
for (auto j : c().m_to_refine) {
for (auto con_id : local_solver->constraints().indices()) {
unsigned num_vars = c().emon(j).vars().size();
for (unsigned i = 0; i < num_vars; ++i) {
auto v = c().emon(j).vars()[i];
for (auto [coeff, u] : local_solver->constraints()[con_id].coeffs())
if (u == v)
add_multiply_constraint(con_id, j, v);
}
}
}
}
// multiply by remaining vars
void mul_saturate::multiply_constraint(lp::lar_base_constraint const& con, monic const& m, lpvar x) {
void mul_saturate::add_multiply_constraint(lp::constraint_index old_ci, lp::lpvar mi, lpvar x) {
lp::lar_base_constraint const& con = local_solver->constraints()[old_ci];
auto const& lhs = con.coeffs();
auto const& rhs = con.rhs();
auto k = con.kind();
auto k = con.kind();
if (k == lp::lconstraint_kind::NE || k == lp::lconstraint_kind::EQ)
return; // not supported
auto sign = false;
svector<lpvar> vars;
bool first = true;
for (auto v : m.vars()) {
if (v != x || !first)
vars.push_back(v);
for (auto v : c().emon(mi).vars()) {
if (v != x || !first)
vars.push_back(v);
else
first = false;
}
vector<std::pair<rational, lpvar>> new_lhs;
// compute sign of vars
for (auto v : vars) {
if (m_seen_vars.contains(v))
continue;
// retrieve bounds of v
// if v has non-negative lower bound add as positive
// if v has non-positive upper bound add as negative
// otherwise, fail
if (local_solver->column_has_lower_bound(v) && !local_solver->get_lower_bound(v).is_neg()) {
m_var_signs.push_back({v, false});
m_seen_vars.insert(v);
}
else if (local_solver->column_has_upper_bound(v) && !local_solver->get_upper_bound(v).is_pos()) {
m_var_signs.push_back({v, true});
m_seen_vars.insert(v);
sign = !sign;
}
else
return;
}
lp::lar_term new_lhs;
rational new_rhs(rhs);
for (auto [coeff, v] : lhs) {
#if 0
vars.push_back(v);
auto new_m = c().emons().find_canonical(vars);
if (!new_m) {
bool is_int = lra.var_is_int(x); // assume all vars in monic have the same type, can be changed for MIP
lpvar new_monic_var = 0; // lra.add_var(is_int);
c().emons().add(new_monic_var, vars);
new_m = c().emons().find_canonical(vars);
SASSERT(new_m);
}
new_lhs.push_back({coeff, new_m->var()});
lpvar new_monic_var = c().m_add_monomial(vars);
auto const& new_m = c().emons()[new_monic_var];
verbose_stream() << vars << " v " << new_m.var() << " coeff " << coeff << "\n";
new_lhs.add_monomial(coeff, new_m.var());
vars.pop_back();
#endif
}
if (rhs != 0) {
new_lhs.push_back({-rhs, m.var()});
if (vars.size() == 1) {
new_lhs.add_monomial(-rhs, vars[0]);
verbose_stream() << "rhs mul " << -rhs << " * j" << vars[0] << "\n";
}
else {
#if 0
lpvar new_monic_var = c().m_add_monomial(vars);
auto const& new_m = c().emons()[new_monic_var];
verbose_stream() << vars << " v " << new_m.var() << " coeff " << coeff << "\n";
new_lhs.add_monomial(-rhs, new_m.var());
verbose_stream() << "rhs mul " << -rhs << " * j" << new_m.var() << "\n";
#endif
}
new_rhs = 0;
}
// compute sign of vars
for (auto v : vars)
if (c().val(v).is_neg())
sign = !sign;
if (sign) {
switch (k) {
case lp::lconstraint_kind::LE: k = lp::lconstraint_kind::GE; break;
@ -101,7 +171,11 @@ namespace nla {
case lp::lconstraint_kind::GT: k = lp::lconstraint_kind::LT; break;
default: break;
}
}
// instead of adding a constraint here, add row to tableau based on the new_lhs, new_rhs, k.
}
c().display_constraint(verbose_stream(), old_ci) << " -> ";
c().display_constraint(verbose_stream(), new_lhs, k, new_rhs) << "\n";
// TODO:
// auto new_ci = lra.m_add_constraint(new_lhs, k, new_rhs);
// m_new_mul_constraints.insert(new_ci, old_ci);
}
}

12
src/math/lp/nla_mul_saturate.h
View file

@ -9,8 +9,16 @@ namespace nla {
class core;
class lar_solver;
class mul_saturate : common {
lp::lar_solver& lra;
void multiply_constraint(lp::lar_base_constraint const& c, monic const& m, lpvar x);
// source of multiplication constraint
u_map<lp::constraint_index> m_new_mul_constraints;
svector<std::pair<lpvar, bool>> m_var_signs;
tracked_uint_set m_seen_vars;
scoped_ptr<lp::lar_solver> local_solver;
void init_solver();
void add_multiply_constraints();
void add_multiply_constraint(lp::constraint_index con_id, lp::lpvar mi, lpvar x);
lbool solve(lp::explanation& ex);
void add_lemma(lp::explanation const& ex1);
public:
mul_saturate(core* core);

69
src/math/lp/nla_pp.cpp
View file

@ -50,7 +50,8 @@ std::ostream& core::print_factor(const factor& f, std::ostream& out) const {
out << "- ";
if (f.is_var()) {
out << "VAR, " << pp(f.var());
} else {
}
else {
out << "MON, v" << m_emons[f.var()] << " = ";
print_product(m_emons[f.var()].rvars(), out);
}
@ -61,7 +62,8 @@ std::ostream& core::print_factor(const factor& f, std::ostream& out) const {
std::ostream& core::print_factor_with_vars(const factor& f, std::ostream& out) const {
if (f.is_var()) {
out << pp(f.var());
} else {
}
else {
out << " MON = " << pp_mon_with_vars(*this, m_emons[f.var()]);
}
return out;
@ -133,9 +135,8 @@ std::ostream& core::print_var(lpvar j, std::ostream& out) const {
lra.print_column_info(j, out);
signed_var jr = m_evars.find(j);
out << "root=";
if (jr.sign()) {
out << "-";
}
if (jr.sign())
out << "-";
out << lra.get_variable_name(jr.var()) << "\n";
return out;
@ -245,23 +246,25 @@ std::string core::var_str(lpvar j) const {
return result;
}
std::ostream& core::display_coeff(std::ostream& out, bool first, lp::mpq const& p) const {
if (first && p == 1)
return out;
if (first && p > 0)
out << p;
else if (p == 1)
out << " + ";
else if (p > 0)
out << " + " << p << " * ";
else if (p == -1)
out << " - ";
else if (first)
out << p << " * ";
else
out << " - " << -p << " * ";
return out;
}
std::ostream& core::display_row(std::ostream& out, lp::row_strip<lp::mpq> const& row) const {
auto display_coeff = [&](bool first, lp::mpq const& p) {
if (first && p == 1)
return;
if (first && p > 0)
out << p;
else if (p == 1)
out << " + ";
else if (p > 0)
out << " + " << p << " * ";
else if (p == -1)
out << " - ";
else if (first)
out << p << " * ";
else
out << " - " << -p << " * ";
};
auto display_var = [&](bool first, lp::mpq p, lp::lpvar v) {
if (is_monic_var(v)) {
for (auto w : m_emons[v].vars())
@ -270,7 +273,7 @@ std::ostream& core::display_row(std::ostream& out, lp::row_strip<lp::mpq> const&
else
p *= m_evars.find(v).rsign();
display_coeff(first, p);
display_coeff(out, first, p);
if (is_monic_var(v)) {
bool first = true;
for (auto w : m_emons[v].vars())
@ -356,6 +359,28 @@ std::ostream& core::display_declarations_smt(std::ostream& out) const {
return out;
}
std::ostream& core::display_constraint(std::ostream& out, lp::constraint_index ci) const {
auto const& c = lra.constraints()[ci];
return display_constraint(out, c.coeffs(), c.kind(), c.rhs());
}
std::ostream& core::display_constraint(std::ostream& out, lp::lar_term const& lhs, lp::lconstraint_kind k, lp::mpq const& rhs) const {
return display_constraint(out, lhs.coeffs_as_vector(), k, rhs);
}
std::ostream& core::display_constraint(std::ostream& out, vector<std::pair<rational, lpvar>> const & lhs, lp::lconstraint_kind k, lp::mpq const& rhs) const {
bool first = true;
for (auto [coeff, v] : lhs) {
display_coeff(out, first, coeff);
first = false;
if (is_monic_var(v))
print_product(m_emons[v], out);
else
out << "j" << v;
}
return out << " " << k << " " << rhs;
}
std::ostream& core::display_constraint_smt(std::ostream& out, unsigned id, lp::lar_base_constraint const& c) const {
auto k = c.kind();
auto rhs = c.rhs();

6
src/smt/smt_context.h
View file

@ -70,8 +70,8 @@ namespace smt {
struct enode_pp {
context const& ctx;
enode* n;
enode_pp(enode* n, context const& ctx): ctx(ctx), n(n) {}
enode const* n;
enode_pp(enode const* n, context const& ctx): ctx(ctx), n(n) {}
};
struct replay_unit {
@ -1414,7 +1414,7 @@ namespace smt {
void display_asserted_formulas(std::ostream & out) const;
enode_pp pp(enode* n) { return enode_pp(n, *this); }
enode_pp pp(enode const* n) { return enode_pp(n, *this); }
std::ostream& display_literal(std::ostream & out, literal l) const;

2
src/smt/smt_context_pp.cpp
View file

@ -692,7 +692,7 @@ namespace smt {
std::ostream& operator<<(std::ostream& out, enode_pp const& p) {
ast_manager& m = p.ctx.get_manager();
enode* n = p.n;
enode const* n = p.n;
return out << n->get_owner_id() << ": " << mk_bounded_pp(n->get_expr(), m);
}

5
src/smt/smt_theory.cpp
View file

@ -59,6 +59,11 @@ namespace smt {
}
}
bool theory::is_attached_to_var(enode const *n) const {
theory_var v = n->get_th_var(get_id());
return v != null_theory_var && get_enode(v) == n;
}
void theory::display_var2enode(std::ostream & out) const {
unsigned sz = m_var2enode.size();
for (unsigned v = 0; v < sz; v++) {

5
src/smt/smt_theory.h
View file

@ -97,10 +97,7 @@ namespace smt {
but it may be inherited from another enode n' during an
equivalence class merge. That is, get_enode(v) != n.
*/
bool is_attached_to_var(enode const * n) const {
theory_var v = n->get_th_var(get_id());
return v != null_theory_var && get_enode(v) == n;
}
bool is_attached_to_var(enode const *n) const;
struct scoped_trace_stream {
ast_manager& m;

30
src/smt/theory_lra.cpp
View file

@ -890,7 +890,7 @@ public:
mk_is_int_axiom(n);
}
bool internalize_atom(app * atom, bool gate_ctx) {
void internalize_atom(app * atom) {
TRACE(arith_internalize, tout << bpp(atom) << "\n";);
SASSERT(!ctx().b_internalized(atom));
expr* n1, *n2;
@ -918,12 +918,12 @@ public:
}
else if (a.is_is_int(atom)) {
internalize_is_int(atom);
return true;
return;
}
else {
TRACE(arith, tout << "Could not internalize " << mk_pp(atom, m) << "\n";);
found_unsupported(atom);
return true;
return;
}
if (is_int(v) && !r.is_int())
@ -936,7 +936,6 @@ public:
m_bool_var2bound.insert(bv, b);
mk_bound_axioms(*b);
TRACE(arith_internalize, tout << "Internalized " << bv << ": " << bpp(atom) << "\n";);
return true;
}
bool internalize_term(app * term) {
@ -1712,7 +1711,7 @@ public:
return FC_GIVEUP;
}
// create an eq atom representing "term = offset"
// create an eq atom representing "term = offset"
app_ref mk_eq(lp::lar_term const& term, rational const& offset) {
u_map<rational> coeffs;
term2coeffs(term, coeffs);
@ -1730,15 +1729,10 @@ public:
return atom;
}
}
// create a bound atom representing term >= k is lower_bound is true, and term <= k if it is false
expr_ref mk_bound(lp::lar_term const& term, rational const& k, bool lower_bound) {
rational offset;
expr_ref t(m);
return mk_bound(term, k, lower_bound, offset, t);
}
expr_ref mk_bound(lp::lar_term const& term, rational const& k, bool lower_bound, rational& offset, expr_ref& t) {
offset = k;
expr_ref mk_bound(lp::lar_term const& term, rational const& k, bool lower_bound) {
rational offset = k;
expr_ref t(m);
u_map<rational> coeffs;
term2coeffs(term, coeffs);
bool is_int = true;
@ -1925,9 +1919,7 @@ public:
TRACE(arith, tout << "branch\n";);
bool u = m_lia->is_upper();
auto const & k = m_lia->offset();
rational offset;
expr_ref t(m);
expr_ref b = mk_bound(m_lia->get_term(), k, !u, offset, t);
expr_ref b = mk_bound(m_lia->get_term(), k, !u);
if (m.has_trace_stream()) {
app_ref body(m);
body = m.mk_or(b, m.mk_not(b));
@ -4192,16 +4184,13 @@ public:
unsigned init_range() const { return 5; }
unsigned max_range() const { return 20; }
void setup() {
m_bounded_range_lit = null_literal;
m_bound_terms.reset();
m_bound_predicate = nullptr;
}
void validate_model(proto_model& mdl) {
rational r1, r2;
expr_ref res(m);
if (!m_model_is_initialized)
@ -4240,7 +4229,8 @@ void theory_lra::init() {
m_imp->init();
}
bool theory_lra::internalize_atom(app * atom, bool gate_ctx) {
return m_imp->internalize_atom(atom, gate_ctx);
m_imp->internalize_atom(atom);
return true;
}
bool theory_lra::internalize_term(app * term) {
return m_imp->internalize_term(term);