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https://github.com/Z3Prover/z3
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port sample cell projection
Signed-off-by: Lev Nachmanson <levnach@hotmail.com>
This commit is contained in:
Lev Nachmanson
Lev Nachmanson
parent
3e518b9e8b
commit
6ce0fcd3ef
4 changed files with 285 additions and 22 deletions
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@ -45,6 +45,8 @@ namespace nlsat {
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bool m_minimize_cores;
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bool m_factor;
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bool m_signed_project;
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bool m_cell_sample;
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struct todo_set {
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polynomial::cache & m_cache;
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@ -130,7 +132,7 @@ namespace nlsat {
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evaluator & m_evaluator;
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imp(solver & s, assignment const & x2v, polynomial::cache & u, atom_vector const & atoms, atom_vector const & x2eq,
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evaluator & ev):
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evaluator & ev, bool is_sample):
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m_solver(s),
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m_assignment(x2v),
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m_atoms(atoms),
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@ -148,6 +150,9 @@ namespace nlsat {
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m_core1(s),
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m_core2(s),
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m_result(nullptr),
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m_cell_sample(is_sample),
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m_evaluator(ev) {
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m_simplify_cores = false;
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m_full_dimensional = false;
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@ -646,6 +651,51 @@ namespace nlsat {
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m_todo.insert(p);
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}
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}
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void add_sample_coeff(polynomial_ref_vector &ps, var x){
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polynomial_ref p(m_pm);
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polynomial_ref lc(m_pm);
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unsigned sz = ps.size();
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for (unsigned i = 0; i < sz; i++){
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p = ps.get(i);
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unsigned k = degree(p, x);
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SASSERT(k > 0);
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TRACE("nlsat_explain", tout << "add_lc, x: "; display_var(tout, x); tout << "\nk: " << k << "\n"; display(tout, p); tout << "\n";);
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for(; k > 0; k--){
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lc = m_pm.coeff(p, x, k);
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add_factors(lc);
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if (m_pm.nonzero_const_coeff(p, x, k)){
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TRACE("nlsat_explain", tout << "constant coefficient, skipping...\n";);
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break;
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}
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}
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SASSERT(sign(lc) != 0);
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SASSERT(!is_const(lc));
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}
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}
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void psc_resultant_sample(polynomial_ref_vector &ps, var x, polynomial_ref_vector & samples){
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polynomial_ref p(m_pm);
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polynomial_ref q(m_pm);
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// polynomial_ref_vector samples(m_pm);
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// samples.reset();
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// sample_poly(ps, x, samples);
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SASSERT(samples.size() <= 2);
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for (unsigned i = 0; i < ps.size(); i++){
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p = ps.get(i);
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for (unsigned j = 0; j < samples.size(); j++){
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q = samples.get(j);
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if (!m_pm.eq(p, q)) {
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psc(p, q, x);
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}
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}
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}
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}
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/**
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\brief Add leading coefficients of the polynomials in ps.
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@ -973,6 +1023,116 @@ namespace nlsat {
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add_simple_assumption(k, p, lsign);
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}
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void cac_add_cell_lits(polynomial_ref_vector & ps, var y, polynomial_ref_vector & res) {
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res.reset();
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SASSERT(m_assignment.is_assigned(y));
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bool lower_inf = true;
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bool upper_inf = true;
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scoped_anum_vector & roots = m_roots_tmp;
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scoped_anum lower(m_am);
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scoped_anum upper(m_am);
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anum const & y_val = m_assignment.value(y);
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TRACE("nlsat_explain", tout << "adding literals for "; display_var(tout, y); tout << " -> ";
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m_am.display_decimal(tout, y_val); tout << "\n";);
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polynomial_ref p_lower(m_pm);
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unsigned i_lower = UINT_MAX;
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polynomial_ref p_upper(m_pm);
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unsigned i_upper = UINT_MAX;
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polynomial_ref p(m_pm);
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unsigned sz = ps.size();
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for (unsigned k = 0; k < sz; k++) {
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p = ps.get(k);
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if (max_var(p) != y)
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continue;
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roots.reset();
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// Variable y is assigned in m_assignment. We must temporarily unassign it.
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// Otherwise, the isolate_roots procedure will assume p is a constant polynomial.
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m_am.isolate_roots(p, undef_var_assignment(m_assignment, y), roots);
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unsigned num_roots = roots.size();
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//#linxi begin add_cell_lits faster
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bool all_lt = true;
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for (unsigned i = 0; i < num_roots; i++) {
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int s = m_am.compare(y_val, roots[i]);
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TRACE("nlsat_explain",
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m_am.display_decimal(tout << "comparing root: ", roots[i]); tout << "\n";
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m_am.display_decimal(tout << "with y_val:", y_val);
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tout << "\nsign " << s << "\n";
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tout << "poly: " << p << "\n";
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);
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if (s == 0) {
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// y_val == roots[i]
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// add literal
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// ! (y = root_i(p))
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add_root_literal(atom::ROOT_EQ, y, i+1, p);
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res.push_back(p);
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return;
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}
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else if (s < 0) {
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// y_val < roots[i]
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if (i > 0) {
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// y_val > roots[j]
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int j = i - 1;
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if (lower_inf || m_am.lt(lower, roots[j])) {
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lower_inf = false;
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m_am.set(lower, roots[j]);
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p_lower = p;
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i_lower = j + 1;
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}
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}
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if (upper_inf || m_am.lt(roots[i], upper)) {
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upper_inf = false;
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m_am.set(upper, roots[i]);
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p_upper = p;
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i_upper = i + 1;
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}
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all_lt = false;
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break;
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}
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// else if (s < 0) {
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// // y_val < roots[i]
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// // check if roots[i] is a better upper bound
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// if (upper_inf || m_am.lt(roots[i], upper)) {
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// upper_inf = false;
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// m_am.set(upper, roots[i]);
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// p_upper = p;
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// i_upper = i+1;
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// }
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// }
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// else if (s > 0) {
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// // roots[i] < y_val
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// // check if roots[i] is a better lower bound
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// if (lower_inf || m_am.lt(lower, roots[i])) {
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// lower_inf = false;
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// m_am.set(lower, roots[i]);
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// p_lower = p;
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// i_lower = i+1;
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// }
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// }
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}
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if (all_lt && num_roots > 0) {
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int j = num_roots - 1;
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if (lower_inf || m_am.lt(lower, roots[j])) {
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lower_inf = false;
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m_am.set(lower, roots[j]);
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p_lower = p;
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i_lower = j + 1;
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}
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}
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//#linxi end add_cell_lits faster
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}
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if (!lower_inf) {
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res.push_back(p_lower);
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add_root_literal(m_full_dimensional ? atom::ROOT_GE : atom::ROOT_GT, y, i_lower, p_lower);
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}
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if (!upper_inf) {
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res.push_back(p_upper);
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add_root_literal(m_full_dimensional ? atom::ROOT_LE : atom::ROOT_LT, y, i_upper, p_upper);
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}
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}
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/**
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Add one or two literals that specify in which cell of variable y the current interpretation is.
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One literal is added for the cases:
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@ -1016,6 +1176,8 @@ namespace nlsat {
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// Otherwise, the isolate_roots procedure will assume p is a constant polynomial.
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m_am.isolate_roots(p, undef_var_assignment(m_assignment, y), roots);
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unsigned num_roots = roots.size();
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//#linxi begin add_cell_lits faster
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bool all_lt = true;
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for (unsigned i = 0; i < num_roots; i++) {
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int s = m_am.compare(y_val, roots[i]);
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TRACE("nlsat_explain",
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@ -1033,27 +1195,58 @@ namespace nlsat {
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}
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else if (s < 0) {
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// y_val < roots[i]
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// check if roots[i] is a better upper bound
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if (i > 0) {
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// y_val > roots[j]
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int j = i - 1;
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if (lower_inf || m_am.lt(lower, roots[j])) {
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lower_inf = false;
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m_am.set(lower, roots[j]);
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p_lower = p;
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i_lower = j + 1;
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}
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}
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if (upper_inf || m_am.lt(roots[i], upper)) {
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upper_inf = false;
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m_am.set(upper, roots[i]);
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p_upper = p;
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i_upper = i+1;
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i_upper = i + 1;
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}
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all_lt = false;
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break;
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}
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else if (s > 0) {
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// roots[i] < y_val
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// else if (s < 0) {
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// // y_val < roots[i]
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// // check if roots[i] is a better upper bound
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// if (upper_inf || m_am.lt(roots[i], upper)) {
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// upper_inf = false;
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// m_am.set(upper, roots[i]);
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// p_upper = p;
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// i_upper = i+1;
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// }
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// }
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// else if (s > 0) {
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// // roots[i] < y_val
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// check if roots[i] is a better lower bound
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if (lower_inf || m_am.lt(lower, roots[i])) {
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lower_inf = false;
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m_am.set(lower, roots[i]);
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p_lower = p;
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i_lower = i+1;
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}
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// // check if roots[i] is a better lower bound
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// if (lower_inf || m_am.lt(lower, roots[i])) {
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// lower_inf = false;
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// m_am.set(lower, roots[i]);
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// p_lower = p;
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// i_lower = i+1;
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// }
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// }
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}
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if (all_lt && num_roots > 0) {
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int j = num_roots - 1;
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if (lower_inf || m_am.lt(lower, roots[j])) {
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lower_inf = false;
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m_am.set(lower, roots[j]);
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p_lower = p;
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i_lower = j + 1;
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}
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}
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//#linxi end add_cell_lits faster
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}
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if (!lower_inf) {
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@ -1064,6 +1257,7 @@ namespace nlsat {
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}
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}
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/**
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\brief Return true if all polynomials in ps are univariate in x.
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*/
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@ -1082,7 +1276,8 @@ namespace nlsat {
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/**
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\brief Apply model-based projection operation defined in our paper.
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*/
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void project(polynomial_ref_vector & ps, var max_x) {
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void project_original(polynomial_ref_vector & ps, var max_x) {
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if (ps.empty())
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return;
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m_todo.reset();
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@ -1094,12 +1289,12 @@ namespace nlsat {
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if (x < max_x)
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add_cell_lits(ps, x);
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while (true) {
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TRACE("nlsat_explain", tout << "project loop, processing var "; display_var(tout, x); tout << "\npolynomials\n";
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display(tout, ps); tout << "\n";);
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if (all_univ(ps, x) && m_todo.empty()) {
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m_todo.reset();
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break;
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}
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TRACE("nlsat_explain", tout << "project loop, processing var "; display_var(tout, x); tout << "\npolynomials\n";
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display(tout, ps); tout << "\n";);
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add_lc(ps, x);
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psc_discriminant(ps, x);
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psc_resultant(ps, x);
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@ -1109,6 +1304,72 @@ namespace nlsat {
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add_cell_lits(ps, x);
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}
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}
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void project_cdcac(polynomial_ref_vector & ps, var max_x) {
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// whz
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bool first = true;
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if (ps.empty())
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return;
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m_todo.reset();
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for (poly* p : ps) {
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m_todo.insert(p);
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}
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var x = m_todo.remove_max_polys(ps);
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// Remark: after vanishing coefficients are eliminated, ps may not contain max_x anymore
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polynomial_ref_vector samples(m_pm);
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if (x < max_x){
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cac_add_cell_lits(ps, x, samples);
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}
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while (true) {
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if (all_univ(ps, x) && m_todo.empty()) {
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m_todo.reset();
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break;
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}
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TRACE("nlsat_explain", tout << "project loop, processing var "; display_var(tout, x); tout << "\npolynomials\n";
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display(tout, ps); tout << "\n";);
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/**
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* Sample Projection
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* Reference:
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* Haokun Li and Bican Xia.
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* "Solving Satisfiability of Polynomial Formulas By Sample - Cell Projection"
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* https://arxiv.org/abs/2003.00409
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*/
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if (first) {
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add_lc(ps, x);
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psc_discriminant(ps, x);
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psc_resultant(ps, x);
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first = false;
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}
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else {
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add_lc(ps, x);
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// add_sample_coeff(ps, x);
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psc_discriminant(ps, x);
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psc_resultant_sample(ps, x, samples);
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}
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if (m_todo.empty())
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break;
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x = m_todo.remove_max_polys(ps);
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cac_add_cell_lits(ps, x, samples);
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}
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}
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void project(polynomial_ref_vector & ps, var max_x) {
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if (m_cell_sample) {
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project_cdcac(ps, max_x);
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}
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else {
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project_original(ps, max_x);
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}
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}
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bool check_already_added() const {
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for (bool b : m_already_added_literal) {
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@ -1474,7 +1735,7 @@ namespace nlsat {
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var max_x = max_var(m_ps);
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TRACE("nlsat_explain", tout << "polynomials in the conflict:\n"; display(tout, m_ps); tout << "\n";);
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elim_vanishing(m_ps);
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TRACE("nlsat_explain", tout << "elim vanishing x" << max_x << "\n"; display(tout, m_ps); tout << "\n";);
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TRACE("nlsat_explain", tout << "elim vanishing\n"; display(tout, m_ps); tout << "\n";);
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project(m_ps, max_x);
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TRACE("nlsat_explain", tout << "after projection\n"; display(tout, m_ps); tout << "\n";);
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}
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@ -1936,8 +2197,8 @@ namespace nlsat {
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};
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explain::explain(solver & s, assignment const & x2v, polynomial::cache & u,
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atom_vector const& atoms, atom_vector const& x2eq, evaluator & ev) {
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m_imp = alloc(imp, s, x2v, u, atoms, x2eq, ev);
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atom_vector const& atoms, atom_vector const& x2eq, evaluator & ev, bool is_sample) {
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m_imp = alloc(imp, s, x2v, u, atoms, x2eq, ev, is_sample);
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}
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explain::~explain() {
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@ -34,7 +34,8 @@ namespace nlsat {
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imp * m_imp;
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public:
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explain(solver & s, assignment const & x2v, polynomial::cache & u,
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atom_vector const& atoms, atom_vector const& x2eq, evaluator & ev);
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atom_vector const& atoms, atom_vector const& x2eq, evaluator & ev, bool is_sample);
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~explain();
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void reset();
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@ -14,6 +14,7 @@ def_module_params('nlsat',
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('shuffle_vars', BOOL, False, "use a random variable order."),
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('inline_vars', BOOL, False, "inline variables that can be isolated from equations (not supported in incremental mode)"),
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('seed', UINT, 0, "random seed."),
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('factor', BOOL, True, "factor polynomials produced during conflict resolution.")
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('factor', BOOL, True, "factor polynomials produced during conflict resolution."),
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('cell_sample', BOOL, True, "cell sample projection"),
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))
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@ -253,7 +253,7 @@ namespace nlsat {
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m_simplify(s, m_atoms, m_clauses, m_learned, m_pm),
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m_display_var(m_perm),
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m_display_assumption(nullptr),
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m_explain(s, m_assignment, m_cache, m_atoms, m_var2eq, m_evaluator),
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m_explain(s, m_assignment, m_cache, m_atoms, m_var2eq, m_evaluator, nlsat_params(c.m_params).cell_sample()),
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m_scope_lvl(0),
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m_lemma(s),
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m_lazy_clause(s),
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