diff --git a/src/nlsat/levelwise.cpp b/src/nlsat/levelwise.cpp index 58129e0b9..fdfb80fb0 100644 --- a/src/nlsat/levelwise.cpp +++ b/src/nlsat/levelwise.cpp @@ -55,6 +55,8 @@ namespace nlsat { unsigned m_level = 0; // current level being processed unsigned m_spanning_tree_threshold = 3; // minimum both-side count for spanning tree + bool m_witness_subs_lc = true; + bool m_witness_subs_disc = false; unsigned m_l_rf = UINT_MAX; // position of lower bound in m_rel.m_rfunc unsigned m_u_rf = UINT_MAX; // position of upper bound in m_rel.m_rfunc, UINT_MAX in section case @@ -260,6 +262,8 @@ namespace nlsat { m_I.emplace_back(m_pm); m_spanning_tree_threshold = m_solver.lws_spt_threshold(); + m_witness_subs_lc = m_solver.lws_witness_subs_lc(); + m_witness_subs_disc = m_solver.lws_witness_subs_disc(); } // Handle a polynomial whose every coefficient evaluates to zero at the sample. @@ -443,7 +447,7 @@ namespace nlsat { lc = m_pm.coeff(p, x, deg); TRACE(lws, m_pm.display(tout << " adding lc: ", lc) << "\n";); request_factorized(lc); - if (add_nzero_coeff && lc && sign(lc)) + if (add_nzero_coeff && m_witness_subs_disc && lc && sign(lc)) add_nzero_coeff = false; } @@ -455,7 +459,7 @@ namespace nlsat { // If p is nullified at some point then at this point discriminant well be evaluated // to zero, as can be seen from the Sylvester matrix which would // have at least one zero row. - if (add_nzero_coeff && sign(disc)) // we can avoid adding a nonzero_coeff if sign(disc) != 0 + if (add_nzero_coeff && m_witness_subs_disc && sign(disc)) // we can avoid adding a nonzero_coeff if sign(disc) != 0 add_nzero_coeff = false; } } @@ -1165,7 +1169,7 @@ namespace nlsat { // No need for an additional coefficient witness in this case. polynomial_ref witness = m_witnesses[i]; if (add_lc && witness && !is_const(witness)) - if (lc && !is_zero(lc) && sign(lc)) + if (lc && !is_zero(lc) && m_witness_subs_lc && sign(lc)) witness = polynomial_ref(m_pm); add_projection_for_poly(p, m_level, witness, add_lc, add_disc); @@ -1300,25 +1304,27 @@ namespace nlsat { collect_non_null_witnesses(); add_adjacent_root_resultants(); - // Projections (coeff witness, disc, leading coeff). + // Projection: witness, disc, lc for (unsigned i = 0; i < m_level_ps.size(); ++i) { polynomial_ref p(m_level_ps.get(i), m_pm); polynomial_ref lc(m_pm); unsigned deg = m_pm.degree(p, m_n); lc = m_pm.coeff(p, m_n, deg); + // Projective delineability optimization, Lemma 3.2 of "Projective Delineability + // for Single Cell Construction": if p is projectively delineable on R, + // ldcf(p)(s) != 0, and p has no real roots at s, then p is delineable on R + // without requiring sign-invariance of the leading coefficient. + // Projective delineability is ensured by adding the discriminant, Theorem 3.1, + // and non-nullification is ensured by the witness. bool add_lc = true; - if (!poly_has_roots(i)) - if (lc && !is_zero(lc) && sign(lc)) - add_lc = false; + if (!poly_has_roots(i) && lc && !is_zero(lc) && sign(lc)) { + add_lc = false; + polynomial_ref null_ref(m_pm); + m_witnesses[i] = null_ref; + } - // if the leading coefficient is already non-zero at the sample - // AND we're adding lc, we do not need to project an additional non-null coefficient witness. - polynomial_ref witness = m_witnesses[i]; - if (add_lc && witness && !is_const(witness)) - if (lc && !is_zero(lc) && sign(lc)) - witness = polynomial_ref(m_pm); // zero the witnsee as lc will be the witness - add_projection_for_poly(p, m_n, witness, add_lc, true); //true to add the discriminant + add_projection_for_poly(p, m_n, m_witnesses[i], add_lc, true); //true to add the discriminant } } diff --git a/src/nlsat/nlsat_params.pyg b/src/nlsat/nlsat_params.pyg index d63a96e91..048fcf521 100644 --- a/src/nlsat/nlsat_params.pyg +++ b/src/nlsat/nlsat_params.pyg @@ -24,5 +24,7 @@ def_module_params('nlsat', ('known_sat_assignment_file_name', STRING, "", "the file name of a known solution: used for debugging only"), ('lws', BOOL, True, "apply levelwise."), ('lws_spt_threshold', UINT, 4, "minimum both-side polynomial count to apply spanning tree optimization; < 2 disables spanning tree"), + ('lws_witness_subs_lc', BOOL, True, "try substitute the non-nullified witness by the lc"), + ('lws_witness_subs_disc', BOOL, True, "try substitute the non-nullified witness by the discriminant"), ('canonicalize', BOOL, True, "canonicalize polynomials.") )) diff --git a/src/nlsat/nlsat_solver.cpp b/src/nlsat/nlsat_solver.cpp index fef3bcccf..e5e104a33 100644 --- a/src/nlsat/nlsat_solver.cpp +++ b/src/nlsat/nlsat_solver.cpp @@ -250,7 +250,9 @@ namespace nlsat { std::string m_debug_known_solution_file_name; bool m_apply_lws; bool m_last_conflict_used_lws = false; // Track if last conflict explanation used levelwise - unsigned m_lws_spt_threshold = 3; + unsigned m_lws_spt_threshold = 3; + bool m_lws_witness_subs_lc = true; + bool m_lws_witness_subs_disc = false; imp(solver& s, ctx& c): m_ctx(c), m_solver(s), @@ -312,6 +314,8 @@ namespace nlsat { m_debug_known_solution_file_name = p.known_sat_assignment_file_name(); m_apply_lws = p.lws(); m_lws_spt_threshold = p.lws_spt_threshold(); // 0 disables spanning tree + m_lws_witness_subs_lc = p. lws_witness_subs_lc(); + m_lws_witness_subs_disc = p.lws_witness_subs_disc(); m_check_lemmas |= !(m_debug_known_solution_file_name.empty()); m_ism.set_seed(m_random_seed); @@ -4718,4 +4722,6 @@ namespace nlsat { } bool solver::apply_levelwise() const { return m_imp->m_apply_lws; } unsigned solver::lws_spt_threshold() const { return m_imp->m_lws_spt_threshold; } + bool solver::lws_witness_subs_lc() const { return m_imp->m_lws_witness_subs_lc; } + bool solver::lws_witness_subs_disc() const { return m_imp->m_lws_witness_subs_disc; } }; diff --git a/src/nlsat/nlsat_solver.h b/src/nlsat/nlsat_solver.h index 566a7c09e..ff970fefa 100644 --- a/src/nlsat/nlsat_solver.h +++ b/src/nlsat/nlsat_solver.h @@ -249,6 +249,8 @@ namespace nlsat { assignment& sample(); bool apply_levelwise() const; unsigned lws_spt_threshold() const; + bool lws_witness_subs_lc() const; + bool lws_witness_subs_disc() const; void reset(); void collect_statistics(statistics & st); void reset_statistics();