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https://github.com/Z3Prover/z3
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fix a typo in poly_has_roots
Signed-off-by: Lev Nachmanson <levnach@hotmail.com>
This commit is contained in:
Lev Nachmanson
parent
60f9edb65f
commit
a19db1f7a7
3 changed files with 289 additions and 3 deletions
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@ -28,6 +28,112 @@ Notes:
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#include <iostream>
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#include <vector>
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// Helper function to check if a point (given by counter_as) is inside a levelwise cell.
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// Returns true if the point is inside ALL cell intervals, false otherwise.
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// Prints diagnostic info about which constraint was violated (if any).
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static bool is_point_inside_cell(
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anum_manager& am,
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polynomial::manager& pm,
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std_vector<nlsat::levelwise::root_function_interval> const& cell,
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nlsat::assignment const& counter_as,
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bool verbose = true)
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{
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for (unsigned level = 0; level < cell.size(); ++level) {
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auto const& interval = cell[level];
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// Skip whole-line sectors - no constraint
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if (!interval.is_section() && interval.l_inf() && interval.u_inf())
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continue;
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// Get the value at this level from counter_as
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if (!counter_as.is_assigned(level))
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continue; // Variable not assigned in counterexample
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scoped_anum counter_val(am);
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am.set(counter_val, counter_as.value(level));
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// Build partial assignment up to this level (exclusive) for root isolation
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nlsat::assignment partial_as(am);
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for (unsigned j = 0; j < level; ++j) {
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if (counter_as.is_assigned(j)) {
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scoped_anum v(am);
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am.set(v, counter_as.value(j));
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partial_as.set(j, v);
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}
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}
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if (interval.is_section()) {
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// Section: counter must equal the root
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polynomial_ref section_p(interval.l, pm);
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scoped_anum_vector roots(am);
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am.isolate_roots(section_p, nlsat::undef_var_assignment(partial_as, level), roots);
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if (roots.size() >= interval.l_index) {
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bool at_root = am.eq(counter_val, roots[interval.l_index - 1]);
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if (!at_root) {
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if (verbose) {
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std::cout << " Level " << level << ": OUTSIDE (not at section root)\n";
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std::cout << " Section root = ";
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am.display_decimal(std::cout, roots[interval.l_index - 1], 6);
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std::cout << ", counter = ";
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am.display_decimal(std::cout, counter_val, 6);
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std::cout << "\n";
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}
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return false;
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}
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}
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} else {
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// Sector: check lower and upper bounds
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if (!interval.l_inf()) {
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polynomial_ref lower_p(interval.l, pm);
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scoped_anum_vector lower_roots(am);
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am.isolate_roots(lower_p, nlsat::undef_var_assignment(partial_as, level), lower_roots);
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if (lower_roots.size() >= interval.l_index) {
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int cmp = am.compare(counter_val, lower_roots[interval.l_index - 1]);
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if (cmp <= 0) { // counter <= lower bound, violates (lower, ...)
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if (verbose) {
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std::cout << " Level " << level << ": OUTSIDE (at or below lower bound)\n";
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std::cout << " Lower bound = ";
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am.display_decimal(std::cout, lower_roots[interval.l_index - 1], 6);
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std::cout << ", counter = ";
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am.display_decimal(std::cout, counter_val, 6);
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std::cout << "\n";
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}
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return false;
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}
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}
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}
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if (!interval.u_inf()) {
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polynomial_ref upper_p(interval.u, pm);
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scoped_anum_vector upper_roots(am);
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am.isolate_roots(upper_p, nlsat::undef_var_assignment(partial_as, level), upper_roots);
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if (upper_roots.size() >= interval.u_index) {
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int cmp = am.compare(counter_val, upper_roots[interval.u_index - 1]);
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if (cmp >= 0) { // counter >= upper bound, violates (..., upper)
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if (verbose) {
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std::cout << " Level " << level << ": OUTSIDE (at or above upper bound)\n";
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std::cout << " Upper bound = ";
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am.display_decimal(std::cout, upper_roots[interval.u_index - 1], 6);
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std::cout << ", counter = ";
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am.display_decimal(std::cout, counter_val, 6);
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std::cout << "\n";
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}
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return false;
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}
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}
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}
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}
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}
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if (verbose) {
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std::cout << " Point is INSIDE the cell (all constraints satisfied)\n";
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}
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return true;
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}
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nlsat::interval_set_ref tst_interval(nlsat::interval_set_ref const & s1,
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nlsat::interval_set_ref const & s2,
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unsigned expected_num_intervals,
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@ -2061,9 +2167,188 @@ static void tst_unsound_lws_disc_zero() {
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std::cout << "\n=== END tst_unsound_lws_disc_zero ===\n\n";
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}
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// Test case for unsound lemma from ppblockterm.t2__p7867_terminationG_0.smt2
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// Issue z3-76w: levelwise produces unsound cell
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static void tst_unsound_lws_ppblockterm() {
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std::cout << "=== tst_unsound_lws_ppblockterm ===\n";
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params_ref ps;
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ps.set_bool("lws", true);
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reslimit rlim;
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nlsat::solver s(rlim, ps, false);
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anum_manager & am = s.am();
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nlsat::pmanager & pm = s.pm();
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polynomial::cache cache(pm);
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// Create 25 variables x0 to x24
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nlsat::var vars[25];
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polynomial_ref xvars[25] = {
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polynomial_ref(pm), polynomial_ref(pm), polynomial_ref(pm), polynomial_ref(pm), polynomial_ref(pm),
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polynomial_ref(pm), polynomial_ref(pm), polynomial_ref(pm), polynomial_ref(pm), polynomial_ref(pm),
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polynomial_ref(pm), polynomial_ref(pm), polynomial_ref(pm), polynomial_ref(pm), polynomial_ref(pm),
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polynomial_ref(pm), polynomial_ref(pm), polynomial_ref(pm), polynomial_ref(pm), polynomial_ref(pm),
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polynomial_ref(pm), polynomial_ref(pm), polynomial_ref(pm), polynomial_ref(pm), polynomial_ref(pm)
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};
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for (unsigned i = 0; i < 25; i++) {
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vars[i] = s.mk_var(false);
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xvars[i] = pm.mk_polynomial(vars[i]);
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}
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// Aliases for readability
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polynomial_ref &x2 = xvars[2], &x4 = xvars[4], &x5 = xvars[5];
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polynomial_ref &x9 = xvars[9], &x10 = xvars[10], &x11 = xvars[11];
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polynomial_ref &x12 = xvars[12], &x13 = xvars[13], &x15 = xvars[15];
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polynomial_ref &x16 = xvars[16], &x19 = xvars[19], &x24 = xvars[24];
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// p[0]: x16 + x9
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polynomial_ref p0(pm);
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p0 = x16 + x9;
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// p[1]: x16 x24 + x9 x24 + x13 x19 + x5 x19 + x12 x15 + x10 x15 - 2
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polynomial_ref p1(pm);
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p1 = x16 * x24 + x9 * x24 + x13 * x19 + x5 * x19 + x12 * x15 + x10 * x15 - 2;
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// p[2]: x4
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polynomial_ref p2(pm);
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p2 = x4;
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// p[3]: x4 x24 + x2 x19 + x11 x15
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polynomial_ref p3(pm);
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p3 = x4 * x24 + x2 * x19 + x11 * x15;
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std::cout << "Input polynomials:\n";
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std::cout << " p0: " << p0 << "\n";
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std::cout << " p1: " << p1 << "\n";
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std::cout << " p2: " << p2 << "\n";
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std::cout << " p3: " << p3 << "\n\n";
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// Set sample point values
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// x0->1, x1->1, x2->-1, x3->-1, x4->1, x5->-1, x6->1, x7->2, x8->1
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// x9->1, x10->-1, x11->1, x12->-2, x13->-2, x14->-2, x15->0, x16->2
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// x17->0, x18->0, x19->0, x20->0, x21->0, x22->0, x23->0
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int sample_vals[24] = {1, 1, -1, -1, 1, -1, 1, 2, 1, 1, -1, 1, -2, -2, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0};
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scoped_anum val(am);
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nlsat::assignment sample_as(am);
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for (unsigned i = 0; i < 24; i++) {
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am.set(val, sample_vals[i]);
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sample_as.set(vars[i], val);
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}
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s.set_rvalues(sample_as);
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std::cout << "Sample point (x0..x23):\n";
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for (unsigned i = 0; i < 24; i++) {
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std::cout << " x" << i << " -> " << sample_vals[i] << "\n";
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}
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std::cout << "\n";
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// Evaluate polynomials at sample (with x24 = 0 for checking)
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am.set(val, 0);
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sample_as.set(vars[24], val);
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std::cout << "Polynomial signs at sample (x24=0):\n";
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std::cout << " p0 sign: " << am.eval_sign_at(p0, sample_as) << "\n";
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std::cout << " p1 sign: " << am.eval_sign_at(p1, sample_as) << "\n";
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std::cout << " p2 sign: " << am.eval_sign_at(p2, sample_as) << "\n";
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std::cout << " p3 sign: " << am.eval_sign_at(p3, sample_as) << "\n\n";
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// Counterexample from the unsound lemma:
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// x2=-1, x4=1, x5=0, x9=0, x10=0, x11=-1, x12=-1, x13=-2, x15=3, x16=2, x19=0, x24=3
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nlsat::assignment counter_as(am);
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am.set(val, -1); counter_as.set(vars[2], val);
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am.set(val, 1); counter_as.set(vars[4], val);
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am.set(val, 0); counter_as.set(vars[5], val);
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am.set(val, 0); counter_as.set(vars[9], val);
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am.set(val, 0); counter_as.set(vars[10], val);
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am.set(val, -1); counter_as.set(vars[11], val);
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am.set(val, -1); counter_as.set(vars[12], val);
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am.set(val, -2); counter_as.set(vars[13], val);
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am.set(val, 3); counter_as.set(vars[15], val);
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am.set(val, 2); counter_as.set(vars[16], val);
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am.set(val, 0); counter_as.set(vars[19], val);
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am.set(val, 3); counter_as.set(vars[24], val);
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std::cout << "Counterexample point:\n";
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std::cout << " x2=-1, x4=1, x5=0, x9=0, x10=0, x11=-1, x12=-1, x13=-2, x15=3, x16=2, x19=0, x24=3\n\n";
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std::cout << "Polynomial signs at counterexample:\n";
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std::cout << " p0 sign: " << am.eval_sign_at(p0, counter_as) << "\n";
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std::cout << " p1 sign: " << am.eval_sign_at(p1, counter_as) << "\n";
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std::cout << " p2 sign: " << am.eval_sign_at(p2, counter_as) << "\n";
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std::cout << " p3 sign: " << am.eval_sign_at(p3, counter_as) << "\n\n";
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// Build polynomial vector
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polynomial_ref_vector polys(pm);
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polys.push_back(p0);
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polys.push_back(p1);
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polys.push_back(p2);
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polys.push_back(p3);
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unsigned max_x = vars[24]; // x24 is the highest variable
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std::cout << "Running levelwise with max_x = x24...\n";
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nlsat::levelwise lws(s, polys, max_x, s.sample(), pm, am, cache);
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auto cell = lws.single_cell();
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if (lws.failed()) {
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std::cout << "Levelwise FAILED\n";
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} else {
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std::cout << "Levelwise succeeded\n";
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std::cout << "--- LEMMA from levelwise ---\n";
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for (unsigned i = 0; i < cell.size(); i++) {
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auto const& interval = cell[i];
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std::cout << "Level x" << i << ": ";
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if (interval.is_section()) {
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std::cout << "section at root[" << interval.l_index << "] of " << interval.l << "\n";
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} else {
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if (interval.l_inf())
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std::cout << "(-oo, ";
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else
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std::cout << "(root[" << interval.l_index << "] of " << interval.l << ", ";
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if (interval.u_inf())
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std::cout << "+oo)";
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else
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std::cout << "root[" << interval.u_index << "] of " << interval.u << ")";
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std::cout << "\n";
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}
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}
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std::cout << "--- END LEMMA ---\n\n";
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// Check polynomial signs at sample and counterexample
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int p0_sample = am.eval_sign_at(p0, sample_as);
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int p1_sample = am.eval_sign_at(p1, sample_as);
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int p2_sample = am.eval_sign_at(p2, sample_as);
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int p3_sample = am.eval_sign_at(p3, sample_as);
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int p0_counter = am.eval_sign_at(p0, counter_as);
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int p1_counter = am.eval_sign_at(p1, counter_as);
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int p2_counter = am.eval_sign_at(p2, counter_as);
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int p3_counter = am.eval_sign_at(p3, counter_as);
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bool signs_differ = (p0_sample != p0_counter) || (p1_sample != p1_counter) ||
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(p2_sample != p2_counter) || (p3_sample != p3_counter);
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if (signs_differ) {
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std::cout << "Polynomial signs DIFFER between sample and counterexample.\n";
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} else {
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std::cout << "Polynomial signs match between sample and counterexample.\n";
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}
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// Verify that the counterexample is OUTSIDE the cell (cell is sound)
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std::cout << "\nChecking if counterexample is inside cell:\n";
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bool inside = is_point_inside_cell(am, pm, cell, counter_as);
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// For a sound cell with differing signs, counterexample must be OUTSIDE
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ENSURE(!inside);
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std::cout << "SUCCESS: Counterexample is OUTSIDE the cell (cell is sound)\n";
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}
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std::cout << "=== END tst_unsound_lws_ppblockterm ===\n\n";
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}
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void tst_nlsat() {
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tst_unsound_lws_disc_zero();
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std::cout << "------------------\n";
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// TODO: Fix z3-76w - ppblockterm test fails because counterexample is inside cell
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// tst_unsound_lws_ppblockterm();
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// std::cout << "------------------\n";
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tst_unsound_lws_n46();
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std::cout << "------------------\n";
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tst_unsound_lws_et4();
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