mirror of
https://github.com/Z3Prover/z3
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adding local optimization to qsat
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner
parent
271b56aa1b
commit
a1aa166ef5
6 changed files with 414 additions and 58 deletions
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@ -20,6 +20,7 @@ Revision History:
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--*/
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#include "qe_arith.h"
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#include "qe_mbp.h"
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#include "ast_util.h"
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#include "arith_decl_plugin.h"
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#include "ast_pp.h"
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@ -49,14 +50,185 @@ namespace qe {
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}
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return is_divides(a, e1, e2, k, t) || is_divides(a, e2, e1, k, t);
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}
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enum ineq_type {
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t_eq,
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t_lt,
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t_le
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};
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struct tableau {
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struct var {
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unsigned m_id;
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rational m_coeff;
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var(unsigned id, rational const& c): m_id(id), m_coeff(c) {}
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};
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struct row {
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vector<var> m_vars; // variables with coefficients
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rational m_coeff; // constant in inequality
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ineq_type m_type; // inequality type
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rational m_value; // value of m_vars + m_coeff under interpretation of m_var2value.
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bool m_alive; // rows can be marked dead if they have been processed.
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};
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vector<row> m_rows;
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vector<unsigned_vector> m_var2rows;
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vector<rational> m_var2value;
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row m_objective;
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void invariant() {
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// variables in each row are sorted.
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}
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mbp::bound_type maximize(rational& value) {
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// tbd
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return mbp::unbounded;
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}
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rational get_coefficient(unsigned row_id, unsigned var_id) {
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row const& r = m_rows[row_id];
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unsigned lo = 0, hi = r.m_vars.size();
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while (lo < hi) {
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unsigned mid = lo + (hi - lo)/2;
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SASSERT(mid < hi);
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unsigned id = r.m_vars[mid].m_id;
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if (id == var_id) {
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lo = mid;
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break;
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}
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if (id < var_id) {
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lo = mid + 1;
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}
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else {
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hi = mid - 1;
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}
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}
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unsigned id = r.m_vars[lo].m_id;
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if (id == var_id) {
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return r.m_vars[lo].m_coeff;
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}
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else {
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return rational::zero();
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}
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}
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void resolve(unsigned row_id1, unsigned row_id2, unsigned x) {
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// row1 is of the form a1*x + t1 <~ 0
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// row2 is of the form a2*x + t2 <~ 0
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// assume that a1, a2 have the same sign.
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// if a1 is positive, then val(t1*a2/a1) <= val(t2*a1/a2)
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// replace row2 with the new inequality of the form:
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// t1 - a1*t2/a2 <~~ 0
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// where <~~ is strict if either <~1 or <~2 is strict.
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// if a1 is negative, then ....
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//
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}
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void multiply(rational const& c, unsigned row_id) {
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if (c.is_one()) {
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return;
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}
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row& r = m_rows[row_id];
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SASSERT(r.m_alive);
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for (unsigned i = 0; i < r.m_vars.size(); ++i) {
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r.m_vars[i].m_coeff *= c;
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}
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r.m_coeff *= c;
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r.m_value *= c;
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}
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// subtract row2 from row1, store result in row2
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vector<var> m_new_vars;
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void subtract(unsigned row_id1, unsigned row_id2) {
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m_new_vars.reset();
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row const& r1 = m_rows[row_id1];
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row& r2 = m_rows[row_id2];
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unsigned i = 0, j = 0;
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for(; i < r1.m_vars.size() || j < r2.m_vars.size(); ) {
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if (j == r2.m_vars.size()) {
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for (; i < r1.m_vars.size(); ++i) {
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m_new_vars.push_back(r1.m_vars[i]);
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m_var2rows[r1.m_vars[i].m_id].push_back(row_id2);
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}
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}
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else if (i == r1.m_vars.size()) {
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for (; j < r2.m_vars.size(); ++j) {
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m_new_vars.push_back(r2.m_vars[j]);
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m_new_vars.back().m_coeff.neg();
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}
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}
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else {
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unsigned v1 = r1.m_vars[i].m_id;
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unsigned v2 = r2.m_vars[j].m_id;
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if (v1 == v2) {
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m_new_vars.push_back(r1.m_vars[i]);
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m_new_vars.back().m_coeff -= r2.m_vars[j].m_coeff;
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++i;
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++j;
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if (m_new_vars.back().m_coeff.is_zero()) {
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m_new_vars.pop_back();
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}
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}
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else if (v1 < v2) {
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m_new_vars.push_back(r1.m_vars[i]);
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m_var2rows[r1.m_vars[i].m_id].push_back(row_id2);
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++i;
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}
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else {
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m_new_vars.push_back(r2.m_vars[j]);
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m_new_vars.back().m_coeff.neg();
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++j;
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}
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}
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}
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r2.m_coeff.neg();
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r2.m_coeff += r1.m_coeff;
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r2.m_vars.swap(m_new_vars);
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r2.m_value.neg();
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r2.m_value += r1.m_value;
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if (r1.m_type == t_lt) {
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r2.m_type = t_lt;
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}
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}
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void display(std::ostream& out) const {
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for (unsigned i = 0; i < m_rows.size(); ++i) {
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display(out, m_rows[i]);
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}
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}
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void display(std::ostream& out, row const& r) const {
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vector<var> const& vars = r.m_vars;
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for (unsigned i = 0; i < vars.size(); ++i) {
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if (i > 0 && vars[i].m_coeff.is_pos()) {
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out << "+ ";
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}
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out << vars[i].m_coeff << "* v" << vars[i].m_id << " ";
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}
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out << r.m_coeff;
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switch (r.m_type) {
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case t_eq:
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out << " = 0\n";
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break;
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case t_lt:
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out << " < 0\n";
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break;
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case t_le:
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out << " <= 0\n";
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break;
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}
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}
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};
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#if 0
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obj_map<expr, unsigned> m_expr2var;
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ptr_vector<expr> m_var2expr;
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#endif
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struct arith_project_plugin::imp {
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enum ineq_type {
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t_eq,
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t_lt,
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t_le
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};
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ast_manager& m;
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arith_util a;
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th_rewriter m_rw;
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@ -84,6 +256,62 @@ namespace qe {
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}
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}
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void insert_mul(expr* x, rational const& v, obj_map<expr, rational>& ts)
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{
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rational w;
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if (ts.find(x, w)) {
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ts.insert(x, w + v);
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}
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else {
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ts.insert(x, v);
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}
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}
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void linearize(model& model, rational const& mul, expr* t, rational& c, obj_map<expr, rational>& ts) {
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expr* t1, *t2, *t3;
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rational mul1;
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expr_ref val(m);
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if (a.is_mul(t, t1, t2) && is_numeral(model, t1, mul1)) {
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linearize(model, mul* mul1, t2, c, ts);
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}
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else if (a.is_mul(t, t1, t2) && is_numeral(model, t2, mul1)) {
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linearize(model, mul* mul1, t1, c, ts);
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}
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else if (a.is_add(t)) {
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app* ap = to_app(t);
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for (unsigned i = 0; i < ap->get_num_args(); ++i) {
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linearize(model, mul, ap->get_arg(i), c, ts);
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}
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}
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else if (a.is_sub(t, t1, t2)) {
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linearize(model, mul, t1, c, ts);
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linearize(model, -mul, t2, c, ts);
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}
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else if (a.is_uminus(t, t1)) {
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linearize(model, -mul, t1, c, ts);
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}
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else if (a.is_numeral(t, mul1)) {
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c += mul*mul1;
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}
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else if (extract_mod(model, t, val)) {
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insert_mul(val, mul, ts);
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}
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else if (m.is_ite(t, t1, t2, t3)) {
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VERIFY(model.eval(t1, val));
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SASSERT(m.is_true(val) || m.is_false(val));
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TRACE("qe", tout << mk_pp(t1, m) << " := " << val << "\n";);
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if (m.is_true(val)) {
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linearize(model, mul, t2, c, ts);
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}
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else {
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linearize(model, mul, t3, c, ts);
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}
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}
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else {
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insert_mul(t, mul, ts);
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}
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}
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void is_linear(model& model, rational const& mul, expr* t, rational& c, expr_ref_vector& ts) {
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expr* t1, *t2, *t3;
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rational mul1;
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@ -853,6 +1081,19 @@ namespace qe {
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}
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return true;
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}
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mbp::bound_type maximize(expr_ref_vector const& fmls, model& mdl, app* t, expr_ref& value, expr_ref& bound) {
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obj_map<expr, rational> ts;
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rational c(0), mul(1);
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linearize(mdl, mul, t, c, ts);
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// pick variables one by one from ts.
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// m_var = alloc(contains_app, m, v);
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// perform upper or lower projection depending on sign of v.
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//
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return mbp::unbounded;
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}
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};
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arith_project_plugin::arith_project_plugin(ast_manager& m) {
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@ -875,6 +1116,10 @@ namespace qe {
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return m_imp->a.get_family_id();
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}
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mbp::bound_type arith_project_plugin::maximize(expr_ref_vector const& fmls, model& mdl, app* t, expr_ref& value, expr_ref& bound) {
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return m_imp->maximize(fmls, mdl, t, value, bound);
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}
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bool arith_project(model& model, app* var, expr_ref_vector& lits) {
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ast_manager& m = lits.get_manager();
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arith_project_plugin ap(m);
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@ -29,6 +29,7 @@ namespace qe {
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virtual bool operator()(model& model, app* var, app_ref_vector& vars, expr_ref_vector& lits);
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virtual bool solve(model& model, app_ref_vector& vars, expr_ref_vector& lits);
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virtual family_id get_family_id();
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mbp::bound_type maximize(expr_ref_vector const& fmls, model& mdl, app* t, expr_ref& value, expr_ref& bound);
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};
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bool arith_project(model& model, app* var, expr_ref_vector& lits);
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@ -213,6 +213,11 @@ class mbp::impl {
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public:
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mbp::bound_type maximize(expr_ref_vector const& fmls, model& mdl, app* t, expr_ref& value, expr_ref& bound) {
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arith_project_plugin arith(m);
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return arith.maximize(fmls, mdl, t, value, bound);
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}
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void extract_literals(model& model, expr_ref_vector& fmls) {
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expr_ref val(m);
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for (unsigned i = 0; i < fmls.size(); ++i) {
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@ -415,3 +420,7 @@ void mbp::solve(model& model, app_ref_vector& vars, expr_ref_vector& fmls) {
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void mbp::extract_literals(model& model, expr_ref_vector& lits) {
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m_impl->extract_literals(model, lits);
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}
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mbp::bound_type mbp::maximize(expr_ref_vector const& fmls, model& mdl, app* t, expr_ref& value, expr_ref& bound) {
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return m_impl->maximize(fmls, mdl, t, value, bound);
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}
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@ -70,6 +70,17 @@ namespace qe {
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Extract literals from formulas based on model.
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*/
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void extract_literals(model& model, expr_ref_vector& lits);
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/**
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\brief
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Maximize objective t under current model for constraints in fmls.
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*/
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enum bound_type {
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unbounded,
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strict,
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non_strict
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};
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bound_type maximize(expr_ref_vector const& fmls, model& mdl, app* t, expr_ref& value, expr_ref& bound);
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};
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}
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183
src/qe/qsat.cpp
183
src/qe/qsat.cpp
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@ -536,6 +536,13 @@ namespace qe {
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);
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}
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};
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enum qsat_mode {
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qsat_qe,
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qsat_qe_rec,
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qsat_sat,
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qsat_maximize
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};
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class qsat : public tactic {
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@ -559,8 +566,7 @@ namespace qe {
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vector<app_ref_vector> m_vars; // variables from alternating prefixes.
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unsigned m_level;
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model_ref m_model;
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bool m_qelim; // perform quantifier elimination
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bool m_force_elim; // force elimination of variables during projection.
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qsat_mode m_mode;
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app_ref_vector m_avars; // variables to project
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app_ref_vector m_free_vars;
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@ -584,12 +590,12 @@ namespace qe {
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SASSERT(validate_model(asms));
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TRACE("qe", k.display(tout); display(tout << "\n", *m_model.get()); display(tout, asms); );
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push();
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break;
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break;
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case l_false:
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switch (m_level) {
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case 0: return l_false;
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case 1:
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if (!m_qelim) return l_true;
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if (m_mode == qsat_sat) return l_true;
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if (m_model.get()) {
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project_qe(asms);
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}
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@ -672,7 +678,7 @@ namespace qe {
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m_pred_abs.get_free_vars(fml, vars);
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m_vars.push_back(vars);
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vars.reset();
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if (m_qelim) {
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if (m_mode != qsat_sat) {
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is_forall = true;
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hoist.pull_quantifier(is_forall, fml, vars);
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m_vars.push_back(vars);
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@ -858,12 +864,18 @@ namespace qe {
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get_core(core, m_level);
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SASSERT(validate_core(core));
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get_vars(m_level);
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m_mbp(m_force_elim, m_avars, mdl, core);
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fml = negate_core(core);
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add_assumption(fml);
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m_answer.push_back(fml);
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m_free_vars.append(m_avars);
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pop(1);
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m_mbp(force_elim(), m_avars, mdl, core);
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if (m_mode == qsat_maximize) {
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maximize(core, mdl);
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pop(1);
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}
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else {
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fml = negate_core(core);
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add_assumption(fml);
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m_answer.push_back(fml);
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m_free_vars.append(m_avars);
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pop(1);
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}
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}
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void project(expr_ref_vector& core) {
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@ -878,7 +890,7 @@ namespace qe {
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get_vars(m_level-1);
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SASSERT(validate_project(mdl, core));
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m_mbp(m_force_elim, m_avars, mdl, core);
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m_mbp(force_elim(), m_avars, mdl, core);
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m_free_vars.append(m_avars);
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fml = negate_core(core);
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unsigned num_scopes = 0;
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@ -889,7 +901,7 @@ namespace qe {
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if (level.max() == UINT_MAX) {
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num_scopes = 2*(m_level/2);
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}
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else if (m_qelim && !m_force_elim) {
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else if (m_mode == qsat_qe_rec) {
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num_scopes = 2;
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}
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else {
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@ -903,7 +915,7 @@ namespace qe {
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pop(num_scopes);
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TRACE("qe", tout << "backtrack: " << num_scopes << " new level: " << m_level << "\nproject:\n" << core << "\n|->\n" << fml << "\n";);
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if (m_level == 0 && m_qelim) {
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if (m_level == 0 && m_mode != qsat_sat) {
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add_assumption(fml);
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}
|
||||
else {
|
||||
|
|
@ -919,9 +931,13 @@ namespace qe {
|
|||
}
|
||||
}
|
||||
|
||||
expr_ref negate_core(expr_ref_vector& core) {
|
||||
expr_ref negate_core(expr_ref_vector const& core) {
|
||||
return ::push_not(::mk_and(core));
|
||||
}
|
||||
|
||||
bool force_elim() const {
|
||||
return m_mode != qsat_qe_rec;
|
||||
}
|
||||
|
||||
expr_ref elim_rec(expr* fml) {
|
||||
expr_ref tmp(m);
|
||||
|
|
@ -1135,7 +1151,7 @@ namespace qe {
|
|||
|
||||
public:
|
||||
|
||||
qsat(ast_manager& m, params_ref const& p, bool qelim, bool force_elim):
|
||||
qsat(ast_manager& m, params_ref const& p, qsat_mode mode):
|
||||
m(m),
|
||||
m_mbp(m),
|
||||
m_fa(m),
|
||||
|
|
@ -1144,10 +1160,10 @@ namespace qe {
|
|||
m_answer(m),
|
||||
m_asms(m),
|
||||
m_level(0),
|
||||
m_qelim(qelim),
|
||||
m_force_elim(force_elim),
|
||||
m_mode(mode),
|
||||
m_avars(m),
|
||||
m_free_vars(m)
|
||||
m_free_vars(m),
|
||||
m_value(m)
|
||||
{
|
||||
reset();
|
||||
}
|
||||
|
|
@ -1182,7 +1198,7 @@ namespace qe {
|
|||
// fail if cores. (TBD)
|
||||
// fail if proofs. (TBD)
|
||||
|
||||
if (!m_force_elim) {
|
||||
if (m_mode == qsat_qe_rec) {
|
||||
fml = elim_rec(fml);
|
||||
in->reset();
|
||||
in->inc_depth();
|
||||
|
|
@ -1193,7 +1209,7 @@ namespace qe {
|
|||
|
||||
reset();
|
||||
TRACE("qe", tout << fml << "\n";);
|
||||
if (m_qelim) {
|
||||
if (m_mode != qsat_sat) {
|
||||
fml = push_not(fml);
|
||||
}
|
||||
hoist(fml);
|
||||
|
|
@ -1211,11 +1227,12 @@ namespace qe {
|
|||
case l_false:
|
||||
in->reset();
|
||||
in->inc_depth();
|
||||
if (m_qelim) {
|
||||
if (m_mode == qsat_qe) {
|
||||
fml = ::mk_and(m_answer);
|
||||
in->assert_expr(fml);
|
||||
}
|
||||
else {
|
||||
SASSERT(m_mode == qsat_sat);
|
||||
in->assert_expr(m.mk_false());
|
||||
}
|
||||
result.push_back(in.get());
|
||||
|
|
@ -1262,12 +1279,110 @@ namespace qe {
|
|||
}
|
||||
|
||||
tactic * translate(ast_manager & m) {
|
||||
return alloc(qsat, m, m_params, m_qelim, m_force_elim);
|
||||
}
|
||||
return alloc(qsat, m, m_params, m_mode);
|
||||
}
|
||||
|
||||
app* m_objective;
|
||||
expr_ref m_value;
|
||||
mbp::bound_type m_bound;
|
||||
bool m_was_sat;
|
||||
|
||||
lbool maximize(expr_ref_vector const& fmls, app* t, expr_ref& value, mbp::bound_type& bound) {
|
||||
expr_ref_vector defs(m);
|
||||
expr_ref fml = negate_core(fmls);
|
||||
hoist(fml);
|
||||
m_objective = t;
|
||||
m_value = 0;
|
||||
m_bound = mbp::unbounded;
|
||||
m_was_sat = false;
|
||||
m_pred_abs.abstract_atoms(fml, defs);
|
||||
fml = m_pred_abs.mk_abstract(fml);
|
||||
m_ex.assert_expr(mk_and(defs));
|
||||
m_fa.assert_expr(mk_and(defs));
|
||||
m_ex.assert_expr(fml);
|
||||
m_fa.assert_expr(m.mk_not(fml));
|
||||
lbool is_sat = check_sat();
|
||||
switch (is_sat) {
|
||||
case l_false:
|
||||
if (!m_was_sat) {
|
||||
return l_false;
|
||||
}
|
||||
break;
|
||||
case l_true:
|
||||
UNREACHABLE();
|
||||
break;
|
||||
case l_undef:
|
||||
std::string s = m_ex.k().last_failure_as_string();
|
||||
if (s == "ok") {
|
||||
s = m_fa.k().last_failure_as_string();
|
||||
}
|
||||
throw tactic_exception(s.c_str());
|
||||
}
|
||||
value = m_value;
|
||||
bound = m_bound;
|
||||
return l_true;
|
||||
}
|
||||
|
||||
void maximize(expr_ref_vector const& core, model& mdl) {
|
||||
TRACE("qe", tout << "maximize: " << core << "\n";);
|
||||
m_was_sat |= !core.empty();
|
||||
if (core.empty()) {
|
||||
m_ex.assert_expr(m.mk_false());
|
||||
m_fa.assert_expr(m.mk_false());
|
||||
return;
|
||||
}
|
||||
expr_ref bound(m);
|
||||
m_bound = m_mbp.maximize(core, mdl, m_objective, m_value, bound);
|
||||
switch (m_bound) {
|
||||
case mbp::unbounded:
|
||||
m_ex.assert_expr(m.mk_false());
|
||||
m_fa.assert_expr(m.mk_false());
|
||||
break;
|
||||
case mbp::strict:
|
||||
m_ex.assert_expr(bound);
|
||||
break;
|
||||
case mbp::non_strict:
|
||||
m_ex.assert_expr(bound);
|
||||
break;
|
||||
}
|
||||
}
|
||||
|
||||
};
|
||||
|
||||
|
||||
lbool maximize(expr_ref_vector const& fmls, app* t, expr_ref& value, mbp::bound_type& bound, params_ref const& p) {
|
||||
ast_manager& m = fmls.get_manager();
|
||||
qsat qs(m, p, qsat_maximize);
|
||||
return qs.maximize(fmls, t, value, bound);
|
||||
}
|
||||
};
|
||||
|
||||
tactic * mk_qsat_tactic(ast_manager& m, params_ref const& p) {
|
||||
return alloc(qe::qsat, m, p, qe::qsat_sat);
|
||||
}
|
||||
|
||||
tactic * mk_qe2_tactic(ast_manager& m, params_ref const& p) {
|
||||
return alloc(qe::qsat, m, p, qe::qsat_qe);
|
||||
}
|
||||
|
||||
tactic * mk_qe_rec_tactic(ast_manager& m, params_ref const& p) {
|
||||
return alloc(qe::qsat, m, p, qe::qsat_qe_rec);
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
#if 0
|
||||
|
||||
class min_max_opt {
|
||||
struct imp;
|
||||
imp* m_imp;
|
||||
public:
|
||||
min_max_opt(ast_manager& m);
|
||||
~min_max_opt();
|
||||
void add(expr* e);
|
||||
void add(expr_ref_vector const& fmls);
|
||||
lbool check(svector<bool> const& is_max, app_ref_vector const& vars, app* t);
|
||||
};
|
||||
|
||||
struct min_max_opt::imp {
|
||||
ast_manager& m;
|
||||
|
|
@ -1346,20 +1461,4 @@ namespace qe {
|
|||
return m_imp->check(is_max, vars, t);
|
||||
}
|
||||
|
||||
|
||||
|
||||
};
|
||||
|
||||
tactic * mk_qsat_tactic(ast_manager& m, params_ref const& p) {
|
||||
return alloc(qe::qsat, m, p, false, true);
|
||||
}
|
||||
|
||||
tactic * mk_qe2_tactic(ast_manager& m, params_ref const& p) {
|
||||
return alloc(qe::qsat, m, p, true, true);
|
||||
}
|
||||
|
||||
tactic * mk_qe_rec_tactic(ast_manager& m, params_ref const& p) {
|
||||
return alloc(qe::qsat, m, p, true, false);
|
||||
}
|
||||
|
||||
|
||||
#endif
|
||||
|
|
|
|||
|
|
@ -23,6 +23,7 @@ Revision History:
|
|||
|
||||
#include "tactic.h"
|
||||
#include "filter_model_converter.h"
|
||||
#include "qe_mbp.h"
|
||||
|
||||
namespace qe {
|
||||
|
||||
|
|
@ -113,17 +114,7 @@ namespace qe {
|
|||
void collect_statistics(statistics& st) const;
|
||||
};
|
||||
|
||||
class min_max_opt {
|
||||
struct imp;
|
||||
imp* m_imp;
|
||||
public:
|
||||
min_max_opt(ast_manager& m);
|
||||
~min_max_opt();
|
||||
void add(expr* e);
|
||||
void add(expr_ref_vector const& fmls);
|
||||
lbool check(svector<bool> const& is_max, app_ref_vector const& vars, app* t);
|
||||
};
|
||||
|
||||
lbool maximize(expr_ref_vector const& fmls, app* t, expr_ref& value, mbp::bound_type& bound, params_ref const& p);
|
||||
|
||||
}
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue