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adding pre-processing of BP constraints
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
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Nikolaj Bjorner
parent
670f56e5e4
commit
24f2fd380c
9 changed files with 679 additions and 281 deletions
263
src/ast/rewriter/pb_rewriter_def.h
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263
src/ast/rewriter/pb_rewriter_def.h
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/*++
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Copyright (c) 2013 Microsoft Corporation
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Module Name:
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pb_rewriter_def.h
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Abstract:
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Basic rewriting rules for PB constraints.
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Author:
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Nikolaj Bjorner (nbjorner) 2013-14-12
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Notes:
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--*/
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#ifndef _PB_REWRITER_DEF_H_
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#define _PB_REWRITER_DEF_H_
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#include"pb_rewriter.h"
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template<typename PBU>
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void pb_rewriter_util<PBU>::display(std::ostream& out, typename PBU::args_t& args, typename PBU::numeral& k) {
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for (unsigned i = 0; i < args.size(); ++i) {
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out << args[i].second << " * ";
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m_util.display(out, args[i].first);
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out << " ";
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if (i+1 < args.size()) out << "+ ";
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}
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out << " >= " << k << "\n";
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}
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template<typename PBU>
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void pb_rewriter_util<PBU>::unique(typename PBU::args_t& args, typename PBU::numeral& k) {
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TRACE("pb", display(tout << "pre-unique:", args, k););
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for (unsigned i = 0; i < args.size(); ++i) {
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if (m_util.is_negated(args[i].first)) {
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args[i].first = m_util.negate(args[i].first);
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k -= args[i].second;
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args[i].second = -args[i].second;
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}
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}
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// remove constants
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for (unsigned i = 0; i < args.size(); ++i) {
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if (m_util.is_true(args[i].first)) {
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k -= args[i].second;
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std::swap(args[i], args[args.size()-1]);
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args.pop_back();
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--i;
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}
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else if (m_util.is_false(args[i].first)) {
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std::swap(args[i], args[args.size()-1]);
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args.pop_back();
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--i;
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}
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}
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// sort and coalesce arguments:
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PBU::compare cmp;
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std::sort(args.begin(), args.end(), cmp);
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unsigned i = 0, j = 1;
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for (; j < args.size(); ++i) {
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SASSERT(j > i);
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for (; j < args.size() && args[j].first == args[i].first; ++j) {
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args[i].second += args[j].second;
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}
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if (j < args.size()) {
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args[i+1].first = args[j].first;
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args[i+1].second = args[j].second;
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++j;
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}
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}
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if (i + 1 < args.size()) {
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args.resize(i+1);
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}
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TRACE("pb", display(tout << "post-unique:", args, k););
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}
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template<typename PBU>
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lbool pb_rewriter_util<PBU>::normalize(typename PBU::args_t& args, typename PBU::numeral& k) {
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TRACE("pb", display(tout << "pre-normalize:", args, k););
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//
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// Ensure all coefficients are positive:
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// c*l + y >= k
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// <=>
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// c*(1-~l) + y >= k
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// <=>
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// c - c*~l + y >= k
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// <=>
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// -c*~l + y >= k - c
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//
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PBU::numeral sum(0);
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for (unsigned i = 0; i < args.size(); ++i) {
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PBU::numeral c = args[i].second;
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if (c.is_neg()) {
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args[i].second = -c;
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args[i].first = m_util.negate(args[i].first);
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k -= c;
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}
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sum += args[i].second;
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}
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// detect tautologies:
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if (k <= PBU::numeral::zero()) {
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args.reset();
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k = PBU::numeral::zero();
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return l_true;
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}
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// detect infeasible constraints:
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if (sum < k) {
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args.reset();
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k = PBU::numeral::one();
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return l_false;
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}
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bool all_int = true;
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for (unsigned i = 0; all_int && i < args.size(); ++i) {
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all_int = args[i].second.is_int();
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}
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if (!all_int) {
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// normalize to integers.
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PBU::numeral d(denominator(k));
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for (unsigned i = 0; i < args.size(); ++i) {
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d = lcm(d, denominator(args[i].second));
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}
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SASSERT(!d.is_one());
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k *= d;
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for (unsigned i = 0; i < args.size(); ++i) {
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args[i].second *= d;
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}
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}
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// Ensure the largest coefficient is not larger than k:
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sum = PBU::numeral::zero();
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for (unsigned i = 0; i < args.size(); ++i) {
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PBU::numeral c = args[i].second;
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if (c > k) {
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args[i].second = k;
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}
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sum += args[i].second;
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}
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SASSERT(!args.empty());
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// normalize tight inequalities to unit coefficients.
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if (sum == k) {
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for (unsigned i = 0; i < args.size(); ++i) {
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args[i].second = PBU::numeral::one();
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}
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k = PBU::numeral(args.size());
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}
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// apply cutting plane reduction:
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PBU::numeral g(0);
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for (unsigned i = 0; !g.is_one() && i < args.size(); ++i) {
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PBU::numeral c = args[i].second;
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if (c != k) {
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if (g.is_zero()) {
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g = c;
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}
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else {
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g = gcd(g, c);
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}
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}
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}
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if (g.is_zero()) {
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// all coefficients are equal to k.
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for (unsigned i = 0; i < args.size(); ++i) {
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SASSERT(args[i].second == k);
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args[i].second = PBU::numeral::one();
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}
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k = PBU::numeral::one();
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}
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else if (g > PBU::numeral::one()) {
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IF_VERBOSE(3, verbose_stream() << "cut " << g << "\n";
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display(verbose_stream(), args, k);
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);
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//
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// Example 5x + 5y + 2z + 2u >= 5
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// becomes 3x + 3y + z + u >= 3
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//
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PBU::numeral k_new = div(k, g);
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if (!(k % g).is_zero()) { // k_new is the ceiling of k / g.
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k_new++;
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}
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for (unsigned i = 0; i < args.size(); ++i) {
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SASSERT(args[i].second.is_pos());
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PBU::numeral c = args[i].second;
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if (c == k) {
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c = k_new;
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}
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else {
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c = div(c, g);
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}
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args[i].second = c;
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SASSERT(args[i].second.is_pos());
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}
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k = k_new;
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}
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//
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// normalize coefficients that fall within a range
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// k/n <= ... < k/(n-1) for some n = 1,2,...
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//
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// e.g, k/n <= min <= max < k/(n-1)
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// k/min <= n, n-1 < k/max
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// . floor(k/max) = ceil(k/min) - 1
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// . floor(k/max) < k/max
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//
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// example: k = 5, min = 3, max = 4: 5/3 -> 2 5/4 -> 1, n = 2
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// replace all coefficients by 1, and k by 2.
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//
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if (!k.is_one()) {
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PBU::numeral min = args[0].second, max = args[0].second;
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for (unsigned i = 1; i < args.size(); ++i) {
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if (args[i].second < min) min = args[i].second;
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if (args[i].second > max) max = args[i].second;
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}
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PBU::numeral n0 = k/max;
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PBU::numeral n1 = floor(n0);
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PBU::numeral n2 = ceil(k/min) - PBU::numeral::one();
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if (n1 == n2 && !n0.is_int()) {
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IF_VERBOSE(3, display(verbose_stream() << "set cardinality\n", args, k););
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for (unsigned i = 0; i < args.size(); ++i) {
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args[i].second = PBU::numeral::one();
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}
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k = n1 + PBU::numeral::one();
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}
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}
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return l_undef;
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}
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template<typename PBU>
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void pb_rewriter_util<PBU>::prune(typename PBU::args_t& args, typename PBU::numeral& k) {
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PBU::numeral nlt(0);
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unsigned occ = 0;
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for (unsigned i = 0; nlt < k && i < args.size(); ++i) {
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if (args[i].second < k) {
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nlt += args[i].second;
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++occ;
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}
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}
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if (0 < occ && nlt < k) {
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for (unsigned i = 0; i < args.size(); ++i) {
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if (args[i].second < k) {
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args[i] = args.back();
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args.pop_back();
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--i;
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}
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}
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normalize(args, k);
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}
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}
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#endif
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