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gt encoding of pb constraints

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2017-04-16 12:07:16 +09:00
parent b70096a97f
commit 41e1b9f3fe
2 changed files with 183 additions and 17 deletions
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146
src/ast/rewriter/pb2bv_rewriter.cpp
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@ -5,7 +5,7 @@ Module Name:
pb2bv_rewriter.cpp
Abstract:
Abstralct:
Conversion from pseudo-booleans to bit-vectors.
@ -25,6 +25,7 @@ Notes:
#include"ast_util.h"
#include"ast_pp.h"
#include"lbool.h"
#include"uint_set.h"
const unsigned g_primes[7] = { 2, 3, 5, 7, 11, 13, 17};
@ -111,7 +112,13 @@ struct pb2bv_rewriter::imp {
if (k.is_neg()) {
return expr_ref((is_le == l_false)?m.mk_true():m.mk_false(), m);
}
expr_ref result(m);
switch (is_le) {
case l_true: if (mk_le_tot(sz, args, k, result)) return result; else break;
case l_false: if (mk_ge_tot(sz, args, k, result)) return result; else break;
case l_undef: break;
}
#if 0
expr_ref result(m);
switch (is_le) {
@ -172,6 +179,141 @@ struct pb2bv_rewriter::imp {
}
}
/**
\brief Totalizer encoding. Based on a version by Miguel.
*/
bool mk_le_tot(unsigned sz, expr * const * args, rational const& _k, expr_ref& result) {
SASSERT(sz == m_coeffs.size());
if (!_k.is_unsigned() || sz == 0) return false;
unsigned k = _k.get_unsigned();
expr_ref_vector args1(m);
rational bound;
flip(sz, args, args1, _k, bound);
if (bound.get_unsigned() < k) {
return mk_ge_tot(sz, args1.c_ptr(), bound, result);
}
if (k > 20) {
return false;
}
result = m.mk_not(bounded_addition(sz, args, k + 1));
TRACE("pb", tout << result << "\n";);
return true;
}
bool mk_ge_tot(unsigned sz, expr * const * args, rational const& _k, expr_ref& result) {
SASSERT(sz == m_coeffs.size());
if (!_k.is_unsigned() || sz == 0) return false;
unsigned k = _k.get_unsigned();
expr_ref_vector args1(m);
rational bound;
flip(sz, args, args1, _k, bound);
if (bound.get_unsigned() < k) {
return mk_le_tot(sz, args1.c_ptr(), bound, result);
}
if (k > 20) {
return false;
}
result = bounded_addition(sz, args, k);
TRACE("pb", tout << result << "\n";);
return true;
}
void flip(unsigned sz, expr* const* args, expr_ref_vector& args1, rational const& k, rational& bound) {
bound = -k;
for (unsigned i = 0; i < sz; ++i) {
args1.push_back(mk_not(args[i]));
bound += m_coeffs[i];
}
}
expr_ref bounded_addition(unsigned sz, expr * const * args, unsigned k) {
SASSERT(sz > 0);
expr_ref result(m);
vector<expr_ref_vector> es;
vector<unsigned_vector> coeffs;
for (unsigned i = 0; i < m_coeffs.size(); ++i) {
unsigned_vector v;
expr_ref_vector e(m);
unsigned c = m_coeffs[i].get_unsigned();
v.push_back(c >= k ? k : c);
e.push_back(args[i]);
es.push_back(e);
coeffs.push_back(v);
}
while (es.size() > 1) {
for (unsigned i = 0; i + 1 < es.size(); i += 2) {
expr_ref_vector o(m);
unsigned_vector oc;
tot_adder(es[i], coeffs[i], es[i + 1], coeffs[i + 1], k, o, oc);
es[i / 2].set(o);
coeffs[i / 2] = oc;
}
if ((es.size() % 2) == 1) {
es[es.size() / 2].set(es.back());
coeffs[es.size() / 2] = coeffs.back();
}
es.shrink((1 + es.size())/2);
coeffs.shrink((1 + coeffs.size())/2);
}
SASSERT(coeffs.size() == 1);
SASSERT(coeffs[0].back() <= k);
if (coeffs[0].back() == k) {
result = es[0].back();
}
else {
result = m.mk_false();
}
return result;
}
void tot_adder(expr_ref_vector const& l, unsigned_vector const& lc,
expr_ref_vector const& r, unsigned_vector const& rc,
unsigned k,
expr_ref_vector& o, unsigned_vector & oc) {
SASSERT(l.size() == lc.size());
SASSERT(r.size() == rc.size());
uint_set sums;
vector<expr_ref_vector> trail;
u_map<unsigned> sum2def;
for (unsigned i = 0; i <= l.size(); ++i) {
for (unsigned j = (i == 0) ? 1 : 0; j <= r.size(); ++j) {
unsigned sum = std::min(k, ((i == 0) ? 0 : lc[i - 1]) + ((j == 0) ? 0 : rc[j - 1]));
sums.insert(sum);
}
}
uint_set::iterator it = sums.begin(), end = sums.end();
for (; it != end; ++it) {
oc.push_back(*it);
}
std::sort(oc.begin(), oc.end());
DEBUG_CODE(
for (unsigned i = 0; i + 1 < oc.size(); ++i) {
SASSERT(oc[i] < oc[i+1]);
});
for (unsigned i = 0; i < oc.size(); ++i) {
sum2def.insert(oc[i], i);
trail.push_back(expr_ref_vector(m));
}
for (unsigned i = 0; i <= l.size(); ++i) {
for (unsigned j = (i == 0) ? 1 : 0; j <= r.size(); ++j) {
if (i != 0 && j != 0 && (lc[i - 1] >= k || rc[j - 1] >= k)) continue;
unsigned sum = std::min(k, ((i == 0) ? 0 : lc[i - 1]) + ((j == 0) ? 0 : rc[j - 1]));
expr_ref_vector ands(m);
if (i != 0) {
ands.push_back(l[i - 1]);
}
if (j != 0) {
ands.push_back(r[j - 1]);
}
trail[sum2def.find(sum)].push_back(::mk_and(ands));
}
}
for (unsigned i = 0; i < oc.size(); ++i) {
o.push_back(::mk_or(trail[sum2def.find(oc[i])]));
}
}
/**
\brief MiniSat+ based encoding of PB constraints.
The procedure is described in "Translating Pseudo-Boolean Constraints into SAT "