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/******************************************************************************
* Top contributors (to current version):
* Andrew Reynolds
*
* This file is part of the cvc5 project.
*
* Copyright (c) 2009-2021 by the authors listed in the file AUTHORS
* in the top-level source directory and their institutional affiliations.
* All rights reserved. See the file COPYING in the top-level source
* directory for licensing information.
* ****************************************************************************
*
* Branch and bound for arithmetic
*/
#include "theory/arith/branch_and_bound.h"
#include "options/arith_options.h"
#include "proof/eager_proof_generator.h"
#include "proof/proof_node.h"
#include "theory/arith/arith_utilities.h"
#include "theory/rewriter.h"
#include "theory/theory.h"
using namespace cvc5::kind;
namespace cvc5 {
namespace theory {
namespace arith {
BranchAndBound::BranchAndBound(Env& env,
ArithState& s,
InferenceManager& im,
PreprocessRewriteEq& ppre,
ProofNodeManager* pnm)
: EnvObj(env),
d_astate(s),
d_im(im),
d_ppre(ppre),
d_pfGen(new EagerProofGenerator(pnm, userContext())),
d_pnm(pnm)
{
}
TrustNode BranchAndBound::branchIntegerVariable(TNode var, Rational value)
{
TrustNode lem = TrustNode::null();
NodeManager* nm = NodeManager::currentNM();
Integer floor = value.floor();
if (options().arith.brabTest)
{
Trace("integers") << "branch-round-and-bound enabled" << std::endl;
Integer ceil = value.ceiling();
Rational f = value - floor;
// Multiply by -1 to get abs value.
Rational c = (value - ceil) * (-1);
Integer nearest = (c > f) ? floor : ceil;
// Prioritize trying a simple rounding of the real solution first,
// it that fails, fall back on original branch and bound strategy.
Node ub = rewrite(nm->mkNode(LEQ, var, mkRationalNode(nearest - 1)));
Node lb = rewrite(nm->mkNode(GEQ, var, mkRationalNode(nearest + 1)));
Node right = nm->mkNode(OR, ub, lb);
Node rawEq = nm->mkNode(EQUAL, var, mkRationalNode(nearest));
Node eq = rewrite(rawEq);
// Also preprocess it before we send it out. This is important since
// arithmetic may prefer eliminating equalities.
TrustNode teq;
if (Theory::theoryOf(eq) == THEORY_ARITH)
{
teq = d_ppre.ppRewriteEq(eq);
eq = teq.isNull() ? eq : teq.getNode();
}
Node literal = d_astate.getValuation().ensureLiteral(eq);
Trace("integers") << "eq: " << eq << "\nto: " << literal << std::endl;
d_im.requirePhase(literal, true);
Node l = nm->mkNode(OR, literal, right);
Trace("integers") << "l: " << l << std::endl;
if (proofsEnabled())
{
Node less = nm->mkNode(LT, var, mkRationalNode(nearest));
Node greater = nm->mkNode(GT, var, mkRationalNode(nearest));
// TODO (project #37): justify. Thread proofs through *ensureLiteral*.
Debug("integers::pf") << "less: " << less << std::endl;
Debug("integers::pf") << "greater: " << greater << std::endl;
Debug("integers::pf") << "literal: " << literal << std::endl;
Debug("integers::pf") << "eq: " << eq << std::endl;
Debug("integers::pf") << "rawEq: " << rawEq << std::endl;
Pf pfNotLit = d_pnm->mkAssume(literal.negate());
// rewrite notLiteral to notRawEq, using teq.
Pf pfNotRawEq =
literal == rawEq
? pfNotLit
: d_pnm->mkNode(
PfRule::MACRO_SR_PRED_TRANSFORM,
{pfNotLit,
teq.getGenerator()->getProofFor(teq.getProven())},
{rawEq.negate()});
Pf pfBot = d_pnm->mkNode(
PfRule::CONTRA,
{d_pnm->mkNode(PfRule::ARITH_TRICHOTOMY,
{d_pnm->mkAssume(less.negate()), pfNotRawEq},
{greater}),
d_pnm->mkAssume(greater.negate())},
{});
std::vector<Node> assumptions = {
literal.negate(), less.negate(), greater.negate()};
// Proof of (not (and (not (= v i)) (not (< v i)) (not (> v i))))
Pf pfNotAnd = d_pnm->mkScope(pfBot, assumptions);
Pf pfL = d_pnm->mkNode(PfRule::MACRO_SR_PRED_TRANSFORM,
{d_pnm->mkNode(PfRule::NOT_AND, {pfNotAnd}, {})},
{l});
lem = d_pfGen->mkTrustNode(l, pfL);
}
else
{
lem = TrustNode::mkTrustLemma(l, nullptr);
}
}
else
{
Node ub = rewrite(nm->mkNode(LEQ, var, mkRationalNode(floor)));
Node lb = ub.notNode();
if (proofsEnabled())
{
lem =
d_pfGen->mkTrustNode(nm->mkNode(OR, ub, lb), PfRule::SPLIT, {}, {ub});
}
else
{
lem = TrustNode::mkTrustLemma(nm->mkNode(OR, ub, lb), nullptr);
}
}
Trace("integers") << "integers: branch & bound: " << lem << std::endl;
return lem;
}
bool BranchAndBound::proofsEnabled() const { return d_pnm != nullptr; }
} // namespace arith
} // namespace theory
} // namespace cvc5
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