Based on #4774, this PR adds a new CadSolver class that allows the NonlinearExtension to actually employ the CAD-based method. In more detail:
add --nl-cad option
add CadSolver class that wraps cad::CDCAC with support for checks, model construction and conflict generation
add new Inference types for the NlLemma class
use CadSolver in NonlinearExtension (if --nl-cad is given)
theory/arith/linear_equality.h
theory/arith/matrix.cpp
theory/arith/matrix.h
+ theory/arith/nl/cad_solver.cpp
+ theory/arith/nl/cad_solver.h
theory/arith/nl/cad/cdcac.cpp
theory/arith/nl/cad/cdcac.h
theory/arith/nl/cad/cdcac_utils.cpp
default = "true"
read_only = true
help = "whether to use simple rounding, similar to a unit-cube test, for integers"
+
+[[option]]
+ name = "nlCad"
+ category = "regular"
+ long = "nl-cad"
+ type = "bool"
+ default = "false"
+ help = "whether to use the cylindrical algebraic decomposition solver for non-linear arithmetic"
+
--- /dev/null
+/********************* */
+/*! \file cad_solver.cpp
+ ** \verbatim
+ ** Top contributors (to current version):
+ ** Gereon Kremer
+ ** This file is part of the CVC4 project.
+ ** Copyright (c) 2009-2019 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.\endverbatim
+ **
+ ** \brief Implementation of new non-linear solver
+ **/
+
+#include "theory/arith/nl/cad_solver.h"
+
+#ifdef CVC4_POLY_IMP
+#include <poly/polyxx.h>
+#endif
+
+#include "inference.h"
+#include "theory/arith/nl/cad/cdcac.h"
+#include "theory/arith/nl/poly_conversion.h"
+#include "util/poly_util.h"
+
+namespace CVC4 {
+namespace theory {
+namespace arith {
+namespace nl {
+
+CadSolver::CadSolver(TheoryArith& containing, NlModel& model)
+ : d_foundSatisfiability(false), d_containing(containing), d_model(model)
+{
+ d_ranVariable =
+ NodeManager::currentNM()->mkSkolem("__z",
+ NodeManager::currentNM()->realType(),
+ "",
+ NodeManager::SKOLEM_EXACT_NAME);
+}
+
+CadSolver::~CadSolver() {}
+
+void CadSolver::initLastCall(const std::vector<Node>& assertions)
+{
+#ifdef CVC4_POLY_IMP
+ if (Trace.isOn("nl-cad"))
+ {
+ Trace("nl-cad") << "CadSolver::initLastCall" << std::endl;
+ Trace("nl-cad") << "* Assertions: " << std::endl;
+ for (const Node& a : assertions)
+ {
+ Trace("nl-cad") << " " << a << std::endl;
+ }
+ }
+ // store or process assertions
+ d_CAC.reset();
+ for (const Node& a : assertions)
+ {
+ d_CAC.getConstraints().addConstraint(a);
+ }
+ d_CAC.computeVariableOrdering();
+#else
+ Warning() << "Tried to use CadSolver but libpoly is not available. Compile "
+ "with --poly."
+ << std::endl;
+#endif
+}
+
+std::vector<NlLemma> CadSolver::checkFull()
+{
+#ifdef CVC4_POLY_IMP
+ std::vector<NlLemma> lems;
+ auto covering = d_CAC.getUnsatCover();
+ if (covering.empty())
+ {
+ d_foundSatisfiability = true;
+ Trace("nl-cad") << "SAT: " << d_CAC.getModel() << std::endl;
+ }
+ else
+ {
+ d_foundSatisfiability = false;
+ auto mis = collectConstraints(covering);
+ Trace("nl-cad") << "Collected MIS: " << mis << std::endl;
+ auto* nm = NodeManager::currentNM();
+ for (auto& n : mis)
+ {
+ n = n.negate();
+ }
+ Assert(!mis.empty()) << "Infeasible subset can not be empty";
+ if (mis.size() == 1)
+ {
+ lems.emplace_back(mis.front(), Inference::CAD_CONFLICT);
+ }
+ else
+ {
+ lems.emplace_back(nm->mkNode(Kind::OR, mis), Inference::CAD_CONFLICT);
+ }
+ Trace("nl-cad") << "UNSAT with MIS: " << lems.back().d_lemma << std::endl;
+ }
+ return lems;
+#else
+ Warning() << "Tried to use CadSolver but libpoly is not available. Compile "
+ "with --poly."
+ << std::endl;
+#endif
+}
+
+bool CadSolver::constructModelIfAvailable(std::vector<Node>& assertions)
+{
+#ifdef CVC4_POLY_IMP
+ if (!d_foundSatisfiability)
+ {
+ return false;
+ }
+ assertions.clear();
+ for (const auto& v : d_CAC.getVariableOrdering())
+ {
+ Node variable = d_CAC.getConstraints().varMapper()(v);
+ Node value = value_to_node(d_CAC.getModel().get(v), d_ranVariable);
+ if (value.isConst())
+ {
+ d_model.addCheckModelSubstitution(variable, value);
+ }
+ else
+ {
+ d_model.addCheckModelWitness(variable, value);
+ }
+ Trace("nl-cad") << "-> " << v << " = " << value << std::endl;
+ }
+ return true;
+#else
+ Warning() << "Tried to use CadSolver but libpoly is not available. Compile "
+ "with --poly."
+ << std::endl;
+#endif
+}
+
+} // namespace nl
+} // namespace arith
+} // namespace theory
+} // namespace CVC4
--- /dev/null
+/********************* */
+/*! \file cad_solver.h
+ ** \verbatim
+ ** Top contributors (to current version):
+ ** Gereon Kremer
+ ** This file is part of the CVC4 project.
+ ** Copyright (c) 2009-2019 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.\endverbatim
+ **
+ ** \brief CAD-based solver based on https://arxiv.org/pdf/2003.05633.pdf.
+ **/
+
+#ifndef CVC4__THEORY__ARITH__CAD_SOLVER_H
+#define CVC4__THEORY__ARITH__CAD_SOLVER_H
+
+#include <vector>
+
+#include "expr/node.h"
+#include "theory/arith/nl/cad/cdcac.h"
+#include "theory/arith/nl/nl_model.h"
+#include "theory/arith/theory_arith.h"
+
+namespace CVC4 {
+namespace theory {
+namespace arith {
+namespace nl {
+
+/**
+ * A solver for nonlinear arithmetic that implements the CAD-based method
+ * described in https://arxiv.org/pdf/2003.05633.pdf.
+ */
+class CadSolver
+{
+ public:
+ CadSolver(TheoryArith& containing, NlModel& model);
+ ~CadSolver();
+
+ /**
+ * This is called at the beginning of last call effort check, where
+ * assertions are the set of assertions belonging to arithmetic,
+ * false_asserts is the subset of assertions that are false in the current
+ * model, and xts is the set of extended function terms that are active in
+ * the current context.
+ */
+ void initLastCall(const std::vector<Node>& assertions);
+
+ /**
+ * Perform a full check, returning either {} or a single lemma.
+ * If the result is empty, the input is satisfiable and a model is available
+ * for construct_model_if_available. Otherwise, the single lemma can be used
+ * as an infeasible subset.
+ */
+ std::vector<NlLemma> checkFull();
+
+ /**
+ * If a model is available (indicated by the last call to check_full() or
+ * check_partial()) this method puts a satisfying assignment in d_model,
+ * clears the list of assertions, and returns true.
+ * Otherwise, this method returns false.
+ */
+ bool constructModelIfAvailable(std::vector<Node>& assertions);
+
+ private:
+ /**
+ * The variable used to encode real algebraic numbers to nodes.
+ */
+ Node d_ranVariable;
+
+#ifdef CVC4_POLY_IMP
+ /**
+ * The object implementing the actual decision procedure.
+ */
+ cad::CDCAC d_CAC;
+#endif
+ /**
+ * Indicates whether we found satisfiability in the last call to
+ * checkFullRefine.
+ */
+ bool d_foundSatisfiability;
+
+ /** The theory of arithmetic containing this extension.*/
+ TheoryArith& d_containing;
+ /** Reference to the non-linear model object */
+ NlModel& d_model;
+}; /* class CadSolver */
+
+} // namespace nl
+} // namespace arith
+} // namespace theory
+} // namespace CVC4
+
+#endif /* CVC4__THEORY__ARITH__CAD_SOLVER_H */
T_TANGENT,
// secant refinement, the dual of the above inference
T_SECANT,
+ //-------------------- cad solver
+ // conflict / infeasible subset obtained from cad
+ CAD_CONFLICT,
+ // excludes an interval for a single variable
+ CAD_EXCLUDED_INTERVAL,
//-------------------- unknown
UNKNOWN,
};
d_model(containing.getSatContext()),
d_trSlv(d_model),
d_nlSlv(containing, d_model),
+ d_cadSlv(containing, d_model),
d_iandSlv(containing, d_model),
d_builtModel(containing.getSatContext(), false)
{
return false;
}
}
+ if (options::nlCad())
+ {
+ d_cadSlv.constructModelIfAvailable(passertions);
+ }
Trace("nl-ext-cm") << "-----" << std::endl;
unsigned tdegree = d_trSlv.getTaylorDegree();
// process lemmas that may have been generated by the transcendental solver
filterLemmas(lemmas, lems);
}
-
+ if (options::nlCad())
+ {
+ d_cadSlv.initLastCall(assertions);
+ }
+
// init last call with IAND
d_iandSlv.initLastCall(assertions, false_asserts, xts);
filterLemmas(lemmas, wlems);
}
}
+ if (options::nlCad())
+ {
+ lemmas = d_cadSlv.checkFull();
+ if (lemmas.empty())
+ {
+ Trace("nl-cad") << "nl-cad found SAT!" << std::endl;
+ }
+ filterLemmas(lemmas, wlems);
+ }
// run the full refinement in the IAND solver
lemmas = d_iandSlv.checkFullRefine();
filterLemmas(lemmas, wlems);
#define CVC4__THEORY__ARITH__NL__NONLINEAR_EXTENSION_H
#include <stdint.h>
+
#include <map>
#include <vector>
#include "context/cdlist.h"
#include "expr/kind.h"
#include "expr/node.h"
+#include "theory/arith/nl/cad_solver.h"
#include "theory/arith/nl/iand_solver.h"
#include "theory/arith/nl/nl_lemma_utils.h"
#include "theory/arith/nl/nl_model.h"
* constraints involving nonlinear mulitplication, Cimatti et al., TACAS 2017.
*/
NlSolver d_nlSlv;
+ /** The CAD-based solver */
+ CadSolver d_cadSlv;
/** The integer and solver
*
* This is the subsolver responsible for running the procedure for
projects / cvc5.git / commitdiff