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/********************* */
/*! \file cdcac.h
** \verbatim
** Top contributors (to current version):
** Gereon Kremer
** This file is part of the CVC4 project.
** Copyright (c) 2009-2020 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 Implements the CDCAC approach.
**
** Implements the CDCAC approach as described in
** https://arxiv.org/pdf/2003.05633.pdf.
**/
#include "cvc4_private.h"
#ifndef CVC4__THEORY__ARITH__NL__CAD__CDCAC_H
#define CVC4__THEORY__ARITH__NL__CAD__CDCAC_H
#include "util/real_algebraic_number.h"
#ifdef CVC4_POLY_IMP
#include <poly/polyxx.h>
#include <vector>
#include "theory/arith/nl/cad/cdcac_utils.h"
#include "theory/arith/nl/cad/constraints.h"
#include "theory/arith/nl/cad/variable_ordering.h"
#include "theory/arith/nl/nl_model.h"
namespace CVC4 {
namespace theory {
namespace arith {
namespace nl {
namespace cad {
/**
* This class implements Cylindrical Algebraic Coverings as presented in
* https://arxiv.org/pdf/2003.05633.pdf
*/
class CDCAC
{
public:
/** Initialize without a variable ordering. */
CDCAC();
/** Initialize this method with the given variable ordering. */
CDCAC(const std::vector<poly::Variable>& ordering);
/** Reset this instance. */
void reset();
/** Collect variables from the constraints and compute a variable ordering. */
void computeVariableOrdering();
/**
* Returns the constraints as a non-const reference. Can be used to add new
* constraints.
*/
Constraints& getConstraints();
/** Returns the constraints as a const reference. */
const Constraints& getConstraints() const;
/**
* Returns the current assignment. This is a satisfying model if
* get_unsat_cover() returned an empty vector.
*/
const poly::Assignment& getModel() const;
/** Returns the current variable ordering. */
const std::vector<poly::Variable>& getVariableOrdering() const;
/**
* Collect all unsatisfiable intervals for the given variable.
* Combines unsatisfiable regions from d_constraints evaluated over
* d_assignment. Implements Algorithm 2.
*/
std::vector<CACInterval> getUnsatIntervals(std::size_t cur_variable) const;
/**
* Collects the coefficients required for projection from the given
* polynomial. Implements Algorithm 6.
*/
std::vector<poly::Polynomial> requiredCoefficients(
const poly::Polynomial& p) const;
/**
* Constructs a characterization of the given covering.
* A characterization contains polynomials whose roots bound the region around
* the current assignment. Implements Algorithm 4.
*/
std::vector<poly::Polynomial> constructCharacterization(
std::vector<CACInterval>& intervals);
/**
* Constructs an infeasible interval from a characterization.
* Implements Algorithm 5.
*/
CACInterval intervalFromCharacterization(
const std::vector<poly::Polynomial>& characterization,
std::size_t cur_variable,
const poly::Value& sample);
/**
* Main method that checks for the satisfiability of the constraints.
* Recursively explores possible assignments and excludes regions based on the
* coverings. Returns either a covering for the lowest dimension or an empty
* vector. If the covering is empty, the result is SAT and an assignment can
* be obtained from d_assignment. If the covering is not empty, the result is
* UNSAT and an infeasible subset can be extracted from the returned covering.
* Implements Algorithm 2.
*/
std::vector<CACInterval> getUnsatCover(std::size_t cur_variable = 0);
private:
/**
* The current assignment. When the method terminates with SAT, it contains a
* model for the input constraints.
*/
poly::Assignment d_assignment;
/** The set of input constraints to be checked for consistency. */
Constraints d_constraints;
/** The computed variable ordering used for this method. */
std::vector<poly::Variable> d_variableOrdering;
/** The object computing the variable ordering. */
VariableOrdering d_varOrder;
};
} // namespace cad
} // namespace nl
} // namespace arith
} // namespace theory
} // namespace CVC4
#endif
#endif
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