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/********************* */
/*! \file cdcac_utils.h
** \verbatim
** Top contributors (to current version):
** Gereon Kremer
** This file is part of the CVC4 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.\endverbatim
**
** \brief Implements utilities for cdcac.
**
** Implements utilities for cdcac.
**/
#include "cvc4_private.h"
#ifndef CVC4__THEORY__ARITH__NL__CAD__CDCAC_UTILS_H
#define CVC4__THEORY__ARITH__NL__CAD__CDCAC_UTILS_H
#ifdef CVC4_POLY_IMP
#include <poly/polyxx.h>
#include <vector>
#include "expr/node.h"
#include "theory/arith/nl/cad/projections.h"
namespace cvc5 {
namespace theory {
namespace arith {
namespace nl {
namespace cad {
/**
* An interval as specified in section 4.1 of
* https://arxiv.org/pdf/2003.05633.pdf.
*
* It consists of
* - the actual interval, either an open or a point interal,
* - the characterizing polynomials of the lower and upper bound,
* - the characterizing polynomials in the main variable,
* - the characterizing polynomials in lower variables and
* - the constraints used to derive this interval.
*/
struct CACInterval
{
/** The actual interval. */
poly::Interval d_interval;
/** The polynomials characterizing the lower bound. */
PolyVector d_lowerPolys;
/** The polynomials characterizing the upper bound. */
PolyVector d_upperPolys;
/** The characterizing polynomials in the main variable. */
PolyVector d_mainPolys;
/** The characterizing polynomials in lower variables. */
PolyVector d_downPolys;
/** The constraints used to derive this interval. */
std::vector<Node> d_origins;
};
/** Check whether to intervals are the same. */
bool operator==(const CACInterval& lhs, const CACInterval& rhs);
/** Compare two intervals. */
bool operator<(const CACInterval& lhs, const CACInterval& rhs);
/** Check whether lhs covers rhs. */
bool intervalCovers(const poly::Interval& lhs, const poly::Interval& rhs);
/**
* Check whether two intervals connect, assuming lhs < rhs.
* They connect, if their union has no gap.
*/
bool intervalConnect(const poly::Interval& lhs, const poly::Interval& rhs);
/**
* Sort intervals according to section 4.4.1.
* Also removes fully redundant intervals as in 4.5. 1.
*/
void cleanIntervals(std::vector<CACInterval>& intervals);
/**
* Collect all origins from the list of intervals to construct the origins for a
* whole covering.
*/
std::vector<Node> collectConstraints(const std::vector<CACInterval>& intervals);
/**
* Sample a point outside of the infeasible intervals.
* Stores the sample in sample, returns whether such a sample exists.
* If false is returned, the infeasible intervals cover the real line.
* Implements sample_outside() from section 4.3
*/
bool sampleOutside(const std::vector<CACInterval>& infeasible,
poly::Value& sample);
/**
* Compute the finest square of the upper polynomials of lhs and the lower
* polynomials of rhs. Also pushes reduced polynomials to lower level if
* necessary.
*/
void makeFinestSquareFreeBasis(CACInterval& lhs, CACInterval& rhs);
} // namespace cad
} // namespace nl
} // namespace arith
} // namespace theory
} // namespace cvc5
#endif
#endif
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