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/****************************************************************************** |
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* Top contributors (to current version): |
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* Gereon Kremer |
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* |
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* This file is part of the cvc5 project. |
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* |
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* Copyright (c) 2009-2021 by the authors listed in the file AUTHORS |
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* in the top-level source directory and their institutional affiliations. |
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* All rights reserved. See the file COPYING in the top-level source |
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* directory for licensing information. |
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* **************************************************************************** |
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* |
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* Implements utilities for cdcac. |
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*/ |
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#include "cvc5_private.h" |
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#ifndef CVC5__THEORY__ARITH__NL__CAD__CDCAC_UTILS_H |
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#define CVC5__THEORY__ARITH__NL__CAD__CDCAC_UTILS_H |
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#ifdef CVC5_POLY_IMP |
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#include <poly/polyxx.h> |
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#include <vector> |
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#include "expr/node.h" |
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#include "theory/arith/nl/cad/projections.h" |
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namespace cvc5 { |
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namespace theory { |
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namespace arith { |
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namespace nl { |
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namespace cad { |
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/** |
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* An interval as specified in section 4.1 of |
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* https://arxiv.org/pdf/2003.05633.pdf. |
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* |
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* It consists of |
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* - the actual interval, either an open or a point interal, |
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* - the characterizing polynomials of the lower and upper bound, |
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* - the characterizing polynomials in the main variable, |
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* - the characterizing polynomials in lower variables and |
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* - the constraints used to derive this interval. |
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*/ |
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struct CACInterval |
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{ |
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/** The actual interval. */ |
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poly::Interval d_interval; |
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/** The polynomials characterizing the lower bound. */ |
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PolyVector d_lowerPolys; |
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/** The polynomials characterizing the upper bound. */ |
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PolyVector d_upperPolys; |
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/** The characterizing polynomials in the main variable. */ |
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PolyVector d_mainPolys; |
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/** The characterizing polynomials in lower variables. */ |
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PolyVector d_downPolys; |
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/** The constraints used to derive this interval. */ |
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std::vector<Node> d_origins; |
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}; |
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/** Check whether to intervals are the same. */ |
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bool operator==(const CACInterval& lhs, const CACInterval& rhs); |
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/** Compare two intervals. */ |
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bool operator<(const CACInterval& lhs, const CACInterval& rhs); |
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/** Check whether lhs covers rhs. */ |
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bool intervalCovers(const poly::Interval& lhs, const poly::Interval& rhs); |
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/** |
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* Check whether two intervals connect, assuming lhs < rhs. |
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* They connect, if their union has no gap. |
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*/ |
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bool intervalConnect(const poly::Interval& lhs, const poly::Interval& rhs); |
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/** |
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* Sort intervals according to section 4.4.1. |
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* Also removes fully redundant intervals as in 4.5. 1. |
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*/ |
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void cleanIntervals(std::vector<CACInterval>& intervals); |
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/** |
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* Collect all origins from the list of intervals to construct the origins for a |
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* whole covering. |
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*/ |
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std::vector<Node> collectConstraints(const std::vector<CACInterval>& intervals); |
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/** |
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* Sample a point outside of the infeasible intervals. |
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* Stores the sample in sample, returns whether such a sample exists. |
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* If false is returned, the infeasible intervals cover the real line. |
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* Implements sample_outside() from section 4.3 |
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*/ |
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bool sampleOutside(const std::vector<CACInterval>& infeasible, |
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poly::Value& sample); |
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/** |
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* Compute the finest square of the upper polynomials of lhs and the lower |
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* polynomials of rhs. Also pushes reduced polynomials to lower level if |
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* necessary. |
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*/ |
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void makeFinestSquareFreeBasis(CACInterval& lhs, CACInterval& rhs); |
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} // namespace cad |
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} // namespace nl |
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} // namespace arith |
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} // namespace theory |
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} // namespace cvc5 |
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#endif |
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#endif |