1 |
|
/****************************************************************************** |
2 |
|
* Top contributors (to current version): |
3 |
|
* Gereon Kremer |
4 |
|
* |
5 |
|
* This file is part of the cvc5 project. |
6 |
|
* |
7 |
|
* Copyright (c) 2009-2021 by the authors listed in the file AUTHORS |
8 |
|
* in the top-level source directory and their institutional affiliations. |
9 |
|
* All rights reserved. See the file COPYING in the top-level source |
10 |
|
* directory for licensing information. |
11 |
|
* **************************************************************************** |
12 |
|
* |
13 |
|
* Implements utilities for cdcac. |
14 |
|
*/ |
15 |
|
|
16 |
|
#include "cvc5_private.h" |
17 |
|
|
18 |
|
#ifndef CVC5__THEORY__ARITH__NL__CAD__CDCAC_UTILS_H |
19 |
|
#define CVC5__THEORY__ARITH__NL__CAD__CDCAC_UTILS_H |
20 |
|
|
21 |
|
#ifdef CVC5_POLY_IMP |
22 |
|
|
23 |
|
#include <poly/polyxx.h> |
24 |
|
|
25 |
|
#include <vector> |
26 |
|
|
27 |
|
#include "expr/node.h" |
28 |
|
#include "theory/arith/nl/cad/projections.h" |
29 |
|
|
30 |
|
namespace cvc5 { |
31 |
|
namespace theory { |
32 |
|
namespace arith { |
33 |
|
namespace nl { |
34 |
|
namespace cad { |
35 |
|
|
36 |
|
/** |
37 |
|
* An interval as specified in section 4.1 of |
38 |
|
* https://arxiv.org/pdf/2003.05633.pdf. |
39 |
|
* |
40 |
|
* It consists of |
41 |
|
* - the interval id, used to map the interval to its (partial) proof, |
42 |
|
* - the actual interval, either an open or a point interal, |
43 |
|
* - the characterizing polynomials of the lower and upper bound, |
44 |
|
* - the characterizing polynomials in the main variable, |
45 |
|
* - the characterizing polynomials in lower variables and |
46 |
|
* - the constraints used to derive this interval. |
47 |
|
*/ |
48 |
32740 |
struct CACInterval |
49 |
|
{ |
50 |
|
/** Id of this interval to couple it to the proof */ |
51 |
|
size_t d_id; |
52 |
|
/** The actual interval. */ |
53 |
|
poly::Interval d_interval; |
54 |
|
/** The polynomials characterizing the lower bound. */ |
55 |
|
PolyVector d_lowerPolys; |
56 |
|
/** The polynomials characterizing the upper bound. */ |
57 |
|
PolyVector d_upperPolys; |
58 |
|
/** The characterizing polynomials in the main variable. */ |
59 |
|
PolyVector d_mainPolys; |
60 |
|
/** The characterizing polynomials in lower variables. */ |
61 |
|
PolyVector d_downPolys; |
62 |
|
/** The constraints used to derive this interval. */ |
63 |
|
std::vector<Node> d_origins; |
64 |
|
}; |
65 |
|
/** Check whether to intervals are the same. */ |
66 |
|
bool operator==(const CACInterval& lhs, const CACInterval& rhs); |
67 |
|
/** Compare two intervals. */ |
68 |
|
bool operator<(const CACInterval& lhs, const CACInterval& rhs); |
69 |
|
|
70 |
|
/** Check whether lhs covers rhs. */ |
71 |
|
bool intervalCovers(const poly::Interval& lhs, const poly::Interval& rhs); |
72 |
|
/** |
73 |
|
* Check whether two intervals connect, assuming lhs < rhs. |
74 |
|
* They connect, if their union has no gap. |
75 |
|
*/ |
76 |
|
bool intervalConnect(const poly::Interval& lhs, const poly::Interval& rhs); |
77 |
|
|
78 |
|
/** |
79 |
|
* Sort intervals according to section 4.4.1. |
80 |
|
* Also removes fully redundant intervals as in 4.5. 1. |
81 |
|
*/ |
82 |
|
void cleanIntervals(std::vector<CACInterval>& intervals); |
83 |
|
|
84 |
|
/** |
85 |
|
* Collect all origins from the list of intervals to construct the origins for a |
86 |
|
* whole covering. |
87 |
|
*/ |
88 |
|
std::vector<Node> collectConstraints(const std::vector<CACInterval>& intervals); |
89 |
|
|
90 |
|
/** |
91 |
|
* Sample a point outside of the infeasible intervals. |
92 |
|
* Stores the sample in sample, returns whether such a sample exists. |
93 |
|
* If false is returned, the infeasible intervals cover the real line. |
94 |
|
* Implements sample_outside() from section 4.3 |
95 |
|
*/ |
96 |
|
bool sampleOutside(const std::vector<CACInterval>& infeasible, |
97 |
|
poly::Value& sample); |
98 |
|
|
99 |
|
/** |
100 |
|
* Compute the finest square of the upper polynomials of lhs and the lower |
101 |
|
* polynomials of rhs. Also pushes reduced polynomials to lower level if |
102 |
|
* necessary. |
103 |
|
*/ |
104 |
|
void makeFinestSquareFreeBasis(CACInterval& lhs, CACInterval& rhs); |
105 |
|
|
106 |
|
} // namespace cad |
107 |
|
} // namespace nl |
108 |
|
} // namespace arith |
109 |
|
} // namespace theory |
110 |
|
} // namespace cvc5 |
111 |
|
|
112 |
|
#endif |
113 |
|
|
114 |
|
#endif |