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 the CDCAC approach as described in |
14 |
|
* https://arxiv.org/pdf/2003.05633.pdf. |
15 |
|
*/ |
16 |
|
|
17 |
|
#include "cvc5_private.h" |
18 |
|
|
19 |
|
#ifndef CVC5__THEORY__ARITH__NL__CAD__CDCAC_H |
20 |
|
#define CVC5__THEORY__ARITH__NL__CAD__CDCAC_H |
21 |
|
|
22 |
|
#ifdef CVC5_POLY_IMP |
23 |
|
|
24 |
|
#include <poly/polyxx.h> |
25 |
|
|
26 |
|
#include <vector> |
27 |
|
|
28 |
|
#include "smt/env.h" |
29 |
|
#include "smt/env_obj.h" |
30 |
|
#include "theory/arith/nl/cad/cdcac_utils.h" |
31 |
|
#include "theory/arith/nl/cad/constraints.h" |
32 |
|
#include "theory/arith/nl/cad/proof_generator.h" |
33 |
|
#include "theory/arith/nl/cad/variable_ordering.h" |
34 |
|
|
35 |
|
namespace cvc5 { |
36 |
|
namespace theory { |
37 |
|
namespace arith { |
38 |
|
namespace nl { |
39 |
|
|
40 |
|
class NlModel; |
41 |
|
|
42 |
|
namespace cad { |
43 |
|
|
44 |
|
/** |
45 |
|
* This class implements Cylindrical Algebraic Coverings as presented in |
46 |
|
* https://arxiv.org/pdf/2003.05633.pdf |
47 |
|
*/ |
48 |
5213 |
class CDCAC : protected EnvObj |
49 |
|
{ |
50 |
|
public: |
51 |
|
/** Initialize this method with the given variable ordering. */ |
52 |
|
CDCAC(Env& env, const std::vector<poly::Variable>& ordering = {}); |
53 |
|
|
54 |
|
/** Reset this instance. */ |
55 |
|
void reset(); |
56 |
|
|
57 |
|
/** Collect variables from the constraints and compute a variable ordering. */ |
58 |
|
void computeVariableOrdering(); |
59 |
|
|
60 |
|
/** |
61 |
|
* Extract an initial assignment from the given model. |
62 |
|
* This initial assignment is used to guide sampling if possible. |
63 |
|
* The ran_variable should be the variable used to encode real algebraic |
64 |
|
* numbers in the model and is simply passed on to node_to_value. |
65 |
|
*/ |
66 |
|
void retrieveInitialAssignment(NlModel& model, const Node& ran_variable); |
67 |
|
|
68 |
|
/** |
69 |
|
* Returns the constraints as a non-const reference. Can be used to add new |
70 |
|
* constraints. |
71 |
|
*/ |
72 |
|
Constraints& getConstraints(); |
73 |
|
/** Returns the constraints as a const reference. */ |
74 |
|
const Constraints& getConstraints() const; |
75 |
|
|
76 |
|
/** |
77 |
|
* Returns the current assignment. This is a satisfying model if |
78 |
|
* get_unsat_cover() returned an empty vector. |
79 |
|
*/ |
80 |
|
const poly::Assignment& getModel() const; |
81 |
|
|
82 |
|
/** Returns the current variable ordering. */ |
83 |
|
const std::vector<poly::Variable>& getVariableOrdering() const; |
84 |
|
|
85 |
|
/** |
86 |
|
* Collect all unsatisfiable intervals for the given variable. |
87 |
|
* Combines unsatisfiable regions from d_constraints evaluated over |
88 |
|
* d_assignment. Implements Algorithm 2. |
89 |
|
*/ |
90 |
|
std::vector<CACInterval> getUnsatIntervals(std::size_t cur_variable); |
91 |
|
|
92 |
|
/** |
93 |
|
* Sample outside of the set of intervals. |
94 |
|
* Uses a given initial value from mInitialAssignment if possible. |
95 |
|
* Returns whether a sample was found (true) or the infeasible intervals cover |
96 |
|
* the whole real line (false). |
97 |
|
*/ |
98 |
|
bool sampleOutsideWithInitial(const std::vector<CACInterval>& infeasible, |
99 |
|
poly::Value& sample, |
100 |
|
std::size_t cur_variable); |
101 |
|
|
102 |
|
/** |
103 |
|
* Collects the coefficients required for projection from the given |
104 |
|
* polynomial. Implements Algorithm 6, depending on the command line |
105 |
|
* arguments. Either directly implements Algorithm 6, or improved variants |
106 |
|
* based on Lazard's projection. |
107 |
|
*/ |
108 |
|
PolyVector requiredCoefficients(const poly::Polynomial& p); |
109 |
|
|
110 |
|
/** |
111 |
|
* Constructs a characterization of the given covering. |
112 |
|
* A characterization contains polynomials whose roots bound the region around |
113 |
|
* the current assignment. Implements Algorithm 4. |
114 |
|
*/ |
115 |
|
PolyVector constructCharacterization(std::vector<CACInterval>& intervals); |
116 |
|
|
117 |
|
/** |
118 |
|
* Constructs an infeasible interval from a characterization. |
119 |
|
* Implements Algorithm 5. |
120 |
|
*/ |
121 |
|
CACInterval intervalFromCharacterization(const PolyVector& characterization, |
122 |
|
std::size_t cur_variable, |
123 |
|
const poly::Value& sample); |
124 |
|
|
125 |
|
/** |
126 |
|
* Main method that checks for the satisfiability of the constraints. |
127 |
|
* Recursively explores possible assignments and excludes regions based on the |
128 |
|
* coverings. Returns either a covering for the lowest dimension or an empty |
129 |
|
* vector. If the covering is empty, the result is SAT and an assignment can |
130 |
|
* be obtained from d_assignment. If the covering is not empty, the result is |
131 |
|
* UNSAT and an infeasible subset can be extracted from the returned covering. |
132 |
|
* Implements Algorithm 2. |
133 |
|
* @param curVariable The id of the variable (within d_variableOrdering) to |
134 |
|
* be considered. This argument is used to manage the recursion internally and |
135 |
|
* should always be zero if called externally. |
136 |
|
* @param returnFirstInterval If true, the function returns after the first |
137 |
|
* interval obtained from a recursive call. The result is not (necessarily) an |
138 |
|
* unsat cover, but merely a list of infeasible intervals. |
139 |
|
*/ |
140 |
|
std::vector<CACInterval> getUnsatCover(std::size_t curVariable = 0, |
141 |
|
bool returnFirstInterval = false); |
142 |
|
|
143 |
|
void startNewProof(); |
144 |
|
/** |
145 |
|
* Finish the generated proof (if proofs are enabled) with a scope over the |
146 |
|
* given assertions. |
147 |
|
*/ |
148 |
|
ProofGenerator* closeProof(const std::vector<Node>& assertions); |
149 |
|
|
150 |
|
/** Get the proof generator */ |
151 |
|
CADProofGenerator* getProof() { return d_proof.get(); } |
152 |
|
|
153 |
|
private: |
154 |
|
/** Check whether proofs are enabled */ |
155 |
2539 |
bool isProofEnabled() const { return d_proof != nullptr; } |
156 |
|
|
157 |
|
/** |
158 |
|
* Check whether the current sample satisfies the integrality condition of the |
159 |
|
* current variable. Returns true if the variable is not integral or the |
160 |
|
* sample is integral. |
161 |
|
*/ |
162 |
|
bool checkIntegrality(std::size_t cur_variable, const poly::Value& value); |
163 |
|
/** |
164 |
|
* Constructs an interval that excludes the non-integral region around the |
165 |
|
* current sample. Assumes !check_integrality(cur_variable, value). |
166 |
|
*/ |
167 |
|
CACInterval buildIntegralityInterval(std::size_t cur_variable, |
168 |
|
const poly::Value& value); |
169 |
|
|
170 |
|
/** |
171 |
|
* Check whether the polynomial has a real root above the given value (when |
172 |
|
* evaluated over the current assignment). |
173 |
|
*/ |
174 |
|
bool hasRootAbove(const poly::Polynomial& p, const poly::Value& val) const; |
175 |
|
/** |
176 |
|
* Check whether the polynomial has a real root below the given value (when |
177 |
|
* evaluated over the current assignment). |
178 |
|
*/ |
179 |
|
bool hasRootBelow(const poly::Polynomial& p, const poly::Value& val) const; |
180 |
|
|
181 |
|
/** |
182 |
|
* Sort intervals according to section 4.4.1. and removes fully redundant |
183 |
|
* intervals as in 4.5. 1. by calling out to cleanIntervals. |
184 |
|
* Additionally makes sure to prune proofs for removed intervals. |
185 |
|
*/ |
186 |
|
void pruneRedundantIntervals(std::vector<CACInterval>& intervals); |
187 |
|
|
188 |
|
/** |
189 |
|
* The current assignment. When the method terminates with SAT, it contains a |
190 |
|
* model for the input constraints. |
191 |
|
*/ |
192 |
|
poly::Assignment d_assignment; |
193 |
|
|
194 |
|
/** The set of input constraints to be checked for consistency. */ |
195 |
|
Constraints d_constraints; |
196 |
|
|
197 |
|
/** The computed variable ordering used for this method. */ |
198 |
|
std::vector<poly::Variable> d_variableOrdering; |
199 |
|
|
200 |
|
/** The object computing the variable ordering. */ |
201 |
|
VariableOrdering d_varOrder; |
202 |
|
|
203 |
|
/** The linear assignment used as an initial guess. */ |
204 |
|
std::vector<poly::Value> d_initialAssignment; |
205 |
|
|
206 |
|
/** The proof generator */ |
207 |
|
std::unique_ptr<CADProofGenerator> d_proof; |
208 |
|
}; |
209 |
|
|
210 |
|
} // namespace cad |
211 |
|
} // namespace nl |
212 |
|
} // namespace arith |
213 |
|
} // namespace theory |
214 |
|
} // namespace cvc5 |
215 |
|
|
216 |
|
#endif |
217 |
|
|
218 |
|
#endif |