On CNF Encodings of Decision Diagrams

Abío, Ignasi; Gange, Graeme; Mayer-Eichberger, Valentin; Stuckey, Peter J.

doi:10.1007/978-3-319-33954-2_1

“…Several representations have been studied with respect to different encoding techniques with the purpose of determining which properties of representations are sufficient to ensure propagation strength [1,2,11,12,16,17]. Popular representations in this context are DNNF and BDD and their many variants: deterministic DNNF, smooth DNNF, OBDD.…”

Section: Introductionmentioning

confidence: 99%

A Lower Bound on DNNF Encodings of Pseudo-Boolean Constraints

Colnet

¹

2020

Theory and Applications of Satisfiability Testing – SAT 2020

0

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Two major considerations when encoding pseudo-Boolean (PB) constraints into SAT are the size of the encoding and its propagation strength, that is, the guarantee that it has a good behaviour under unit propagation. Several encodings with propagation strength guarantees rely upon prior compilation of the constraints into DNNF (decomposable negation normal form), BDD (binary decision diagram), or some other sub-variants. However it has been shown that there exist PB-constraints whose ordered BDD (OBDD) representations, and thus the inferred CNF encodings, all have exponential size. Since DNNFs are more succinct than OBDDs, preferring encodings via DNNF to avoid size explosion seems a legitimate choice. Yet in this paper, we prove the existence of PB-constraints whose DNNFs all require exponential size.

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“…Some solvers try to automate this choice: They start with a propagation based approach. If a the propagator for a constraint is used often, a direct SAT encoding for this single constraint is added lazily [3].…”

Section: Constraint Programming With Learningmentioning

confidence: 99%

“…3 shows data collected during a run of CHUFFED on an optimisation benchmark from the MiniZinc Challenge 2013 [100] 2 . In both plots, the horizontal axis represents the time, and the vertical axis shows the current 3cargo: slow convergence towards optimal result.…”

mentioning

confidence: 99%

SAT and CP - Parallelisation and Applications

Ehlers¹

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In this thesis, we consider the parallelisation and application of SAT and CP solvers. In the first chapter, we consider SAT, the decision problem of propositional logic. We discuss details of the implementations of SAT solvers, and show how to improve upon existing sequential solvers. Furthermore, we discuss the parallelisation of these solvers with a focus on the communication of intermediate results within a parallel solver. The second chapter is concerned with Contraint Programing (CP) with learning. Contrary to classical Constraint Programming techniques, this incorporates learning mechanisms as they are used in the field of SAT solving. We present results from parallelising CHUFFED, a learning CP solver. In the final chapter, we discuss Sorting Networks, which are data oblivious sorting algorithms. Their independence of the input data lends them to parallel implementation. We consider the question how many parallel sorting steps are needed to sort some inputs, and present both lower and upper bounds for several cases.

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“…We submitted some SAT formulas on sorting networks to the SAT Competition 2016 [95] 2 . In these, we encoded the search for different sorting networks, using different combinations of the optimisation described in the previous section 3 . Not all submitted formulas were used, however, in some cases formulas were used which described the same setting up to one of the above techniques.…”

Section: Conjecture 427 Let N = 2 K There Is No Prefix On K Layermentioning

confidence: 99%

“…cf. http://baldur.iti.kit.edu/sat-competition-2016/3 The formulas are publicly available at https://github.com/the-kiel/SAT _ benchmarks.…”

mentioning

confidence: 99%

SAT and CP - Parallelisation and Applications

Ehlers¹

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In this thesis, we consider the parallelisation and application of SAT and CP solvers. In the first chapter, we consider SAT, the decision problem of propositional logic. We discuss details of the implementations of SAT solvers, and show how to improve upon existing sequential solvers. Furthermore, we discuss the parallelisation of these solvers with a focus on the communication of intermediate results within a parallel solver. The second chapter is concerned with Contraint Programing (CP) with learning. Contrary to classical Constraint Programming techniques, this incorporates learning mechanisms as they are used in the field of SAT solving. We present results from parallelising CHUFFED, a learning CP solver. In the final chapter, we discuss Sorting Networks, which are data oblivious sorting algorithms. Their independence of the input data lends them to parallel implementation. We consider the question how many parallel sorting steps are needed to sort some inputs, and present both lower and upper bounds for several cases.

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On CNF Encodings of Decision Diagrams

Cited by 16 publications

References 14 publications

A Lower Bound on DNNF Encodings of Pseudo-Boolean Constraints

A Lower Bound on DNNF Encodings of Pseudo-Boolean Constraints

SAT and CP - Parallelisation and Applications

SAT and CP - Parallelisation and Applications

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