Combining Conflict-Driven Clause Learning and Chronological Backtracking for Propositional Model Counting

Möhle, Sibylle; Biere, Armin

doi:10.29007/vgg4

Cited by 4 publications

(21 citation statements)

References 24 publications

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“…The solution to the preimage attack problem is to give the remaining (512 − k) bits. Therefore, the brute complexity of these problems will range from O(2 12 ) to O(2 27 ). The CNF encoding of these problems was created using the SAT instance generator for SHA-1 [30].…”

Section: Case Study On Cryptographic Benchmarksmentioning

confidence: 99%

Designing New Phase Selection Heuristics

Shaw¹,

Meel²

2020

Preprint

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CDCL-based SAT solvers have transformed the field of automated reasoning owing to their demonstrated efficiency at handling problems arising from diverse domains. The success of CDCL solvers is owed to the design of clever heuristics that enable the tight coupling of different components. One of the core components is phase selection, wherein the solver, during branching, decides the polarity of the branch to be explored for a given variable. Most of the state-of-the-art CDCL SAT solvers employ phase-saving as a phase selection heuristic, which was proposed to address the potential inefficiencies arising from far-backtracking. In light of the emergence of chronological backtracking in CDCL solvers, we re-examine the efficiency of phase saving. Our empirical evaluation leads to a surprising conclusion: The usage of saved phase and random selection of polarity for decisions following a chronological backtracking leads to an indistinguishable runtime performance in terms of instances solved and PAR-2 score. We introduce Decaying Polarity Score (DPS) to capture the trend of the polarities attained by the variable, and upon observing lack of performance improvement due to DPS, we turn to a more sophisticated heuristic seeking to capture the activity of literals and the trend of polarities: Literal State Independent Decaying Sum (LSIDS). We find the 2019 winning SAT solver, Maple LCM Dist ChronoBTv3, augmented with LSIDS solves 6 more instances while achieving a reduction of over 125 seconds in PAR-2 score, a significant improvement in the context of the SAT competition.

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Section: Case Study On Cryptographic Benchmarksmentioning

confidence: 99%

Designing New Phase Selection Heuristics

Shaw¹,

Meel²

2020

Preprint

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“…This conversion is used in, e. g., circuit design [14] and has also been studied from a computational complexity point of view [15]. If the models found are pairwise contradicting, the resulting DNF is a Disjoint Sum-of-Product (DSOP) formula, which is relevant in circuit design [16,17], and whose models can be enumerated in polynomial time [18] by simply returning their disjuncts. If the models found are not pairwise contradicting, the resulting formula is still a DNF but does not support polytime model counting.…”

Section: Introductionmentioning

confidence: 99%

“…This (partial) assignment a b is a model of F . As in our previous work on propositional model counting [18], we flip the second decision literal, i. e., assign b the value false, in order to explore the second branch, upon which the literal d is forced to true in order to satisfy clause C 3 . The resulting assignment a ¬b d now falsifies clause C 4 , i. e., sets all its literal to false.…”

Section: Introductionmentioning

confidence: 99%

“…Specifically, after finding a model, the last open (left) decision literal is flipped in order to process neighboring regions of the search space, while in case of a conflict, the solver is able to escape regions without solution early. In our earlier work [18], we developed a calculus for propositional model counting based on chronological CDCL and provided a proof of its correctness. We took a model enumeration approach making our method readily applicable in the context of model enumeration without repetition.…”

Section: Introductionmentioning

confidence: 99%

“…Shorter models are also obtained in the case of model enumeration under projection. Workshop on Trends in Information Processing (YSIP2) 2017 [44] and the 30th International Conference on Tools with Artificial Intelligence (ICTAI) 2018 [37], the 22nd International Conference on Theory and Applications of Satisfiability Testing (SAT) 2019 [43], and the 5th Global Conference on Artificial Intelligence (GCAI) 2019 [18].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On Enumerating Short Projected Models

Möhle¹,

Sebastiani²,

Biere³

2021

Preprint

Self Cite

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Propositional model enumeration, or All-SAT, is the task to record all models of a propositional formula. It is a key task in software and hardware verification, system engineering, and predicate abstraction, to mention a few. It also provides a means to convert a CNF formula into DNF, which is relevant in circuit design. While in some applications enumerating models multiple times causes no harm, in others avoiding repetitions is crucial. We therefore present two model enumeration algorithms, which adopt dual reasoning in order to shorten the found models. The first method enumerates pairwise contradicting models. Repetitions are avoided by the use of so-called blocking clauses, for which we provide a dual encoding. In our second approach we relax the uniqueness constraint. We present an adaptation of the standard conflict-driven clause learning procedure to support model enumeration without blocking clauses. Our procedures are expressed by means of a calculus and proofs of correctness are provided.

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Four Flavors of Entailment

Möhle

Sebastiani

Biere

2020

Theory and Applications of Satisfiability Testing – SAT 2020

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We present a novel approach for enumerating partial models of a propositional formula, inspired by how theory solvers and the SAT solver interact in lazy SMT. Using various forms of dual reasoning allows our CDCL-based algorithm to enumerate partial models with no need for exploring and shrinking full models. Our focus is on model enumeration without repetition, with potential applications in weighted model counting and weighted model integration for probabilistic inference over Boolean and hybrid domains. Chronological backtracking renders the use of blocking clauses obsolete. We provide a formalization and examples. We further discuss important design choices for a future implementation related to the strength of dual reasoning, including unit propagation, using SAT or QBF oracles.

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Combining Conflict-Driven Clause Learning and Chronological Backtracking for Propositional Model Counting

Cited by 4 publications

References 24 publications

Designing New Phase Selection Heuristics

Designing New Phase Selection Heuristics

On Enumerating Short Projected Models

Four Flavors of Entailment

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