Non-clausal Redundancy Properties

Barnett, Lee A.; Biere, Armin

doi:10.1007/978-3-030-79876-5_15

Cited by 3 publications

(1 citation statement)

References 71 publications

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“…We leave it to future work to come up with a space efficient method for autarky reconstruction in incremental SAT Solving. This probably requires a non-clausal reconstruction stack (Barnett & Biere, 2021).…”

Section: Model Reconstructionmentioning

confidence: 99%

Better Decision Heuristics in CDCL through Local Search and Target Phases

Zhang¹,

Fleury²,

Biere³

2022

jair

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On practical applications, state-of-the-art SAT solvers dominantly use the conflict-driven clause learning (CDCL) paradigm. An alternative for satisfiable instances is local search solvers, which is more successful on random and hard combinatorial instances. Although there have been attempts to combine these methods in one framework, a tight integration which improves the state of the art on a broad set of application instances has been missing. We present a combination of techniques that achieves such an improvement. Our first contribution is to maximize in a local search fashion the assignment trail in CDCL, by sticking to and extending promising assignments via a technique called target phases. Second, we relax the CDCL framework by again extending promising branches to complete assignments while ignoring conflicts. These assignments are then used as starting point of local search which tries to find improved assignments with fewer unsatisfied clauses. Third, these improved assignments are imported back to the CDCL loop where they are used to determine the value assigned to decision variables. Finally, the conflict frequency of variables in local search can be exploited during variable selection in branching heuristics of CDCL. We implemented these techniques to improve three representative CDCL solvers (Glucose, MapleLcm DistChronoBT, and Kissat). Experiments on benchmarks from the main tracks of the last three SAT Competitions from 2019 to 2021 and an additional benchmark set from spectrum allocation show that the techniques bring significant improvements, particularly and not surprisingly, on satisfiable real-world application instances. We claim that these techniques were essential to the large increase in performance witnessed in the SAT Competition 2020 where Kissat and Relaxed LcmdCbDl NewTech were leading the field followed by CryptoMiniSAT-Ccnr, which also incorporated similar ideas.

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Section: Model Reconstructionmentioning

confidence: 99%

Better Decision Heuristics in CDCL through Local Search and Target Phases

Zhang¹,

Fleury²,

Biere³

2022

jair

Self Cite

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Clausal Proofs for Pseudo-Boolean Reasoning

Bryant

Biere

Heule

2022

Tools and Algorithms for the Construction and Analysis of Systems

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When augmented with a Pseudo-Boolean (PB) solver, a Boolean satisfiability (SAT) solver can apply apply powerful reasoning methods to determine when a set of parity or cardinality constraints, extracted from the clauses of the input formula, has no solution. By converting the intermediate constraints generated by the PB solver into ordered binary decision diagrams (BDDs), a proof-generating, BDD-based SAT solver can then produce a clausal proof that the input formula is unsatisfiable. Working together, the two solvers can generate proofs of unsatisfiability for problems that are intractable for other proof-generating SAT solvers. The PB solver can, at times, detect that the proof can exploit modular arithmetic to give smaller BDD representations and therefore shorter proofs.

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Verified Propagation Redundancy and Compositional UNSAT Checking in CakeML

Tan

Heule

Myreen

2023

Int J Softw Tools Technol Transfer

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Modern SAT solvers can emit independently-checkable proof certificates to validate their results. The state-of-the-art proof system that allows for compact proof certificates is propagation redundancy ($$\textsf{PR}$$ PR ). However, the only existing method to validate proofs in this system with a formally verified tool requires a transformation to a weaker proof system, which can result in a significant blowup in the size of the proof and increased proof validation time. This article describes the first approach to formally verify $$\textsf{PR}$$ PR proofs on a succinct representation. We present (i) a new Linear PR (LPR) proof format, (ii) an extension of the tool to efficiently convert $$\textsf{PR}$$ PR proofs into LPR format, and (iii) , a verified LPR proof checker developed in CakeML. We also enhance these tools with (iv) a new compositional proof format designed to enable separate (parallel) proof checking. The LPR format is backwards compatible with the existing LRAT format, but extends LRAT with support for the addition of $$\textsf{PR}$$ PR clauses. Moreover, is verified using CakeML ’s binary code extraction toolchain, which yields correctness guarantees for its machine code (binary) implementation. This further distinguishes our clausal proof checker from existing checkers because unverified extraction and compilation tools are removed from its trusted computing base. We experimentally show that: LPR provides efficiency gains over existing proof formats; ’s strong correctness guarantees are obtained without significant sacrifice in its performance; and the compositional proof format enables scalable parallel proof checking for large proofs.

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Non-clausal Redundancy Properties

Cited by 3 publications

References 71 publications

Better Decision Heuristics in CDCL through Local Search and Target Phases

Better Decision Heuristics in CDCL through Local Search and Target Phases

Clausal Proofs for Pseudo-Boolean Reasoning

Verified Propagation Redundancy and Compositional UNSAT Checking in CakeML

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