Trimming while checking clausal proofs

Heule, Marijn J. H.; Hunt, Warren A.; Wetzler, Nathan

doi:10.1109/fmcad.2013.6679408

Cited by 86 publications

(88 citation statements)

References 9 publications

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“…In this paper, we substantially increase the size of the longest sequence of discrepancy 3, from 17, 000 to 127, 645. In addition, we claim that E 2 (3) = 127, 646, making this bound tight, as Plingeling was able to prove unsat and Lingeling generated an UNSAT proof in DRUP format [6]. This paper is organized as follows.…”

mentioning

confidence: 99%

On the Erdős Discrepancy Problem

Bras

Gomes

Selman

2014

Lecture Notes in Computer Science

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Abstract. According to the Erdős discrepancy conjecture, for any infinite ±1 sequence, there exists a homogeneous arithmetic progression of unbounded discrepancy. In other words, for any ±1 sequence (x1, x2, ...) and a discrepancy C, there exist integers m and d such that | m i=1 x i·d | > C. This is an 80-year-old open problem and recent development proved that this conjecture is true for discrepancies up to 2. Paul Erdős also conjectured that this property of unbounded discrepancy even holds for the restricted case of completely multiplicative sequences (CMSs), namely sequences (x1, x2, ...) where x a·b = xa · x b for any a, b ≥ 1. The longest CMS with discrepancy 2 has been proven to be of size 246. In this paper, we prove that any completely multiplicative sequence of size 127, 646 or more has discrepancy at least 4, proving the Erdős discrepancy conjecture for CMSs of discrepancies up to 3. In addition, we prove that this bound is tight and increases the size of the longest known sequence of discrepancy 3 from 17, 000 to 127, 645. Finally, we provide inductive construction rules as well as streamlining methods to improve the lower bounds for sequences of higher discrepancies.

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confidence: 99%

On the Erdős Discrepancy Problem

Bras

Gomes

Selman

2014

Lecture Notes in Computer Science

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“…In the future, we plan to find a backward checking theme similar as in [18], which is known to significantly improve the efficiency, as well as implementing proof construction in the SAT solvers PRiss and Plingeling.…”

Section: Resultsmentioning

confidence: 99%

“…Beame et al characterized learned clauses as trivial resolution derivations [4], which can be efficiently checked in terms of reverse unit propagation. Clause removal [3,12] is also traced in form of deletion information [18]. Later, Järvisalo et al generalized the concept of trivial resolution derivation to resolution asymmetric tautologies (RAT), thus allowing proof generation for most known formula simplification techniques [26].…”

Section: A New Proof Format For Parallel Sat Portfoliosmentioning

confidence: 99%

“…In particular, RAT subsumes extended resolution [43,46], which allows to infer fresh variables. Heule et al developed the drat-trim [19,48] tool based on backward checking [18], which efficiently checks unsatisfiability proofs, as well as the mechanically verified checker written in the ACL2 theorem prover [49].…”

Section: A New Proof Format For Parallel Sat Portfoliosmentioning

confidence: 99%

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Unsatisfiability Proofs for Parallel SAT Solver Portfolios with Clause Sharing and Inprocessing

Philipp¹

EPiC Series in Computing

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State-of-the-art SAT solvers are highly tuned systematic-search procedures augmented with formula simplification techniques. They emit unsatisfiability proofs in the DRAT format to guarantee correctness of their answers. However, the DRAT format is inadequate to model some parallel SAT solvers such as the award-winning system Plingeling. In Plingeling, each solver in the portfolio applies clause addition and elimination techniques. Clause sharing is restricted to clauses that do not contain melted literals. In this paper, we develop a transition system that models the computation of such parallel portfolio solvers. The transition system allows us to formally reason about portfolio solvers, and we show that the formalism is sound and complete. Based on the formalism, we derive a new proof format, called parallel DRAT, which can be used to certify UNSAT answers.

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“…One piece of inspiration for this proposal is the existence of the DRAT proof format for certifying propositional satisfiability (SAT) solvers [26,27]. It is a proof format that-in the context of SATappears to satisfy all the properties listed in the previous section.…”

Section: Some Previous Work and Related Approachesmentioning

confidence: 99%

Checkable Proofs for First-Order Theorem Proving

Reger¹,

Suda²

EPiC Series in Computing

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Inspired by the success of the DRAT proof format for certification of boolean satisfiability (SAT), we argue that a similar goal of having unified automatically checkable proofs should be sought by the developers of automatic first-order theorem provers (ATPs). This would not only help to further increase assurance about the correctness of prover results, but would also be indispensable for tools which rely on ATPs, such as "hammers" employed within interactive theorem provers. The current situation, represented by the TSTP format, is unsatisfactory, because this format does not have a standardised semantics and thus cannot be checked automatically. Providing such semantics, however, is a challenging endeavour. One would ideally like to have a proof format which covers only-satisfiability-preserving operations such as Skolemisation and is versatile enough to encompass various proving methods (i.e. not just superposition) or is perhaps even open-ended towards yet to be conceived methods or at least easily extendable in principle. Going beyond pure first-order logic to theory reasoning in the style of SMT, or beyond proofs to certification of satisfiability are further interesting challenges. Although several projects have already provided partial solutions in this direction, we would like to use the opportunity of ARCADE to further promote the idea and gather critical mass needed for its satisfactory realisation. The challengeWe would like to propose to the first-order ATP community the challenge of designing, implementing and bringing into practice a unified mechanically checkable proof format along with an efficient proof checker. The format should support the whole reasoning pipeline including formula preprocessing, be sufficiently general to cover all the solving techniques currently employed by ATPs, and be open to future extensions for proof recording of techniques yet to be developed. In this paper, we summarise the current situation regarding proof output of ATPs, explain why we think striving for a mechanically checkable proof format is a worthy effort, list the main properties we believe an ideal format should satisfy, attempt to give an overview of work already done in the first-order ATP community and related areas, and, finally, suggest possible avenues and the next steps to be taken for meeting the challenge.At this point we add the disclaimer that other people have already examined this challenge in various ways. We attempt to present this previous work and do not claim that what we are suggesting is novel, but instead we are calling for further work in this area. Our main aim at ARCADE is to solicit opinions from experts on why the proposed idea has not yet made its way to practice and on how exactly should the community proceed to achieve the envisioned goal.

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Trimming while checking clausal proofs

Cited by 86 publications

References 9 publications

On the Erdős Discrepancy Problem

On the Erdős Discrepancy Problem

Unsatisfiability Proofs for Parallel SAT Solver Portfolios with Clause Sharing and Inprocessing

Checkable Proofs for First-Order Theorem Proving

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