DRAT Proofs for XOR Reasoning

Philipp, Tobias; Rebola-Pardo, Adrián

doi:10.1007/978-3-319-48758-8_27

Cited by 8 publications

(18 citation statements)

References 23 publications

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“…Furthermore, no lower bounds are known for the proof complexity of the DRAT proof system, which in fact is as powerful as extended resolution [16]. Thanks to the RAT introduction criterion, DRAT proofs can express several inprocessing techniques that would lead to an exponential blow-up if expressed using only RUP clauses, such as Gaussian elimination and symmetry breaking [12,19,26,27]. Last, DRAT checking can be performed efficiently, with a caveat we explain in Section 2.5.…”

Section: Drat Proofsmentioning

confidence: 99%

Frying the egg, roasting the chicken: unit deletions in DRAT proofs

Altmanninger¹,

Pardo²

2020

Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs

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The clausal proof format DRAT is the standard de facto to certify SAT solvers' unsatisfiability results. DRAT proofs act as logs of clause inferences and clause deletions in the solver. The non-monotonic nature of the proof system makes deletions relevant. State-of-the-art proof checkers ignore deletions of unit clauses, differing from the standard in meaningful ways that require adaptions when proofs are generated or used for purposes other than checking. On the other hand, dealing with unit deletions in the proof checker breaks many of the usual invariants used for efficiency reasons. Furthermore, many SAT solvers introduce spurious unit deletions in proofs. These deletions are never intended to be applied in the checker but are nevertheless introduced, making many proofs generated by state-of-the-art solvers incorrect. We present the first competitive DRAT checker that honors unit deletions, as well as fixes for the spurious deletion issue in proof generation. Our experimental results confirm that unit deletions can be applied with similar average performance to state-of-the-art checkers. We also confirm that a large fraction of the proofs generated during the last SAT solving competition do not respect the DRAT standard. This result was confirmed with proof incorrectness certificates that were independently validated. We find that our proof incorrectness certificates can be of help when debugging SAT solvers and DRAT checkers. CCS Concepts • Theory of computation → Automated reasoning.

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Section: Drat Proofsmentioning

confidence: 99%

Frying the egg, roasting the chicken: unit deletions in DRAT proofs

Altmanninger¹,

Pardo²

2020

Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs

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“…This is very convenient from the perspective of SAT solving: state-of-the-art solvers can perform exponentially better than pure CDCL solvers due to the use of inprocessing techniques such as Gaussian elimination, cardinality resolution and symmetry breaking [44,45,31,32,6,8,1]. Expressing such techniques as RUP inferences can lead to much longer proofs, both in theory [17,48,49] and in practice [40]. This can be avoided by introducing RATs, due to the exponential gap between resolution and extended resolution [29].…”

Section: Drat Proofsmentioning

confidence: 99%

“…However, the aforementioned inprocessing techniques were difficult or impossible to express in the RUP proof system. For this reason, the Delete Resolution Asymmetric Tautology (DRAT) proof system was introduced, as well as proof generation methods for several inprocessing techniques [27,20,40]. DRAT has become a de facto standard as DRAT proof logging was required in the main track of the SAT Competition 2016.…”

Section: Introductionmentioning

confidence: 99%

Towards a Semantics of Unsatisfiability Proofs with Inprocessing

Philipp

Rebola-Pardo

EPiC Series in Computing

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Delete Resolution Asymmetric Tautology (DRAT) proofs have become a de facto standard to certify unsatisfiability results from SAT solvers with inprocessing. However, DRAT shows behaviors notably different from other proof systems: DRAT inferences are nonmonotonic, and clauses that are not consequences of the premises can be derived. In this paper, we clarify some discrepancies on the notions of reverse unit propagation (RUP) clauses and asymmetric tautologies (AT), and furthermore develop the concept of resolution consequences. This allows us to present an intuitive explanation of RAT in terms of permissive definitions. We prove that a formula derived using RATs can be stratified into clause sets depending on which definitions they require, which give a strong invariant along RAT proofs. We furthermore study its interaction with clause deletion, characterizing DRAT derivability as satisfiability-preservation.

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“…The delete resolution asymmetric tautology (DRAT) and delete propagation redundancy (DPR) proof systems were developed to express and check these operations [41,17]. While DRAT proof generation is widely supported [25,28,13], DPR is fairly recent and is yet to be adopted in practice. Recent results show that these proof systems are polynomially equivalent to the extended resolution proof system [16,20], for which no exponential lower bounds are known [22].…”

Section: Introductionmentioning

confidence: 99%

“…Related work DRAT and DPR proofs [41,17] were developed to increase the reliability of SAT solvers' unsatisfiability results by allowing powerful inferences that easily expressed the reasoning techniques used by SAT solvers [25,13,28]. Recent work shows that both proof systems are essentially as expressive as extended resolution [16,20], for which no exponential lower bounds exist [22].…”

Section: Introductionmentioning

confidence: 99%

A Theory of Satisfiability-Preserving Proofs in SAT Solving

Rebola-Pardo¹,

Suda²

EPiC Series in Computing

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We study the semantics of propositional interference-based proof systems such as DRAT and DPR. These are characterized by modifying a CNF formula in ways that preserve satisfiability but not necessarily logical truth. We propose an extension of propositional logic called overwrite logic with a new construct which captures the meta-level reasoning behind interferences. We analyze this new logic from the point of view of expressivity and complexity, showing that while greater expressivity is achieved, the satisfiability problem for overwrite logic is essentially as hard as SAT, and can be reduced in a way that is well-behaved for modern SAT solvers. We also show that DRAT and DPR proofs can be seen as overwrite logic proofs which preserve logical truth. This much stronger invariant than the mere satisfiability preservation maintained by the traditional view gives us better understanding on these practically important proof systems. Finally, we showcase this better understanding by finding intrinsic limitations in interference-based proof systems.

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DRAT Proofs for XOR Reasoning

Cited by 8 publications

References 23 publications

Frying the egg, roasting the chicken: unit deletions in DRAT proofs

Frying the egg, roasting the chicken: unit deletions in DRAT proofs

Towards a Semantics of Unsatisfiability Proofs with Inprocessing

A Theory of Satisfiability-Preserving Proofs in SAT Solving

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