What a Difference a Variable Makes

Heule, Marijn J. H.; Biere, Armin

doi:10.1007/978-3-319-89963-3_5

Cited by 16 publications

(8 citation statements)

References 26 publications

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“…In a more recent paper, we showed that there exists a polynomial-time procedure that translates PR proofs to DRAT proofs by introducing one new variable [11]. Moreover, we proved that extended resolution polynomially simulates the DRAT proof system [20].…”

Section: Open Problems and Future Workmentioning

confidence: 87%

“…We left these proofs out since they are twice as large as the PR proofs and their explanation is less intuitive. A recent result shows that the conversion of a PR proof into a DRAT proof requires only one auxiliary variable [11]. We can thus construct short DRAT proofs without new variables from short PR proofs without new variables.…”

Section: Short Proofs Of the Pigeon Hole Principlementioning

confidence: 99%

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Strong Extension-Free Proof Systems

2019

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We introduce proof systems for propositional logic that admit short proofs of hard formulas as well as the succinct expression of most techniques used by modern SAT solvers. Our proof systems allow the derivation of clauses that are not necessarily implied, but which are redundant in the sense that their addition preserves satisfiability. To guarantee that these added clauses are redundant, we consider various efficiently decidable redundancy criteria which we obtain by first characterizing clause redundancy in terms of a semantic implication relationship and then restricting this relationship so that it becomes decidable in polynomial time. As the restricted implication relation is based on unit propagation-a core technique of SAT solvers-it allows efficient proof checking too. The resulting proof systems are surprisingly strong, even without the introduction of new variables-a key feature of short proofs presented in the proof-complexity literature. We demonstrate the strength of our proof systems on the famous pigeon hole formulas by providing short clausal proofs without new variables.

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Section: Open Problems and Future Workmentioning

confidence: 87%

Section: Short Proofs Of the Pigeon Hole Principlementioning

confidence: 99%

Strong Extension-Free Proof Systems

2019

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“…To verify the proofs for all our experiments, we did the following: We started with the PR proofs produced by our SDCL solver using the filtered positive reduct. We then translated them into DRAT proofs using the pr2drat tool [17]. Finally, we used the drat-trim checker to optimize the proofs (i.e., to remove redundant proof parts) and to convert them into the LRAT format, which is the format supported by the formally verified proof checker.…”

Section: Discussionmentioning

confidence: 99%

“…Our solver also produces PR proofs [19]. We certify their correctness by translating them via DRAT proofs [17] to LRAT proofs, which are then validated by a formally verified proof checker [18].…”

Section: Introductionmentioning

confidence: 99%

Encoding Redundancy for Satisfaction-Driven Clause Learning

Heule

Kiesl

Biere

2019

Tools and Algorithms for the Construction and Analysis of Systems

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Satisfaction-Driven Clause Learning (SDCL) is a recent SAT solving paradigm that aggressively trims the search space of possible truth assignments. To determine if the SAT solver is currently exploring a dispensable part of the search space, SDCL uses the so-called positive reduct of a formula: The positive reduct is an easily solvable propositional formula that is satisfiable if the current assignment of the solver can be safely pruned from the search space. In this paper, we present two novel variants of the positive reduct that allow for even more aggressive pruning. Using one of these variants allows SDCL to solve harder problems, in particular the well-known Tseitin formulas and mutilated chessboard problems. For the first time, we are able to generate and automatically check clausal proofs for large instances of these problems.

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“…At this point there exists only an unverified checker to validate PR proofs, written in C. In order to increase the trust in the correctness of PR proofs, we implemented a tool to convert PR proofs into DRAT proofs [11], which in turn can be validated using verified proof checkers. Thanks to various optimizations, the size increase during conversion is rather modest on available PR proofs, thereby making this a useful certification approach in practice.…”

Section: Prefacementioning

confidence: 99%

Theory and Applications of Satisfiability Testing – SAT 2018

2018

Lecture Notes in Computer Science

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What a Difference a Variable Makes

Cited by 16 publications

References 26 publications

Strong Extension-Free Proof Systems

Strong Extension-Free Proof Systems

Encoding Redundancy for Satisfaction-Driven Clause Learning

Theory and Applications of Satisfiability Testing – SAT 2018

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