DRAT Proofs, Propagation Redundancy, and Extended Resolution

Buss, Samuel R.; Thapen, Neil

doi:10.1007/978-3-030-24258-9_5

Cited by 14 publications

(7 citation statements)

References 23 publications

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“…Using this observation, we strengthen the VeriPB tool recently introduced in , which can be viewed as a generalization to pseudo-Boolean proofs of RUP (Goldberg and Novikov 2003). Borrowing inspiration from (Heule, Kiesl, and Biere 2017;Buss and Thapen 2019), we develop stronger, but still efficient, rules that can handle also extension variables, making VeriPB, in effect, into a strict generalization of DRAT.…”

Section: Our Contributionmentioning

confidence: 86%

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Certifying Parity Reasoning Efficiently Using Pseudo-Boolean Proofs

Gocht¹,

Nordström

2021

AAAI

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The dramatic improvements in combinatorial optimization algorithms over the last decades have had a major impact in artificial intelligence, operations research, and beyond, but the output of current state-of-the-art solvers is often hard to verify and is sometimes wrong. For Boolean satisfiability (SAT) solvers proof logging has been introduced as a way to certify correctness, but the methods used seem hard to generalize to stronger paradigms. What is more, even for enhanced SAT techniques such as parity (XOR) reasoning, cardinality detection, and symmetry handling, it has remained beyond reach to design practically efficient proofs in the standard DRAT format. In this work, we show how to instead use pseudo-Boolean inequalities with extension variables to concisely justify XOR reasoning. Our experimental evaluation of a SAT solver integration shows a dramatic decrease in proof logging and verification time compared to existing DRAT methods. Since our method is a strict generalization of DRAT, and readily lends itself to expressing also 0-1 programming and even constraint programming problems, we hope this work points the way towards a unified approach for efficient machine-verifiable proofs for a rich class of combinatorial optimization paradigms.

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Section: Our Contributionmentioning

confidence: 86%

“…What we need, therefore, is a sufficient criterion for redundancy of pseudo-Boolean constraints that is simple to verify. To this end, we generalize the characterization of redundancy in (Heule, Kiesl, and Biere 2017;Buss and Thapen 2019) from CNF formulas to PB formulas as follows. Proposition 1 (Substitution redundancy).…”

Section: Substitution Redundancymentioning

confidence: 99%

Certifying Parity Reasoning Efficiently Using Pseudo-Boolean Proofs

Gocht¹,

Nordström

2021

AAAI

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“…is part needs to go before the re-encoding proof, because the plus encoding does not have the 8-fold symmetry of the direct encoding. Each of the clauses in the symmetry-breaking predicates have the substitution redundancy (SR) property [5]. is is a very strong redundancy property and checking whether a clause has SR w.r.t.…”

Section: Symmetry Proofmentioning

confidence: 99%

The Packing Chromatic Number of the Infinite Square Grid is 15

Subercaseaux¹,

Heule²

2023

Preprint

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A packing -coloring is a natural variation on the standard notion of graph -coloring, where vertices are assigned numbers from {1, … , }, and any two vertices assigned a common color ∈ {1, … , } need to be at a distance greater than (as opposed to 1, in standard graph colorings). Despite a sequence of incremental work, determining the packing chromatic number of the in nite square grid has remained an open problem since its introduction in 2002. We culminate the search by proving this number to be 15. We achieve this result by improving the best-known method for this problem by roughly two orders of magnitude. e most important technique to boost performance is a novel, surprisingly e ective propositional encoding for packing colorings. Additionally, we developed an alternative symmetry-breaking method. Since both new techniques are more complex than existing techniques for this problem, a veri ed approach is required to trust them. We include both techniques in a proof of unsatis ability, reducing the trusted core to the correctness of the direct encoding.

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“…The redundance-based strengthening rule allows deriving a constraint C from C ∪ D even if C is not implied, provided that it can be shown that any assignment α that satisfies C ∪ D can be transformed into another assignment α f α that satisfies both C ∪ D and C (in case O = O , the condition α f α just means that f α ≤ f α ). This rule is borrowed from (Gocht and Nordström 2021), which in turn relies heavily on (Heule, Kiesl, and Biere 2017;Buss and Thapen 2019). We extend this rule here from decision problems to optimization problems in the natural way.…”

Section: Redundance-based Strengthening Rulementioning

confidence: 99%

Certified Symmetry and Dominance Breaking for Combinatorial Optimisation

Bogaerts

Gocht

McCreesh

et al. 2022

AAAI

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Symmetry and dominance breaking can be crucial for solving hard combinatorial search and optimisation problems, but the correctness of these techniques sometimes relies on subtle arguments. For this reason, it is desirable to produce efficient, machine-verifiable certificates that solutions have been computed correctly. Building on the cutting planes proof system, we develop a certification method for optimisation problems in which symmetry and dominance breaking are easily expressible. Our experimental evaluation demonstrates that we can efficiently verify fully general symmetry breaking in Boolean satisfiability (SAT) solving, thus providing, for the first time, a unified method to certify a range of advanced SAT techniques that also includes XOR and cardinality reasoning. In addition, we apply our method to maximum clique solving and constraint programming as a proof of concept that the approach applies to a wider range of combinatorial problems.

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DRAT Proofs, Propagation Redundancy, and Extended Resolution

Cited by 14 publications

References 23 publications

Certifying Parity Reasoning Efficiently Using Pseudo-Boolean Proofs

Certifying Parity Reasoning Efficiently Using Pseudo-Boolean Proofs

The Packing Chromatic Number of the Infinite Square Grid is 15

Certified Symmetry and Dominance Breaking for Combinatorial Optimisation

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