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Journal Articles Journal of Artificial Intelligence Research Year : 2022

Proofs and Certificates for Max-SAT


Current Max-SAT solvers are able to efficiently compute the optimal value of an input instance but they do not provide any certificate of its validity. In this paper, we present a tool, called MS-Builder, which generates certificates for the Max-SAT problem in the particular form of a sequence of equivalence-preserving transformations. To generate a certificate, MS-Builder iteratively calls a SAT oracle to get a SAT resolution refutation which is handled and adapted into a sound refutation for Max-SAT. In particular, we prove that the size of the computed Max-SAT refutation is linear with respect to the size of the initial refutation if it is semi-read-once, tree-like regular, tree-like or semi-tree-like. Additionally, we propose an extendable tool, called MS-Checker, able to verify the validity of any Max-SAT certificate using Max-SAT inference rules. Both tools are evaluated on the unweighted and weighted benchmark instances of the 2020 Max-SAT Evaluation.
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Dates and versions

hal-03977496 , version 1 (11-03-2023)



Matthieu Py, Mohamed Sami Cherif, Djamal Habet. Proofs and Certificates for Max-SAT. Journal of Artificial Intelligence Research, 2022, 75, pp.1373-1400. ⟨10.1613/jair.1.13811⟩. ⟨hal-03977496⟩
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