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Propositional proof systems based on maximum satisfiability

Abstract : The paper describes the use of dual-rail MaxSAT systems to solve Boolean satisfiability (SAT), namely to determine if a set of clauses is satisfiable. The MaxSAT problem is the problem of satisfying the maximum number of clauses in an instance of SAT. The dual-rail encoding adds extra variables for the complements of variables, and allows encoding an instance of SAT as a Horn MaxSAT problem. We discuss three implementations of dual-rail MaxSAT: core-guided systems, minimal hitting set (MaxHS) systems, and MaxSAT resolution inference systems. All three of these can be more efficient than resolution and thus than conflict-driven clause learning (CDCL). All three systems can give polynomial size refutations for the pigeonhole principle, the doubled pigeonhole principle and the mutilated chessboard principles. The dual-rail MaxHS MaxSat system can give polynomial size proofs of the parity principle. However, dual-rail MaxSAT resolution requires exponential size proofs for the parity principle; this is proved by showing that constant depth Frege augmented with the pigeonhole principle can polynomially simulate dual-rail MaxSAT resolution. Consequently, dual-rail MaxSAT resolution does not simulate cutting planes. We further show that core-guided dual-rail MaxSAT and weighted dual-rail MaxSAT resolution polynomially simulate resolution. Finally, we report the results of experiments with core-guided dual-rail MaxSAT and MaxHS dual-rail MaxSAT showing strong performance by these systems.
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Contributor : Joao Marques-Silva Connect in order to contact the contributor
Submitted on : Friday, August 6, 2021 - 7:33:12 PM
Last modification on : Friday, August 27, 2021 - 10:50:39 AM


Distributed under a Creative Commons Attribution 4.0 International License



Maria Luisa Bonet, Sam Buss, Alexey Ignatiev, Antonio Morgado, João Marques Silva. Propositional proof systems based on maximum satisfiability. Artificial Intelligence, Elsevier, 2021, 300, pp.1-59. ⟨10.1016/j.artint.2021.103552⟩. ⟨hal-03317630⟩



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