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From Crossing-Free Resolution to Max-SAT Resolution

Authors Mohamed Sami Cherif , Djamal Habet, Matthieu Py

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Mohamed Sami Cherif
  • Aix-Marseille Univ, Université de Toulon, CNRS, LIS, France
Djamal Habet
  • Aix-Marseille Univ, Université de Toulon, CNRS, LIS, France
Matthieu Py
  • Aix-Marseille Univ, Université de Toulon, CNRS, LIS, France

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Mohamed Sami Cherif, Djamal Habet, and Matthieu Py. From Crossing-Free Resolution to Max-SAT Resolution. In 28th International Conference on Principles and Practice of Constraint Programming (CP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 235, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.CP.2022.12

Abstract

Adapting a SAT resolution proof into a Max-SAT resolution proof without considerably increasing its size is an open problem. Read-once resolution, where each clause is used at most once in the proof, represents the only fragment of resolution for which an adaptation using exclusively Max-SAT resolution is known and trivial. Proofs containing non read-once clauses are difficult to adapt because the Max-SAT resolution rule replaces the premises by the conclusions. This paper contributes to this open problem by defining, for the first time since the introduction of Max-SAT resolution, a new fragment of resolution whose proofs can be adapted to Max-SAT resolution proofs without substantially increasing their size. In this fragment, called crossing-free resolution, non read-once clauses are used independently to infer new information thus enabling to bring along each non read-once clause while unfolding the proof until a substitute is required.

Subject Classification

ACM Subject Classification
  • Theory of computation → Proof theory
Keywords
  • Satisfiability
  • Proof
  • Max-SAT Resolution

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