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From Crossing-Free Resolution to Max-SAT Resolution

Authors: Mohamed Sami Cherif, Djamal Habet, and Matthieu Py

Published in: LIPIcs, Volume 235, 28th International Conference on Principles and Practice of Constraint Programming (CP 2022)


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.

Cite as

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)


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@InProceedings{cherif_et_al:LIPIcs.CP.2022.12,
  author =	{Cherif, Mohamed Sami and Habet, Djamal and Py, Matthieu},
  title =	{{From Crossing-Free Resolution to Max-SAT Resolution}},
  booktitle =	{28th International Conference on Principles and Practice of Constraint Programming (CP 2022)},
  pages =	{12:1--12:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-240-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{235},
  editor =	{Solnon, Christine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2022.12},
  URN =		{urn:nbn:de:0030-drops-166412},
  doi =		{10.4230/LIPIcs.CP.2022.12},
  annote =	{Keywords: Satisfiability, Proof, Max-SAT Resolution}
}
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