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NP-Completeness of Refutability by Literal-Once Resolution

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Automated Reasoning (IJCAR 2001)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2083))

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Abstract

A boolean formula in conjunctive normal form (CNF) F is refuted by literal–once resolution if the empty clause is inferred from F by resolving on each literal of F at most once. Literal–once resolution refutations can be found nondeterministically in polynomial time, though this restricted system is not complete. We show that despite of the weakness of literal–once resolution, the recognition of CNF-formulas which are refutable by literal–once resolution is NP–complete. We study the relationship between literal–once resolution and read-once resolution (introduced by Iwama and Miyano). Further we answer a question posed by Kullmann related to minimal unsatisfiability.

This work has been supported by the Austrian Science Fund, P13417-MAT.

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Author information

Authors and Affiliations

  1. Institute of Discrete Mathematics, Austrian Academy of Sciences, Sonnenfelsgasse 19, 1010, Vienna, Austria

    Stefan Szeider

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  1. Stefan Szeider
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Editors and Affiliations

  1. Automated Reasoning Project and Department of Computer Science, Australian National University, Canberra, ACT, 0200, Australia

    Rajeev Goré

  2. AG Theoretische Informatik und Logik, Institut für Computersprachen, Technische Universität Wien, Favoritenstr. 9, E185-2, 1040, Wien, Austria

    Alexander Leitsch

  3. Institut für Informatik, Technische Universität München, 80290, München, Germany

    Tobias Nipkow

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Szeider, S. (2001). NP-Completeness of Refutability by Literal-Once Resolution. In: Goré, R., Leitsch, A., Nipkow, T. (eds) Automated Reasoning. IJCAR 2001. Lecture Notes in Computer Science, vol 2083. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45744-5_13

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  • DOI: https://doi.org/10.1007/3-540-45744-5_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42254-9

  • Online ISBN: 978-3-540-45744-2

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