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A Faster Clause-Shortening Algorithm for SAT with No Restriction on Clause Length

Article type: Research Article

Authors: Dantsin, Evgeny | Wolpert, Alexander

Affiliations: Department of Computer Science, Roosevelt University, 430 S. Michigan Av., Chicago, IL 60605, USA. E-mails: [email protected], [email protected]

Keywords: SAT with no restriction on clause length, upper bound, clause shortening

DOI: 10.3233/SAT190002

Journal: Journal on Satisfiability, Boolean Modeling and Computation, vol. 1, no. 1, pp. 49-60, 2006

Received 1 July 2005
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Revision received 1 November 2005
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Published: 1 November 2005
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Abstract

We give a randomized algorithm for testing satisfiability of Boolean formulas in conjunctive normal form with no restriction on clause length. This algorithm uses the clause-shortening approach proposed by Schuler [14]. The running time of the algorithm is O(2n(1−1/α)) where α=ln(m/n)+O(lnlnm) and n, m are respectively the number of variables and the number of clauses in the input formula. This bound is asymptotically better than the previously best known 2n(1−1/log(2m)) bound for SAT.

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