Satisfiability of acyclic and almost acyclic CNF formulas (II)

Authors:
Sebastian Ordyniak;Daniel Paulusma;Stefan Szeider
Affiliations:
Institute of Information Systems, Vienna University of Technology, Vienna, Austria;School of Engineering and Computing Sciences, Durham University, Durham, UK;Institute of Information Systems, Vienna University of Technology, Vienna, Austria
Venue:
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
Year:
2011

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Abstract

In the first part of this work (FSTTCS'10) we have shown that the satisfiability of CNF formulas with β-acyclic hypergraphs can be decided in polynomial time. In this paper we continue and extend this work. The decision algorithm for β-acyclic formulas is based on a special type of Davis-Putnam resolution where each resolvent is a subset of a parent clause. We generalize the class of β-acyclic formulas to more general CNF formulas for which this type of Davis-Putnam resolution still applies. We then compare the class of β-acyclic formulas and this superclass with a number of known polynomial formula classes.