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Satisfiability of acyclic and almost acyclic CNF formulas (II).

Ordyniak, S. and Paulusma, Daniel and Szeider, S. (2011) 'Satisfiability of acyclic and almost acyclic CNF formulas (II).', in Theory and Applications of Satisfiability Testing - SAT 2011, 14th International Conference, SAT 2011, Ann Arbor, MI, USA, June 19-22, 2011 ; proceedings. Berlin: Springer, pp. 47-60. Lecture notes in computer science. (6695).


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.

Item Type:Book chapter
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Date of first online publication:2011
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