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

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.