Abstract

Resolution has not been an effective tool for deciding satisfiability of propositional CNF formulas, due to explosion of the search space, particularly when the formula is satisfiable. A new pruning method is described, which is designed to eliminate certain refutation attempts that cannot succeed. The method exploits the concept of "autarky", which was introduced by Monien and Speckenmeyer. New forms of lemma creation are also introduced, which eliminate the need to carry out refutation attempts that must succeed. The resulting algorithm, called "Modoc", is a modification of propositional model elimination. Informally, an autarky is a "self-sufficient" model for some clauses, but which does not affect the remaining clauses of the formula. Whereas Monien and Speckenmeyer's work was oriented toward finding a model, our method has as its primary goal to find a refutation in the style of model elimination. However, Modoc finds a model if it fails to find a refutation, essentially by combi...

Citations