Lemma and Cut Strategies

Resolution has not been an eeective tool for deciding satissability of propositional CNF formulas, due to explosion of the search space, particularly when the formula is satissable. However, a new pruning method, which is designed to eliminate certain refutation attempts that cannot succeed, has been shown to eliminate much of the redundancy of propositional model elimination. The pruning method exploits the concept of \autarky", which was introduced by Monien and Speckenmeyer. Informally, an autarky is a \self-suucient" model for some clauses, but which does not aaect the remaining clauses of the formula. Autarky pruning permits the algorithm, called \Modoc", to be \two-sided" in the sense that it constructs a model if the formula is satissable and constructs a refutation proof if it is not. This talk describes new \lemma" and \cut" strategies that are eecient to apply in the setting of propositional resolution. It builds upon the C-literal strategy proposed by Shostak, and studied further by Letz, Mayr and Goller. Methods for \eager" lemmas, \quasi-persistent" lemmas, and two forms of controlled cut have been incorporated into Modoc. While these strategies are not necessary for the theoretical completeness of Modoc, experiments show them to greatly increase the eeciency in practice. Experimental data based on an implementation in C is reported. On random 3CNF formulas at the \hard" ratio of 4.27 clauses per variable, Modoc is not as eeective as recently reported model-searching methods. On more structured formulas from applications, such as circuit-fault detection, it is superior. This performance is achieved in spite of the fact that Modoc incorporates almost no heuristics to guide its searches.