Lemma and cut strategies for propositional model elimination

Abstract

This paper describes new “lemma” and “cut” strategies that are efficient to apply in the setting of propositional Model Elimination. Previous strategies for managing lemmas and C-literals in Model Elimination were oriented toward first-order theorem proving. The original “cumulative” strategy remembers lemmas forever, and was found to be too inefficient. The previously reported C-literal and unit-lemma strategies, such as “strong regularity”, forget them unnecessarily soon in the propositional domain. An intermediate strategy, called “quasi-persistent” lemmas, is introduced. Supplementing this strategy, methods for “eager” lemmas and two forms of controlled “cut” provide further efficiencies. The techniques have been incorporated into “Modoc”, which is an implementation of Model Elimination, extended with a new pruning method that is designed to eliminate certain refutation attempts that cannot succeed. Experimental data show that on random 3CNF formulas at the “hard” ratio of 4.27 clauses per variable, Modoc is not as effective as recently reported model-searching methods. However, on more structured formulas from applications, such as circuit-fault detection, it is superior.