On Conjunctive Normal Form Satisfiability

This paper focuses on algorithms that solve CSAT (conjunctive normal form satisfiability) by searching for a satisfying truth assignment for the given formula F. We identify four basic ways to improve the basic search procedure: constraint propagators, simplifying transformations, heuristics, and other miscellaneous improvements. In each of these categories, we survey the existing improvements and suggest new ones. We lower the average time it takes to perform the simplest kind of constraint propagation from O(L) to O(L/P), where L is the length of F and P is the number of propositions in F; this is optimal. We lower the current upper bound for CSAT from O(20.128 L) to O(20.128 (L-N)), where N is the number of clauses in F. Finally, we experimentally determine the fastest possible algorithm with respect to each of the basic improvements we consider.