New Worst-Case Upper Bounds for SAT

In 1980 Monien and Speckenmeyer proved that satisfiability of a propositional formula consisting of K clauses (of arbitrary length) can be checked in time of the order 2^sup K / 3^. Recently Kullmann and Luckhardt proved the worst-case upper bound 2^sup L / 9^, where L is the length of the input formula. The algorithms leading to these bounds are based on the splitting method, which goes back to the Davis-Putnam procedure. Transformation rules (pure literal elimination, unit propagation, etc.) constitute a substantial part of this method. In this paper we present a new transformation rule and two algorithms using this rule. We prove that these algorithms have the worst-case upper bounds 2^sup 0. 30897 K^ and 2^sup 0. 10299 L^, respectively.[PUBLICATION ABSTRACT]