Two new upper bounds for SAT
Edward Alekseevich Hirsch · 1998
In 1980 B. Monien and E. Speckenmeyer proved that satisfiability of a propositional formula consisting of K clauses can be checked in time of the order 2^{K/3}. Recently O. Kullmann and H. Luckhardt proved the bound 2^{L/9}, where L is the length of the input formula. The algorithms leading to these bounds (like many other SAT algorithms) are based on splitting, i.e., they reduce SAT for a formula F to SAT for several simpler formulas F1 , F2 , ... , Fm . These algorithms simplify each of F1 , F2 , ... , Fm according to some transformation rules such as the elimination of pure literals, the unit propagation rule etc. In this paper we present a new transformation rule and two algorithms using this rule. These algorithms have the bounds 2^{0.30897K} and 2^{0.10537L}, respectively.