Two new upper bounds for SAT

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, ..., F_m. These algorithms simplify each of F₁, F₂, ..., F_m 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^{0.30897 K} and 2^{0.10537 L} respectively.