Solving satisfiability in less than 2 n steps

Abstract

In this paper we describe and analyse an algorithm for solving the satisfiability problem. If E is a boolean formula in conjunctive normal form with n variables and r clauses, then we will show that this algorithm solves the satisfiability problem for formulas with at most k literals per clause in time O(| F|· α k n ), where α k is the greatest number satisfying α k = 2−1/ α k k−1 (in the case of 3-satisfiability α 3 = 1,6181).