An algorithm for the satisfiability problem of formulas in conjunctive normal form

Abstract

We consider the satisfiability problem on Boolean formulas in conjunctive normal form. We show that a satisfying assignment of a formula can be found in polynomial time with a success probability of 2 − n(1−1/(1+log m)) , where n and m are the number of variables and the number of clauses of the formula, respectively. If the number of clauses of the formulas is bounded by n c for some constant c, this gives an expected run time of O( p( n)·2 n(1−1/(1+ clog n)) ) for a polynomial p.