Abstract

In this paper we describe and analyse an improved algorithm for solving the 3-Satisfiability problem. The algorithm makes use of the concept 'Pure literal look ahead'. If F is a boolean formula in conjunctive normal form with n variables, then we will show that this algorithm solves the 3-Satisfiability problem in time less than O(1; 497 n ). 1 INTRODUCTION Let V = fv 1 ; v 2 ; : : : ; v n g be a set of boolean variables. For each variable v i there is a positive literal, denoted by v i , and a negative literal, denoted by v i . The literal v i has value true if and only if the variable v i has value true, and the literal v i has value true if and only if the variable v i has value false. The literals v i and v i will be called complemented and L = fv 1 ; v 1 ; v 2 ; v 2 ; : : : ; v n ; v n g is the set of literals corresponding to V . For L 0 ` L we set Lit(L 0 ) := fv; v j v 2 L 0 or v 2 L 0 g. A k-clause (k 1) is a subset of k different literals of L. For a literal v...

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