GSAT with Adaptive Score Function

Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract GSAT is a well-known satisfiability search algorithm. In this paper we consider a modification of GSAT. In particular, we consider an adaptive score function. Investigation of efficient satisfiability algorithms and encoding different hard problems as instances of satisfiability has caused considerable interest recently (see e.g. [1, 2]). GSAT is a well-known satisfiability algorithm [3]. Note that GSAT applies only to clausal formulas. The notion of score plays a key role in GSAT. Although, some modification of the score function are considered , usually, the score function is the number of clauses of formula which are falsified by the truth assignment (see e.g. [4]). In this paper we consider a modification of the score function for clausal formulas with different types of clauses. At first, we consider a general schema for standard GSAT (see Figure 1). We use the notation from [5]. Let f (z[1],. .. , z[n]) be a CNF. Let T be a truth assignment for the variables of f. The function score(T, f) is the number of clauses of f which are falsified by T. GSAT performs an search for a satisfying truth assignment for the variables of f , starting from a random assignment provided by initial(f). The successive assignment is obtained by inverting the truth value of one single variable V in T. The value of V is chosen to minimize