On generating all solutions of generalized satisfiability problems

Abstract

We examine whether all solutions of Generalized Satisfiability problems can be generated efficiently. By refining Schaefer's [11] result we show that there exists a class G of problems such that for every problem in there exists a polynomial delay generating algorithm and for every Generalized Satisfiability problem not in G such an algorithm does not exist unless P = NP. The class G is made up of the problems equivalent to the satisfiability problem for conjunction of Horn clauses, anti-Horn clauses, 2-clauses or XOR-clauses.