Computational Complexity of Some Restricted Instances of 3SAT

Abstract We prove results on the computational complexity of instances of 3SAT in which every variable occurs 3 or 4 times. 1 Introduction An instance of k-SAT is a set of clauses that are disjunctions of exactly k literals. The problem is to determine whether there is an assignment of truth values to the variables such that all the clauses are satisfied. It is well known that 2-SAT can be solved in polynomial time, while Cook [4] showed that k-SAT is NP-hard for k * 3. This leads to the general question of exploring the boundary region between polynomial time and NP-hard satisfiability problems, by considering more or less restricted problem instances (of course, this is most interesting if P6=NP)