On the Completeness of WalkSAT for 2-SAT?

WalkSAT is a highly successful local search algorithm for the Satissability problem. We show that for 2-SAT, it is complete in that it can reach a solution (if one exists) from any starting point. We leave open the more important case of 3-SAT. WalkSAT is a highly successful local search algorithm for the Satissability problem 2]. The algorithm has been shown to work well on random 3-SAT formulae, and has been extensively studied, for example in 1]. We show that for 2-SAT, it is complete in that it can reach a solution (if one exists) from any starting point. This is in response to a question posed by Holger Hoos. This 2-SAT case may be a known result, but it is new to us. Let S = (U; C) be an instance of SAT, and T : U ! ftrue; falseg be a truth assignment. The assignment T partitions C into unsatissed and satissed clauses, C U and C s. We use the notation Tb u to indicate the the truth assignment obtained from T by complementing the assignment of the variable u. A variable u 2 U is said to be free (under an assignment T) if u or b u occurs in a clause C 2 C U and for all d 2 C S under T, d 2 C S under T 0 = Tb u. We can now describe the WALKSAT algorithm. an EPSRC visiting fellowship, GR/M54605. We thank members of APES for their help, and Holger Hoos for suggesting the problem to us. We are members of the