An exact algorithm for the Boolean connectivity problem for k-CNF

Abstract

We present an exact algorithm for a PSPACE-complete problem, denoted by CONNkSAT, which asks if the solution space for a given k-CNF formula is connected on the n-dimensional hypercube. The problem is known to be PSPACE-complete for k ≥ 3, and polynomial solvable for k ≤ 2 [6]. We show that CONN kSAT for k ≥ 3 is solvable in time for some constant εk > 0, where εk depends only on k, but not on n. This result is considered to be interesting due to the following fact shown by [5]: QBF-3-SAT, which is a typical PSPACE-complete problem, is not solvable in time O((2 - ε)n) for any constant ε > 0, provided that the SAT problem (with no restriction to the clause length) is not solvable in time O((2 - ε)n ) for any constant ε> 0. © 2010 Springer-Verlag.