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

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 $O((2-\epsilon_k)^n)$ for some constant ek>0, where ek 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−e)n) for any constant e>0, provided that the SAT problem (with no restriction to the clause length) is not solvable in time O((2−e)n) for any constant e>0.