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 whether 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 (Gopalan et al., 2009) [6]. We show that CONNkSAT for k>=3 is solvable in time O((2-@e"k)^n) for some constant @e"k>0, where @e"k depends only on k, but not on n. This result is considered to be interesting due to the following fact shown by Calabro [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.

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