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A satisfiability algorithm for sparse depth two threshold circuits
 In Proceedings of the 54th Annual Symposium on the Foundations of Computer Science (FOCS 2013
, 2013
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An exact algorithm for the Boolean connectivity problem for kCNF, Theoretical Computer Science 412
, 2011
"... We present an exact algorithm for a PSPACEcomplete problem, denoted by CONNkSAT, which asks if the solution space for a given kCNF formula is connected on the ndimensional hypercube. The problem is known to be PSPACEcomplete for k ≥ 3, and polynomial solvable for k ≤ 2 [6]. We show that CONNkSAT ..."
Abstract

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We present an exact algorithm for a PSPACEcomplete problem, denoted by CONNkSAT, which asks if the solution space for a given kCNF formula is connected on the ndimensional hypercube. The problem is known to be PSPACEcomplete for k ≥ 3, and polynomial solvable for k ≤ 2 [6]. We show that CONNkSAT for k ≥ 3 is solvable in time O((2 − k)n) for some constant k> 0, where k depends only on k, but not on n. This result is considered to be interesting due to the following fact shown by [5]: QBF3SAT, which is a typical PSPACEcomplete problem, is not solvable in time O((2 − )n) for any constant > 0, provided that the SAT problem (with no restriction to the clause length) is not solvable in time O((2 − )n) for any constant > 0. Keywords: exponentialtime algorithms, Boolean connectivity, CNF satisfiability