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The Exact Satisfiability problem, XSAT, is defined as the problem of finding a satisfying assignment to a formula in CNF such that there is exactly one literal in each clause assigned to be “1” and the other literals in the same clause are set to “0”. If we restrict the length of each clause to be at most 3 literals, then it is known as the X3SAT problem. In this paper, we consider the problem of counting the number of satisfying assignments to the X3SAT problem, which is also known as #X3SAT.

A Faster Exact Algorithm to Count X3SAT Solutions