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The rigorous theoretical analyses of algorithms for exact 3-satisfiability(X3SAT) have been proposed in the literature. As we know, previous algorithmsfor solving X3SAT have been analyzed only regarding the number of variables asthe parameter. However, the time complexity for solving X3SAT instances dependsnot only on the number of variables, but also on the number of clauses.Therefore, it is significant to exploit the time complexity from the otherpoint of view, i.e. the number of clauses. In this paper, we present algorithmsfor solving X3SAT with rigorous complexity analyses using the number of clausesas the parameter. By analyzing the algorithms, we obtain the new worst-caseupper bounds O(1.15855m), where m is the number of clauses.

New Worst-Case Upper Bound for X3SAT