New Worst-Case Upper Bound for X3SAT

TL;DR

This paper introduces a new worst-case upper bound for solving X3SAT problems based on the number of clauses, improving understanding of its computational complexity.

Contribution

It provides the first complexity analysis of X3SAT algorithms using the number of clauses as the parameter, establishing a new upper bound.

Findings

New worst-case upper bound: O(1.15855^m) where m is the number of clauses.

Algorithms analyzed with respect to clause count, not just variables.

Advances theoretical understanding of X3SAT complexity.

Abstract

The rigorous theoretical analyses of algorithms for exact 3-satisfiability (X3SAT) have been proposed in the literature. As we know, previous algorithms for solving X3SAT have been analyzed only regarding the number of variables as the parameter. However, the time complexity for solving X3SAT instances depends not only on the number of variables, but also on the number of clauses. Therefore, it is significant to exploit the time complexity from the other point of view, i.e. the number of clauses. In this paper, we present algorithms for solving X3SAT with rigorous complexity analyses using the number of clauses as the parameter. By analyzing the algorithms, we obtain the new worst-case upper bounds O(1.15855m), where m is the number of clauses.