New Worst-Case Upper Bound for #XSAT

Abstract: An algorithm running in O(1.1995n) is presented for counting models for exact satisfiability formulae(#XSAT). This is faster than the previously best algorithm which runs in O(1.2190n). In order to improve the efficiency of the algorithm, a new principle, i.e. the common literals principle, is addressed to simplify formulae. This allows us to eliminate more common literals. In addition, we firstly inject the resolution principles into solving #XSAT problem, and therefore this further improves the efficiency of the algorithm.