New Worst-Case Upper Bound for X3SAT

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.

[1]  Peter Jonsson,et al.  An algorithm for counting maximum weighted independent sets and its applications , 2002, SODA '02.

[2]  Stefan Porschen.  On Some Weighted Satisfiability and Graph Problems , 2005, SOFSEM.

[3]  Minghao Yin,et al.  New Worst-Case Upper Bound for #2-SAT and #3-SAT with the Number of Clauses as the Parameter , 2010, AAAI.

[4]  David Peleg,et al.  Faster exact solutions for some NP-hard problems , 2002, Theor. Comput. Sci..

[5]  Stefan Porschen,et al.  Exact 3-Satisfiability Is Decidable in Time O (2 0.16254 n ) , 2005 .

[6]  Henry A. Kautz,et al.  Performing Bayesian Inference by Weighted Model Counting , 2005, AAAI.

[7]  Bolette Ammitzbøll Madsen.  An algorithm for exact satisfiability analysed with the number of clauses as parameter , 2006 .

[8]  James D. Park,et al.  MAP Complexity Results and Approximation Methods , 2002, UAI.

[9]  Edward A. Hirsch,et al.  New Worst-Case Upper Bounds for SAT , 2000, Journal of Automated Reasoning.

[10]  Bolette Ammitzbøll Jurik,et al.  An algorithm for Exact Satisfiability analysed with the number of clauses as parameter , 2006, Inf. Process. Lett..

[11]  Leslie G. Valiant,et al.  The Complexity of Computing the Permanent , 1979, Theor. Comput. Sci..

[12]  Stefan Porschen,et al.  Exact 3-satisfiability is decidable in time O(20.16254n) , 2005, Annals of Mathematics and Artificial Intelligence.

[13]  Thomas J. Schaefer,et al.  The complexity of satisfiability problems , 1978, STOC.

[14]  Jesper Makholm Byskov,et al.  New Algorithms for Exact Satisfiability , 2003 .

[15]  A. S. Kulikov.  An upper bound O(20.16254n) for exact 3-satisfiability: a simpler proof , 2005 .

[16]  Stefan Porschen.  Counting All Solutions of Minimum Weight Exact Satisfiability , 2006, CIAC.

[17]  Konstantin Kutzkov,et al.  Using CSP To Improve Deterministic 3-SAT , 2010, 1007.1166.

[18]  Peter Jonsson,et al.  Algorithms for four variants of the exact satisfiability problem , 2004, Theor. Comput. Sci..

[19]  Armando Tacchella,et al.  Theory and Applications of Satisfiability Testing , 2003, Lecture Notes in Computer Science.