Complete Boolean Satisfiability Solving Algorithms Based on Local Search
Boolean satisfiability (SAT) is a well-known problem in computer science, artificial intelligence, and operations research. This paper focuses on the satisfiability problem of Model RB structure that is similar to graph coloring problems and others. We propose a translation method and three effective complete SAT solving algorithms based on the characterization of Model RB structure. We translate clauses into a graph with exclusive sets and relative sets. In order to reduce search depth, we determine search order using vertex weights and clique in the graph. The results show that our algorithms are much more effective than the best SAT solvers in numerous Model RB benchmarks, especially in those large benchmark instances.
KeywordsBoolean satisfiability set clique local search complete search
Unable to display preview. Download preview PDF.
- Cook S A. The complexity of theorem-proving procedures. In Proc. the 3rd Symp. Theory of Comput., May 1971, pp.151-158.Google Scholar
- Larrabee T. Test pattern generation using Boolean satisfiability. IEEE Trans. CAD, 1992, 11(1): 4–15.Google Scholar
- Biere A, Cimatti A, Clarke E M, Fujita M, Zhu Y. Symbolic model checking using SAT procedures instead of BDDs. In Proc. the 36th Conf. Design Automation, June 1999, pp.317-320.Google Scholar
- Bjesse P, Leonard T, Mokkedem A. Finding bugs in an Alpha microprocessor using satisfiability solvers. In Lecture Notes in Computer Science 2102, Berry G, Comon H, Finkel A (eds.), Springer-Verlag, 2001, pp.454-464.Google Scholar
- Hung W N N, Narasimhan N. Reference model based RTL verification: An integrated approach. In Proc. the 9th HLDVT, November 2004, pp.9-13.Google Scholar
- Hung W N N, Song X, Yang G, Yang J, Perkowski M. Optimal synthesis of multiple output Boolean functions using a set of quantum gates by symbolic reachability analysis. IEEE Trans. CAD, 2006, 25(9): 1652–1663.Google Scholar
- Wood R G, Rutenbar R A. FPGA routing and routability estimation via Boolean satisfiability. In Proc. the 5th Int. Symp. Field-Programmable Gate Arrays, Feb. 1997, pp.119-125.Google Scholar
- Gu J. Local search for satisfiability (SAT) problem. Trans. Systems, Man, and Cybernetics, 1993, 23(4): 1108–1129.Google Scholar
- Selman B, Kautz H A, Cohen B. Noise strategies for improving local search. In Proc. the 12th National Conference on Artificial Intelligence, July 31-August 4, 1994, pp.337-343.Google Scholar
- Zhao C, Zhou H, Zheng Z, Xu K. A message-passing approach to random constraint satisfaction problems with growing domains. Journal of Statistical Mechanics: Theory and Experiment, 2011, P02019.Google Scholar
- Selman B, Levesque H, Mitchell D. A new method for solving hard satisfiability problems. In Proc. the 10th National Conference on Artificial Intelligence, July 1992, pp.440-446.Google Scholar
- Zhang L, Madigan C, Moskewicz M et al. Efficient conflict driven learning in a Boolean satisfiability solver. In Proc. Int. Conf. Computer-Aided Design, Nov. 2001, pp.279-285.Google Scholar
- Goldberg E, Novikov Y. BerkMin: A fast and robust SATsolver. In Proc. Design Automation and Test in Europe, March 2002, pp.142-149.Google Scholar
- Pipatsrisawat K, Darwiche A. RSat 1.03: SAT solver description. Technical Report D-152, Automated Reasoning Group, Computer Science Department, UCLA, 2006.Google Scholar
- Jiang W, Liu T, Ren T, Xu K. Two hardness results on feedback vertex sets. In Lecture Notes in Computer Science 6681, Atallah M, Li X, Zhu B (eds.), Springer, 2011, pp.233-243.Google Scholar
- Liu T, Lin X, Wang C, Su K, Xu K. Large hinge width on sparse random hypergraphs. In Proc. the 22nd Int. Joint Conf. Artificial Intelligence, July 2011, pp.611-616.Google Scholar
- Wang C, Liu T, Cui P, Xu K. A note on treewidth in random graphs. In Lecture Notes in Computer Science 6831, Wang W, Zhu X, Du D (eds.), Springer-Verlag, 2011, pp.491-499.Google Scholar
- Zhang L. SAT-solving: From Davis-Putnam to Zchaff and beyond, 2003. http://research.microsoft.com/enus/people/lintaoz/sat-course1.pdf.
- Cai S, Su K, Chen Q. EWLS: A new local search for minimum vertex cover. In Proc. the 24th AAAI Conference on Artificial Intelligence, July 2010, pp.45-50.Google Scholar
- Richter C G S, Helmert M. A stochastic local search approach to vertex cover. In Proc. the 30th Annual German Conference on Artificial Intelligence, Sept. 2007, pp.412-426.Google Scholar