Abstract
In this paper, we propose an OBDD-based algorithm called greedy clique decomposition, which is a new variable grouping heuristic method, to solve difficult SAT problems. We implement our algorithm and compare it with several state-of-art SAT solvers including Minisat, Ebddres and TTS. We show that with this new heuristic method, our implementation of an OBDD-based satisfiability solver can perform better for selected difficult SAT problems, whose conflict graphs possess a clique-like structure.
Supported by the Beijing Forestry University Young Scientist Fund No. BLX2009013, the Chinese National 973 Plan (No.2010CB328103), the ARC grants FT0991785 and DP120102489, the National Natural Science Foundation of China under Grant No. 60833001, and the CAS Innovation Program.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Stephen, A.: Cook. The Complexity of Theorem-Proving Procedures. In: STOC, pp. 151–158. ACM (1971)
Velev, M.N., Bryant, R.E.: Effective use of Boolean satisfiability procedures in the formal verification of superscalar and VLIW microprocessors. J. Symb. Comput. 35(2), 73–106 (2003)
Nam, G.-J., Sakallah, K.A., Rutenbar, R.A.: A new FPGA detailed routing approach via search-based Boolean satisfiability. IEEE Trans. on CAD of Integrated Circuits and Systems 21(6), 674–684 (2002)
Kautz, H.A., Selman, B.: Planning as Satisfiability. In: ECAI, pp. 359–363 (1992)
Franco, J., Kouril, M., Schlipf, J., Ward, J., Weaver, S., Dransfield, M., Vanfleet, W.M.: SBSAT: a State-Based, BDD-Based Satisfiability Solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 398–410. Springer, Heidelberg (2004)
Damiano, R.F., Kukula, J.H.: Checking satisfiability of a conjunction of BDDs. In: DAC, pp. 818–823. ACM (2003)
Pan, G., Vardi, M.Y.: Search vs. Symbolic Techniques in Satisfiability Solving. In: H. Hoos, H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 235–250. Springer, Heidelberg (2005)
Rish, I., Dechter, R.: Resolution versus Search: Two Strategies for SAT. J. Autom. Reasoning 24(1/2), 225–275 (2000)
Groote, J.F., Zantema, H.: Resolution and binary decision diagrams cannot simulate each other polynomially. Discrete Applied Mathematics 130(2), 157–171 (2003)
Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an Efficient SAT Solver. In: DAC, pp. 530–535. ACM (2001)
Chen, W., Zhang, W.: A direct construction of polynomial-size OBDD proof of pigeon hole problem. Inf. Process. Lett. 109(10), 472–477 (2009)
Surynek, P.: Solving Difficult SAT Instances Using Greedy Clique Decomposition. In: Miguel, I., Ruml, W. (eds.) SARA 2007. LNCS (LNAI), vol. 4612, pp. 359–374. Springer, Heidelberg (2007)
Bryant, R.E.: Graph-Based Algorithms for Boolean Function Manipulation. IEEE Trans. Computers 35(8), 677–691 (1986)
McMillan, K.L.: Symbolic Model Checking. Kluwer Academic Publishers ACM (1993)
Yue, W., Xu, Y., Su, K.: BDDRPA*: An Efficient BDD-Based Incremental Heuristic Search Algorithm for Replanning. In: Sattar, A., Kang, B.H. (eds.) AI 2006. LNCS (LNAI), vol. 4304, pp. 627–636. Springer, Heidelberg (2006)
Xu, Y., Yue, W.: A Generalized Framework for BDD-based Replanning A* Search. In: Kim, H.-K., Lee, R.Y. (eds.) SNPD, pp. 133–139. IEEE Computer Society (2009)
Xu, Y., Yue, W., Su, K.: The BDD-Based Dynamic A* Algorithm for Real-Time Replanning. In: Deng, X., Hopcroft, J.E., Xue, J. (eds.) FAW 2009. LNCS, vol. 5598, pp. 271–282. Springer, Heidelberg (2009)
Pan, G., Vardi, M.Y.: Symbolic Techniques in Satisfiability Solving. J. Autom. Reasoning 35(1-3), 25–50 (2005)
Jussila, T., Sinz, C., Biere, A.: Extended Resolution Proofs for Symbolic SAT Solving with Quantification. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 54–60. Springer, Heidelberg (2006)
Sinz, C., Biere, A.: Extended Resolution Proofs for Conjoining BDDs. In: Grigoriev, D., Harrison, J., Hirsch, E.A. (eds.) CSR 2006. LNCS, vol. 3967, pp. 600–611. Springer, Heidelberg (2006)
Somenzi, F.: CUDD: CU Decision Diagram Package, Release 2.4.1. Technical report, University of Colorado at Boulder (2005)
Aloul, F.A., Ramani, A., Markov, I.L., Sakallah, K.A.: Solving difficult SAT instances in the presence of symmetry. In: DAC 2002: Proceedings of the 39th Conference on Design Automation, pp. 731–736. ACM, New York (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Xu, Y., Chen, W., Su, K., Zhang, W. (2012). Solving Difficult SAT Problems by Using OBDDs and Greedy Clique Decomposition. In: Snoeyink, J., Lu, P., Su, K., Wang, L. (eds) Frontiers in Algorithmics and Algorithmic Aspects in Information and Management. Lecture Notes in Computer Science, vol 7285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29700-7_24
Download citation
DOI: https://doi.org/10.1007/978-3-642-29700-7_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-29699-4
Online ISBN: 978-3-642-29700-7
eBook Packages: Computer ScienceComputer Science (R0)