Abstract
Probabilistic inference techniques can be used to estimate variable bias, or the proportion of solutions to a given SAT problem that fix a variable positively or negatively. Methods like Belief Propagation (BP), Survey Propagation (SP), and Expectation Maximization BP (EMBP) have been used to guess solutions directly, but intuitively they should also prove useful as variable- and value- ordering heuristics within full backtracking (DPLL) search. Here we report on practical design issues for realizing this intuition in the VARSAT system, which is built upon the full-featured MiniSat solver. A second, algorithmic, contribution is to present four novel inference techniques that combine BP/SP models with local/global consistency constraints via the EMBP framework. Empirically, we can also report exponential speed-up over existing complete methods, for random problems at the critically-constrained phase transition region in problem hardness. For industrial problems, VARSAT is slower that MiniSat, but comparable in the number and types problems it is able to solve.
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
Dechter, R., Kask, K., Mateescu, R.: Iterative join-graph propagation. In: Proc. of 18th International Conference on Uncertainty in Artificial Intelligence (UAI 2002), Edmonton, Canada, pp. 128–136 (2002)
Braunstein, A., Mezard, M., Zecchina, R.: Survey propagation: An algorithm for satisfiability. Random Structures and Algorithms 27, 201–226 (2005)
Hsu, E., McIlraith, S.: Characterizing Propagation Methods for Boolean Satisfiability. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 325–338. Springer, Heidelberg (2006)
Achlioptas, D., Ricci-Tersenghi, F.: Random formulas have frozen variables. SIAM Journal of Computing (to appear)
Hsu, E.I.: VARSAT SAT-Solver homepage (2008), http://www.cs.toronto.edu/~eihsu/VARSAT/
Eén, N., Sörensson, N.: An extensible SAT-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)
Jordan, M., Ghahramani, Z., Jaakkola, T., Saul, L.: An introduction to variational methods for graphical models. In: Jordan, M. (ed.) Learning in Graphical Models. MIT Press, Cambridge (1998)
Kask, K., Dechter, R., Gogate, V.: Counting-based look-ahead schemes for constraint satisfaction. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 317–331. Springer, Heidelberg (2004)
Hsu, E., Kitching, M., Bacchus, F., McIlraith, S.: Using EM to find likely assignments for solving CSP’s. In: Proc. of 22nd Conference on Artificial Intelligence (AAAI 2007), Vancouver, Canada (2007)
Kroc, L., Sabharwal, A., Selman, B.: Survey propagation revisited. In: Proc. of 23rd International Conference on Uncertainty in Artificial Intelligence (UAI 2007), Vancouver, Canada (2007)
Pearl, J.: Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann, San Mateo (1988)
Kschischang, F.R., Frey, B.J., Loeliger, H.A.: Factor graphs and the sum-product algorithm. IEEE Transactions on Information Theory 47(2) (2001)
Dempster, A., Laird, N., Rubin, D.: Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society 39(1), 1–39 (1977)
Hsu, E., Muise, C., Beck, J.C., McIlraith, S.: Probabilistically estimating backbones and variable bias: Experimental overview. In: Stuckey, P.J. (ed.) CP 2008. LNCS, vol. 5202. Springer, Heidelberg (2008)
Maneva, E., Mossel, E., Wainwright, M.: A new look at survey propagation and its generalizations. Journal of the ACM 54(4), 2–41 (2007)
Williams, R., Gomes, C., Selman, B.: Backdoors to typical case complexity. In: Proc. of 18th International Joint Conference on Artificial Intelligence (IJCAI 2003), Acapulco, Mexico (2003)
Beck, J.C., Prosser, P., Wallace, R.J.: Trying again to fail-first. In: Faltings, B.V., Petcu, A., Fages, F., Rossi, F. (eds.) CSCLP 2004. LNCS (LNAI), vol. 3419, pp. 41–55. Springer, Heidelberg (2005)
Braunstein, A., Zecchina, R.: Survey propagation as local equilibrium equations. Journal of Statistical Mechanics: Theory and Experiments PO6007 (2004)
Wallace, R.J.: Factor analytic studies of CSP heuristics. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 712–726. Springer, Heidelberg (2005)
Xu, L., Hutter, F., Hoos, H.H., Leyton-Brown, K.: SATzilla: portfolio-based algorithm selection for SAT. Journal of Artificial Intelligence Research 32, 565–606 (2008)
Manolios, P., Zhang, Y.: Implementing survey propagation on graphics processing units. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 311–324. Springer, Heidelberg (2006)
Zhang, W.: Configuration landscape analysis and backbone guided local search. Part I: Satisfiability and maximum satisfiability. Artificial Intelligence 158(1), 1–26 (2004)
Zanarini, A., Pesant, G.: Solution counting algorithms for constraint-centered search heuristics. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 743–757. Springer, Heidelberg (2007)
Fang, H., Ruml, W.: Complete local search for propositional satisfiability. In: Proc. of 19th National Conference on Artificial Intelligence (AAAI 2004), San Jose, CA (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hsu, E.I., McIlraith, S.A. (2009). VARSAT: Integrating Novel Probabilistic Inference Techniques with DPLL Search. In: Kullmann, O. (eds) Theory and Applications of Satisfiability Testing - SAT 2009. SAT 2009. Lecture Notes in Computer Science, vol 5584. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02777-2_35
Download citation
DOI: https://doi.org/10.1007/978-3-642-02777-2_35
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02776-5
Online ISBN: 978-3-642-02777-2
eBook Packages: Computer ScienceComputer Science (R0)