Abstract
In this paper we study the problem of integrating deduction and search with the aid of machine learning techniques to yield practically efficient decision procedures for quantified Boolean formulas (QBFs). We show that effective on-line policies can be learned from the observed performances of deduction and search on representative sets of formulas. Such policies can be leveraged to switch between deduction and search during the solving process. We provide empirical evidence that learned policies perform better than either deduction and search, even when the latter are combined using hand-made policies based on previous works. The fact that even with a proof-of-concept implementation, our approach is competitive with sophisticated state-of-the-art QBF solvers shows the potential of machine learning techniques in the integration of different reasoning methods.
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References
Mneimneh, M., Sakallah, K.: Computing Vertex Eccentricity in Exponentially Large Graphs: QBF Formulation and Solution. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 411–425. Springer, Heidelberg (2004)
Ansotegui, C., Gomes, C.P., Selman, B.: Achille’s heel of QBF. In: Proc. of AAAI, pp. 275–281 (2005)
Egly, U., Eiter, T., Tompits, H., Woltran, S.: Solving Advanced Reasoning Tasks Using Quantified Boolean Formulas. In: Seventeenth National Conference on Artificial Intelligence (AAAI 2000), pp. 417–422. MIT Press, Cambridge (2000)
Giunchiglia, E., Narizzano, M., Tacchella, A.: Clause-Term Resolution and Learning in Quantified Boolean Logic Satisfiability. Artificial Intelligence Research 26, 371–416 (2006), http://www.jair.org/vol/vol26.html
Benedetti, M.: sKizzo: a Suite to Evaluate and Certify QBFs. In: Nieuwenhuis, R. (ed.) CADE 2005. LNCS (LNAI), vol. 3632, pp. 369–376. Springer, Heidelberg (2005)
Biere, A.: Resolve and Expand. In: Hoos, H.H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 59–70. Springer, Heidelberg (2005)
Pan, G., Vardi, M.Y.: Symbolic Decision Procedures for QBF. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 453–467. Springer, Heidelberg (2004)
Pulina, L., Tacchella, A.: A self-adaptive multi-engine solver for quantified Boolean formulas. Constraints 14(1), 80–116 (2009)
Samulowitz, H., Memisevic, R.: Learning to Solve QBF. In: Proc. of 22nd Conference on Artificial Intelligence (AAAI 2007), pp. 255–260 (2007)
Peschiera, C., Pulina, L., Tacchella, A.: 6th QBF solvers evaluation (2008), http://www.qbfeval.org/2008
Kleine-Büning, H., Karpinski, M., Flögel, A.: Resolution for Quantified Boolean Formulas. Information and Computation 117(1), 12–18 (1995)
Giunchiglia, E., Narizzano, M., Tacchella, A.: Backjumping for Quantified Boolean Logic Satisfiability. In: Seventeenth International Joint Conference on Artificial Intelligence (IJCAI 2001). Morgan Kaufmann, San Francisco (2001)
Rish, I., Dechter, R.: Resolution versus search: Two strategies for sat. Journal of Automated Reasoning 24(1/2), 225–275 (2000)
Gottlob, G., Leone, N., Scarcello, F.: A comparison of structural CSP decomposition methods. Artificial Intelligence 124, 243–282 (2000)
Chen, H., Dalmau, V.: From Pebble Games to Tractability: An Ambidextrous Consistency Algorithm for Quantified Constraint Satisfaction. In: Ong, L. (ed.) CSL 2005. LNCS, vol. 3634, pp. 232–247. Springer, Heidelberg (2005)
Gottlob, G., Greco, G., Scarcello, F.: The Complexity of Quantified Constraint Satisfaction Problems under Structural Restrictions. In: IJCAI 2005, Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence, pp. 150–155. Professional Book Center (2005)
Pan, G., Vardi, M.Y.: Fixed-Parameter Hierarchies inside PSPACE. In: 21th IEEE Symposium on Logic in Computer Science (LICS 2006), pp. 27–36. IEEE Computer Society, Los Alamitos (2006)
Pulina, L., Tacchella, A.: Treewidth: A useful marker of empirical hardness in quantified boolean logic encodings. In: Cervesato, I., Veith, H., Voronkov, A. (eds.) LPAR 2008. LNCS (LNAI), vol. 5330, pp. 528–542. Springer, Heidelberg (2008)
Quinlan, J.R.: C4.5: Programs for Machine Learning. Morgan Kaufmann Publishers, San Francisco (1993)
Vapnik, V.: The nature of statistical learning. Springer, New York (1995)
Larrosa, J., Dechter, R.: Boosting Search with Variable Elimination in Constraint Optimization and Constraint Satisfaction Problems. Constraints 8(3), 303–326 (2003)
Cadoli, M., Giovanardi, A., Schaerf, M.: An algorithm to evaluate quantified boolean formulae. In: Proc. of AAAI (1998)
Bodlaender, H.L.: A linear time algorithm for finding tree-decompositions of small treewidth. In: 25th Annual ACM Symposium on Theory of Computing, pp. 226–234 (1993)
Witten, I.H., Frank, E.: Data Mining, 2nd edn. Morgan Kaufmann, San Francisco (2005)
Chang, C.-C., Lin, C.-J.: LIBSVM – A Library for Support Vector Machines (2005), http://www.csie.ntu.edu.tw/~cjlin/libsvm/
Yu, Y., Malik, S.: Verifying the Correctness of Quantified Boolean Formula(QBF) Solvers: Theory and Practice. In: ASP-DAC (2005)
Samulowitz, H., Bacchus, F.: Binary Clause Reasoning in QBF. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 353–367. Springer, Heidelberg (2006)
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Pulina, L., Tacchella, A. (2009). Learning to Integrate Deduction and Search in Reasoning about Quantified Boolean Formulas. In: Ghilardi, S., Sebastiani, R. (eds) Frontiers of Combining Systems. FroCoS 2009. Lecture Notes in Computer Science(), vol 5749. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04222-5_22
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DOI: https://doi.org/10.1007/978-3-642-04222-5_22
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