Abstract
In this paper we investigate the use of preprocessing when solving Quantified Boolean Formulas (QBF). Many different problems can be efficiently encoded as QBF instances, and there has been a great deal of recent interest and progress in solving such instances efficiently. Ideas from QBF have also started to migrate to CSP with the exploration of Quantified CSPs which offer an intriguing increase in representational power over traditional CSPs. Here we show that QBF instances can be simplified using techniques related to those used for preprocessing SAT. These simplifications can be performed in polynomial time, and are used to preprocess the instance prior to invoking a worst case exponential algorithm to solve it. We develop a method for preprocessing QBF instances that is empirically very effective. That is, the preprocessed formulas can be solved significantly faster, even when we account for the time required to perform the preprocessing. Our method significantly improves the efficiency of a range of state-of-the-art QBF solvers. Furthermore, our method is able to completely solve some instances just by preprocessing, including some instances that to our knowledge have never been solved before by any QBF solver.
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References
Aspvall, B., Plass, M., Tarjan, R.: A linear-time algorithms for testing the truth of certain quantified boolean formulas. Information Processing Letters 8, 121–123 (1979)
Bacchus, F.: Enhancing davis putnam with extended binary clause reasoning. In: Eighteenth national conference on Artificial intelligence, pp. 613–619 (2002)
Bacchus, F., Winter, J.: Effective preprocessing with hyper-resolution and equality reduction. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 341–355. Springer, Heidelberg (2004)
Benedetti, M.: Skizzo: a QBF decision procedure based on propositional skolemization and symbolic reasoning. Technical Report TR04-11-03 (2004)
Benedetti, M.: Evaluating QBFs via Symbolic Skolemization. In: Baader, F., Voronkov, A. (eds.) LPAR 2004. LNCS, vol. 3452, pp. 285–300. Springer, Heidelberg (2005)
Benedetti, M.: Extracting Certificates from Quantified Boolean Formulas. In: Proc. of 9th International Joint Conference on Artificial Intelligence (IJCAI 2005) (2005)
Benedetti, M.: Quantifier Trees for QBFs. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 378–385. Springer, Heidelberg (2005)
Biere, A.: Resolve and expand. In: Hoos, H.H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 238–246. Springer, Heidelberg (2005)
Büning, H.K., Karpinski, M., Flügel, A.: Resolution for quantified boolean formulas. Inf. Comput. 117(1), 12–18 (1995)
Eén, N., Biere, A.: Effective Preprocessing in SAT Through Variable and Clause Elimination. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 61–75. Springer, Heidelberg (2005)
Egly, U., Eiter, T., Tompits, H., Woltran, S.: Solving advanced reasoning tasks using quantified boolean formulas. In: AAAI/IAAI, pp. 417–422 (2000)
Gent, I.P., Nightingale, P., Stergiou, K.: Qcsp-solve: A solver for quantified constraint satisfaction problems. In: Proceedings of the International Joint Conference on Artifical Intelligence (IJCAI), pp. 138–143 (2005)
Giunchiglia, E., Narizzano, M., Tacchella, A.: Quantified Boolean Formulas satisfiability library (QBFLIB) (2001), http://www.qbflib.org/
Giunchiglia, E., Narizzano, M., Tacchella, A.: QUBE: A system for deciding quantified boolean formulas satisfiability. In: Goré, R.P., Leitsch, A., Nipkow, T. (eds.) IJCAR 2001. LNCS (LNAI), vol. 2083, pp. 364–369. Springer, Heidelberg (2001)
Narizzano, M., Tacchella, A.: QBF evaluation (2005), http://www.qbflib.org/qbfeval/2005
Rintanen, J.: Constructing conditional plans by a theorem-prover. Journal of Artificial Intelligence Research 10, 323–352 (1999)
Samulowitz, H., Bacchus, F.: Using SAT in QBF. In: Principles and Practice of Constraint Programming, pp. 578–592. Springer, New York (2005), Available at: http://www.cs.toronto.edu/~fbacchus/sat.html
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)
Samulowitz, H., Davies, J., Bacchus, F.: QBF Preprocessor Prequel (2006), Available at: http://www.cs.toronto.edu/~fbacchus/sat.html
Stergiou, K.: Repair-based methods for quantified csps. In: Principles and Practice of Constraint Programming, pp. 652–666 (2005)
Zhang, L., Malik, S.: Towards symmetric treatment of conflicts and satisfaction in quantified boolean satisfiability solver. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 185–199. Springer, Heidelberg (2002)
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Samulowitz, H., Davies, J., Bacchus, F. (2006). Preprocessing QBF. In: Benhamou, F. (eds) Principles and Practice of Constraint Programming - CP 2006. CP 2006. Lecture Notes in Computer Science, vol 4204. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11889205_37
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DOI: https://doi.org/10.1007/11889205_37
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-46267-5
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