Abstract
State-of-the-art solvers for Quantified Boolean Formulas (QBF) have employed many techniques from the field of Boolean Satisfiability (SAT) including the use of Conjunctive Normal Form (CNF) in representing the QBF formula. Although CNF has worked well for SAT solvers, recent work has pointed out some inherent problems with using CNF in QBF solvers.
In this paper, we describe a QBF solver, called CirQit (Cir-Q-it) that utilizes a circuit representation rather than CNF. The solver can exploit its circuit representation to avoid many of the problems of CNF. For example, we show how this approach generalizes some previously proposed techniques for overcoming the disadvantages of CNF for QBF solvers. We also show how important techniques like clause and cube learning can be made to work with a circuit representation. Finally, we empirically compare the resulting solver against other state-of-the-art QBF solvers, demonstrating that our approach can often outperform these solvers.
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References
Rintanen, J.: Asymptotically optimal encodings of conformant planning in QBF. In: Proceedings of the AAAI National Conference (AAAI), pp. 1045–1050 (2007)
Egly, U., Eiter, T., Tompits, H., Woltran, S.: Solving advanced reasoning tasks using quantified boolean formulas. In: Proceedings of the AAAI National Conference (AAAI), pp. 417–422. AAAI Press, Menlo Park (2000)
Mangassarian, H., Veneris, A.G., Safarpour, S., Benedetti, M., Smith, D.: A performance-driven QBF-based iterative logic array representation with applications to verification, debug and test. In: International Conference on Computer-Aided Design (ICCAD), pp. 240–245 (2007)
Davis, M., Putnam, H.: A computing procedure for quantification theory. Journal of the ACM 7, 201–215 (1960)
Biere, A.: Resolve and expand. In: Hoos, H.H., Mitchell, D.G. (eds.) SAT 2004, vol. 3542, pp. 59–70. Springer, Heidelberg (2005)
Benedetti, M.: sKizzo: a QBF decision procedure based on propositional skolemization and symbolic reasoning. Technical Report TR04-11-03 (2004)
Thiffault, C., Bacchus, F., Walsh, T.: Solving non-clausal formulas with DPLL search. In: Proceedings of the International Conference on Theory and Applications of Satisfiability Testing (SAT) (2004)
Wu, C.A., Lin, T.H., Lee, C.C., Huang, C.Y.: QuteSAT: a robust circuit-based SAT solver for complex circuit structure. In: Design, Automation and Test in Europe Conference and Exposition (DATE), pp. 1313–1318 (2007)
Sabharwal, A., Ansótegui, C., Gomes, C.P., Hart, J.W., Selman, B.: QBF modeling: Exploiting player symmetry for simplicity and efficiency. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 382–395. Springer, Heidelberg (2006)
Zhang, L.: Solving QBF with combined conjunctive and disjunctive normal form. In: Proceedings of the AAAI National Conference (AAAI) (2006)
Tseitin, G.: On the complexity of proofs in poropositional logics. In: Siekmann, J., Wrightson, G. (eds.) Automation of Reasoning: Classical Papers in Computational Logic 1967–1970, vol. 2. Springer, Heidelberg (1983); Originally published (1970)
Zhang, L., Malik, S.: Towards a symmetric treatment of satisfaction and conflicts in quantified boolean formula evaluation. In: Van Hentenryck, P. (ed.) CP 2002, vol. 2470, pp. 200–215. Springer, Heidelberg (2002)
Tang, D., Malik, S.: Solving quantified boolean formulas with circuit observability don’t cares. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 368–381. Springer, Heidelberg (2006)
Benedetti, M., Lallouet, A., Vautard, J.: QCSP made practical by virtue of restricted quantification. In: Veloso, M.M. (ed.) Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI), pp. 38–43 (2007)
Egly, U., Seidl, M., Woltran, S.: A solver for QBFs in negation normal form. Constraints 14(1), 38–79 (2009)
Giunchiglia, E., Narizzano, M., Tacchella, A.: Quantified Boolean Formulas satisfiability library (QBFLIB) (2001), www.qbflib.org
Stéphan, I.: Boolean propagation based on literals for quantified boolean formulae. In: 17th European Conference on Artificial Intelligence (2006)
Benedetti, M.: skizzo: A suite to evaluate and certify QBFs. In: Nieuwenhuis, R. (ed.) CADE 2005. LNCS, vol. 3632, pp. 369–376. Springer, Heidelberg (2005)
Samulowitz, H., Bacchus, F.: Dynamically partitioning for solving QBF. In: Marques-Silva, J., Sakallah, K.A. (eds.) SAT 2007. LNCS, vol. 4501, pp. 215–229. Springer, Heidelberg (2007)
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, vol. 2083, pp. 364–369. Springer, Heidelberg (2001)
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Goultiaeva, A., Iverson, V., Bacchus, F. (2009). Beyond CNF: A Circuit-Based QBF Solver. 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_38
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DOI: https://doi.org/10.1007/978-3-642-02777-2_38
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