Abstract
Quantified Boolean Formula (QBF) solvers that utilize non-CNF representations are able to reason dually about conflicts and solutions by accessing structural information contained in the non-CNF representation. This structure is not as easily accessed from a CNF representation, hence CNF based solvers are not able to perform the same kind of reasoning. Recent work has shown how this additional structure can be extracted from a non-CNF representation and encoded in a form that can be fed directly to a CNF-based QBF solver without requiring major changes to the solver’s architecture. This combines the benefits of specialized CNF-based techniques and dual reasoning.
This approach, however, only works if one has access to a non-CNF representation of the problem, which is often not the case in practice. In this paper we address this problem and show how working only with the CNF encoding we can successfully extract partial structural information in a form that can be soundly given to a CNF-based solver. This yields performance benefits even though the information extracted is incomplete, and allows CNF-based solvers to obtain some of the benefits of dual reasoning in a more general context. To further increase the applicability of our approach we develop a new method for extracting structure from a CNF generated with the commonly used Plaisted-Greenbaum transformation.
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References
Biere, A., Lonsing, F., Seidl, M.: Blocked clause elimination for QBF. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS, vol. 6803, pp. 101–115. Springer, Heidelberg (2011)
Buning, H.A.K., Lettmann, T.: Propositional logic: deduction and algorithms. Cambridge Tracts in Theoretical Computer Science Series. Cambridge University Press (1999)
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)
Fu, Z., Malik, S.: Extracting logic circuit structure from conjunctive normal form descriptions. In: Proceedings of the 20th International Conference on VLSI Design held jointly with 6th International Conference: Embedded Systems, VLSID 2007, pp. 37–42. IEEE Computer Society, Washington, DC (2007)
Van Gelder, A.: Contributions to the theory of practical quantified boolean formula solving. In: Milano, M. (ed.) CP 2012. LNCS, vol. 7514, pp. 647–663. Springer, Heidelberg (2012)
Giunchiglia, E., Narizzano, M., Tacchella, A.: Quantified Boolean Formulas satisfiability library (QBFLIB) (2001), http://www.qbflib.org
Giunchiglia, E., Marin, P., Narizzano, M.: sQueezeBF: An effective preprocessor for QBFs based on equivalence reasoning. In: Strichman, O., Szeider, S. (eds.) SAT 2010. LNCS, vol. 6175, pp. 85–98. Springer, Heidelberg (2010)
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, p. 364. Springer, Heidelberg (2001)
Giunchiglia, E., Narizzano, M., Tacchella, A.: Clause/term resolution and learning in the evaluation of quantified boolean formulas. Journal of Artificial Intelligence Research (JAIR) 26, 371–416 (2006)
Goultiaeva, A., Bacchus, F.: Exploiting QBF duality on a circuit representation. In: Twenty-Fourth AAAI Conference on Artificial Intelligence (2010)
Goultiaeva, A., Seidl, M., Biere, A.: Bridging the gap between dual propagation and CNF-based QBF solving. In: Proceedings of the Conference on Design, Automation and Test in Europe (2013)
Grégoire, É., Ostrowski, R., Mazure, B., Saïs, L.: Automatic extraction of functional dependencies. In: Hoos, H.H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 122–132. Springer, Heidelberg (2005)
Klieber, W., Sapra, S., Gao, S., Clarke, E.: A non-prenex, non-clausal QBF solver with game-state learning. In: Strichman, O., Szeider, S. (eds.) SAT 2010. LNCS, vol. 6175, pp. 128–142. Springer, Heidelberg (2010)
Lonsing, F., Biere, A.: DepQBF: A dependency-aware QBF solver. Journal on Satisfiability, Boolean Modeling and Computation 7(2-3), 71–76 (2010)
Ostrowski, R., Grégoire, É., Mazure, B., Saïs, L.: Recovering and exploiting structural knowledge from CNF formulas. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 185–199. Springer, Heidelberg (2002)
Pigorsch, F., Scholl, C.: Exploiting structure in an AIG based QBF solver. In: Proceedings of the Conference on Design, Automation and Test in Europe, DATE 2009, pp. 1596–1601. European Design and Automation Association, Leuven (2009)
Plaisted, D.A., Greenbaum, S.: A structure-preserving clause form translation. Journal of Symbolic Computation 2(3), 293–304 (1986)
Samer, M., Szeider, S.: Backdoor sets of quantified boolean formulas. Journal of Automated Reasoning (JAR) 42(1), 77–97 (2009)
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 (1983)
Zhang, L.: Solving QBF with combined conjunctive and disjunctive normal form. In: Twenty-First Conference on Artificial Intelligence (2006)
Zhang, L., Malik, S.: Towards a symmetric treatment of satisfaction and conflicts in quantified boolean formula evaluation. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 200–215. Springer, Heidelberg (2002)
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Goultiaeva, A., Bacchus, F. (2013). Recovering and Utilizing Partial Duality in QBF. In: Järvisalo, M., Van Gelder, A. (eds) Theory and Applications of Satisfiability Testing – SAT 2013. SAT 2013. Lecture Notes in Computer Science, vol 7962. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39071-5_8
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