Abstract
This paper describes the algorithm implemented in the QBF solver CQESTO, which has placed second in the non-CNF track of the last year’s QBF competition. The algorithm is inspired by the CNF-based solver QESTO. Just as QESTO, CQESTO invokes a SAT solver in a black-box fashion. However, it directly operates on the circuit representation of the formula. The paper analyzes the individual operations that the solver performs.
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Notes
- 1.
The implementation enables jumping across multiple levels by backtracking to the maximum level of variables in the core belonging to \(Q_i\).
- 2.
This was also done similarly in Z3 when implementing [4].
References
Ansótegui, C., Gomes, C.P., Selman, B.: The Achilles’ heel of QBF. In: National Conference on Artificial Intelligence and the Seventeenth Innovative Applications of Artificial Intelligence Conference (AAAI), pp. 275–281 (2005)
Balabanov, V., Jiang, J.-H.R., Scholl, C., Mishchenko, A., Brayton, R.K.: 2QBF: challenges and solutions. In: Creignou, N., Le Berre, D. (eds.) SAT 2016. LNCS, vol. 9710, pp. 453–469. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_28
Benedetti, M., Mangassarian, H.: QBF-based formal verification: experience and perspectives. J. Satisfiability Bool. Model. Comput. (JSAT) 5(1–4), 133–191 (2008)
Bjørner, N., Janota, M.: Playing with quantified satisfaction. In: International Conferences on Logic for Programming LPAR-20, Short Presentations, vol. 35, pp. 15–27. EasyChair (2015)
CQESTO website. http://sat.inesc-id.pt/~mikolas/sw/cqesto/res.html
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). https://doi.org/10.1007/978-3-540-24605-3_37
Farzan, A., Kincaid, Z.: Strategy synthesis for linear arithmetic games. In: Proceedings of the ACM on Programming Languages 2 (POPL), pp. 61:1–61:30, December 2017. https://doi.org/10.1145/3158149
Goultiaeva, A., Seidl, M., Biere, A.: Bridging the gap between dual propagation and CNF-based QBF solving. In: Design, Automation & Test in Europe (DATE), pp. 811–814 (2013)
Goultiaeva, A., Van Gelder, A., Bacchus, F.: A uniform approach for generating proofs and strategies for both true and false QBF formulas. In: International Joint Conference on Artificial Intelligence (IJCAI), pp. 546–553 (2011)
Janota, M., Klieber, W., Marques-Silva, J., Clarke, E.: Solving QBF with counterexample guided refinement. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 114–128. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31612-8_10
Janota, M.: Towards generalization in QBF solving via machine learning. In: AAAI Conference on Artificial Intelligence (2018)
Janota, M., Klieber, W., Marques-Silva, J., Clarke, E.: Solving QBF with counterexample guided refinement. Artif. Intell. 234, 1–25 (2016)
Janota, M., Marques-Silva, J.: Abstraction-based algorithm for 2QBF. In: Sakallah, K.A., Simon, L. (eds.) SAT 2011. LNCS, vol. 6695, pp. 230–244. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-21581-0_19
Janota, M., Marques-Silva, J.: Solving QBF by clause selection. In: International Joint Conference on Artificial Intelligence (IJCAI) (2015)
Janota, M., Marques-Silva, J.: An Achilles’ heel of term-resolution. In: Conference on Artificial Intelligence (EPIA), pp. 670–680 (2017)
Jordan, C., Klieber, W., Seidl, M.: Non-CNF QBF solving with QCIR. In: Proceedings of BNP (Workshop) (2016)
Kleine Büning, H., Bubeck, U.: Theory of quantified Boolean formulas. In: Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.) Handbook of Satisfiability. Frontiers in Artificial Intelligence and Applications, vol. 185, pp. 735–760. IOS Press (2009)
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). https://doi.org/10.1007/978-3-642-14186-7_12
Manna, Z., Waldinger, R.: The Logical Basis for Computer Programming, vol. 2. Addison-Wesley, Reading (1985)
Marques Silva, J.P., Sakallah, K.A.: GRASP: a search algorithm for propositional satisfiability. IEEE Trans. Comput. 48(5), 506–521 (1999)
Peitl, T., Slivovsky, F., Szeider, S.: Dependency learning for QBF. In: Gaspers, S., Walsh, T. (eds.) SAT 2017. LNCS, vol. 10491, pp. 298–313. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66263-3_19
QBF Eval 2017 (2017). http://www.qbflib.org/event_page.php?year=2017
Rabe, M.N., Tentrup, L.: CAQE: a certifying QBF solver. In: Formal Methods in Computer-Aided Design, FMCAD, pp. 136–143 (2015)
Reynolds, A., King, T., Kuncak, V.: Solving quantified linear arithmetic by counterexample-guided instantiation. Formal Methods Syst. Des. 51(3), 500–532 (2017). https://doi.org/10.1007/s10703-017-0290-y
Tentrup, L.: Non-prenex QBF solving using abstraction. In: Creignou, N., Le Berre, D. (eds.) SAT 2016. LNCS, vol. 9710, pp. 393–401. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_24
Tseitin, G.S.: On the complexity of derivations in the propositional calculus. In: Slisenko, A.O. (ed.) Studies in Constructive Mathematics and Mathematical Logic Part II (1968)
Tu, K.-H., Hsu, T.-C., Jiang, J.-H.R.: QELL: QBF reasoning with extended clause learning and levelized SAT solving. In: Heule, M., Weaver, S. (eds.) SAT 2015. LNCS, vol. 9340, pp. 343–359. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24318-4_25
Zhang, L.: Solving QBF by combining conjunctive and disjunctive normal forms. In: National Conference on Artificial Intelligence and the Eighteenth Innovative Applications of Artificial Intelligence Conference (AAAI) (2006)
Zhang, L., Malik, S.: Conflict driven learning in a quantified Boolean satisfiability solver. In: International Conference On Computer Aided Design (ICCAD), pp. 442–449 (2002)
Acknowledgments
This work was supported by national funds through Fundação para a Ciência e a Tecnologia (FCT) with reference UID/CEC/50021/2013. The author would like to thank Nikolaj Bjørner and João Marques-Silva for the helpful discussions on the topic.
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Janota, M. (2018). Circuit-Based Search Space Pruning in QBF. In: Beyersdorff, O., Wintersteiger, C. (eds) Theory and Applications of Satisfiability Testing – SAT 2018. SAT 2018. Lecture Notes in Computer Science(), vol 10929. Springer, Cham. https://doi.org/10.1007/978-3-319-94144-8_12
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