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On Unordered BDDs and Quantified Boolean Formulas

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Progress in Artificial Intelligence (EPIA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11805))

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Abstract

This paper proposes to study the synthesis of unordered binary decision diagrams (BDDs) using solvers for Quantified Boolean Formulas (QBF). The synthesis of a BDD falls naturally in the realm of quantified formulas as we are typically looking for a BDD satisfying a certain specification. This means that we ask whether there exists a BDD such that for all inputs the specification is satisfied. We show that this query can be encoded naturally into QBF and experimentally evaluate these queries for the minority function.

The short paper should be seen as a challenge for further research on QBF solving.

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Notes

  1. 1.

    For existing lower bounds for BDD see a survey by Razborov [14].

  2. 2.

    The majority function is obtained by swapping the semantics of 0 and 1, which is easy to do in BDDs.

  3. 3.

    Pudlák gives a \(\varOmega (n\lg n)\) lower-bound for this function [13].

References

  1. Bahar, R.I., et al.: Algebraic decision diagrams and their applications. In: Proceedings International Conference on Computer-Aided Design, pp. 188–191 (1993)

    Google Scholar 

  2. Bryant, R.E.: Graph-based algorithms for Boolean function manipulation. IEEE Trans. Comput. 100(8), 677–691 (1986)

    Article  Google Scholar 

  3. Faymonville, P., Finkbeiner, B., Rabe, M.N., Tentrup, L.: Encodings of bounded synthesis. In: Legay, A., Margaria, T. (eds.) TACAS 2017. LNCS, vol. 10205, pp. 354–370. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-662-54577-5_20

    Chapter  Google Scholar 

  4. Gascón, A., Subramanyan, P., Dutertre, B., Tiwari, A., Jovanovic, D., Malik, S.: Template-based circuit understanding. In: Formal Methods in Computer-Aided Design (FMCAD) (2014)

    Google Scholar 

  5. Janota, M.: Towards generalization in QBF solving via machine learning. In: AAAI Conference on Artificial Intelligence (2018)

    Google Scholar 

  6. Janota, M., Klieber, W., Marques-Silva, J., Clarke, E.: Solving QBF with counterexample guided refinement. Artif. Intell. 234, 1–25 (2016)

    Article  MathSciNet  Google Scholar 

  7. Jo, S., Matsumoto, T., Fujita, M.: SAT-based automatic rectification and debugging of combinational circuits with LUT insertions. In: Asian Test Symposium, pp. 19–24 (2012)

    Google Scholar 

  8. Jordan, C., Klieber, W., Seidl, M.: Non-CNF QBF solving with QCIR. In: Proceedings of BNP (Workshop) (2016)

    Google Scholar 

  9. 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)

    Google Scholar 

  10. Maksimovic, D., Le, B., Veneris, A.G.: Multiple clock domain synchronization in a QBF-based verification environment. In: International Conference on Computer-aided Design (ICCAD) (2014)

    Google Scholar 

  11. Narodytska, N., Legg, A., Bacchus, F., Ryzhyk, L., Walker, A.: Solving games without controllable predecessor. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 533–540. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-08867-9_35

    Chapter  Google Scholar 

  12. Peitl, T., Slivovsky, F., Szeider, S.: Dependency learning for QBF. In: Theory and Applications of Satisfiability Testing (SAT), pp. 298–313 (2017)

    Chapter  Google Scholar 

  13. Pudlák, P.: A lower bound on complexity of branching programs. In: Chytil, M.P., Koubek, V. (eds.) MFCS 1984. LNCS, vol. 176, pp. 480–489. Springer, Heidelberg (1984). https://doi.org/10.1007/BFb0030331

    Chapter  Google Scholar 

  14. Razborov, A.A.: Lower bounds for deterministic and nondeterministic branching programs. In: Budach, L. (ed.) FCT 1991. LNCS, vol. 529, pp. 47–60. Springer, Heidelberg (1991). https://doi.org/10.1007/3-540-54458-5_49

    Chapter  Google Scholar 

  15. Sinz, C.: Towards an optimal CNF encoding of Boolean cardinality constraints. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 827–831. Springer, Heidelberg (2005). https://doi.org/10.1007/11564751_73

    Chapter  MATH  Google Scholar 

  16. 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

    Chapter  Google Scholar 

  17. Tveretina, O., Sinz, C., Zantema, H.: An exponential lower bound on OBDD refutations for pigeonhole formulas. In: Athens Colloquium on Algorithms and Complexity, ACAC, pp. 13–21 (2009). https://doi.org/10.4204/EPTCS.4.2

    Article  Google Scholar 

  18. Umans, C., Villa, T., Sangiovanni-Vincentelli, A.L.: Complexity of two-level logic minimization. IEEE Trans. CAD Integr. Circ. Syst. 25(7), 1230–1246 (2006). https://doi.org/10.1109/TCAD.2005.855944

    Article  Google Scholar 

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Acknowledgments

This work was supported by national funds through FCT - Fundação para a Ciência e a Tecnologia with reference UID/CEC/50021/2019 and the project INFOCOS with reference PTDC/CCI-COM/32378/2017.

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Authors and Affiliations

  1. IST/INESC-ID, Lisbon, Portugal

    Mikoláš Janota

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  1. Mikoláš Janota
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Correspondence to Mikoláš Janota .

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Editors and Affiliations

  1. INESC-TEC, University of Trás-os-Montes and Alto Douro, Vila Real, Portugal

    Paulo Moura Oliveira

  2. University of Minho, Braga, Portugal

    Paulo Novais

  3. LIACC/UP, University of Porto, Porto, Portugal

    Luís Paulo Reis

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Janota, M. (2019). On Unordered BDDs and Quantified Boolean Formulas. In: Moura Oliveira, P., Novais, P., Reis, L. (eds) Progress in Artificial Intelligence. EPIA 2019. Lecture Notes in Computer Science(), vol 11805. Springer, Cham. https://doi.org/10.1007/978-3-030-30244-3_41

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  • DOI: https://doi.org/10.1007/978-3-030-30244-3_41

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-30243-6

  • Online ISBN: 978-3-030-30244-3

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