Skip to main content
SpringerLink
Log in

DQBDD: An Efficient BDD-Based DQBF Solver

  • Conference paper
  • First Online:
Theory and Applications of Satisfiability Testing – SAT 2021 (SAT 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12831))

Abstract

This paper introduces a new DQBF solver called DQBDD, which is based on quantifier localization, quantifier elimination, and translation of formulas to binary decision diagrams (BDDs). In 2020, DQBDD participated for the first time in the Competitive Evaluation of QBF Solvers (QBFEVAL’20) and won the DQBF Solvers Track by a large margin.

This work has been supported by the Czech Ministry of Education, Youth and Sports project LL1908 of the ERC.CZ programme, and the FIT BUT internal project FIT-S-20-6427.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    This is the prenex cleansed QCIR format [17] extended with quantifiers depend(v, v1, ..., vn) representing existential variable v with dependencies v1, ..., vn.

  2. 2.

    We use the version distributed with HQS downloaded on March 18, 2021, from http://abs.informatik.uni-freiburg.de/src/projectfiles/21/HQS.zip.

  3. 3.

    Called with “--qbf_mode true --inst_out_proof false --res_out_proof false”.

  4. 4.

    Downloaded from http://abs.informatik.uni-freiburg.de/src/projectfiles/21/HQS.zip on March 18, 2021.

References

  1. Balabanov, V., Roland Jiang, J.-H.: Reducing satisfiability and reachability to DQBF, 2015. Talk given at International Workshop on Quantified Boolean Formulas - QBF 2015 (2015)

    Google Scholar 

  2. Beyer, D., Löwe, S., Wendler, P.: Reliable benchmarking: requirements and solutions. Int. J. Softw. Tools Technol. Transf. 21(1), 1–29 (2017). https://doi.org/10.1007/s10009-017-0469-y

    Article  Google Scholar 

  3. Biere, A.: Picosat essentials. J. Satisfiability, Boolean Model. Comput. (JSAT). 4, 75–97 (2008)

    Google Scholar 

  4. Bloem, R., Könighofer, R., Seidl, M.: SAT-based synthesis methods for safety specs. In: Verification, Model Checking, and Abstract Interpretation, pp. 1–20 (2014)

    Google Scholar 

  5. Bryant, R.E.: Graph-based algorithms for Boolean function manipulation. IEEE Trans. Comput. 35(8), 677–691 (1986)

    Article  Google Scholar 

  6. Bryant, R.E.: On the complexity of VLSI implementations and graph representations of Boolean functions with application to integer multiplication. IEEE Trans. Comput. 40(2), 205–213 (1991)

    Article  MathSciNet  Google Scholar 

  7. Finkbeiner, B., Tentrup, L.: Fast DQBF refutation. In: Sinz, C., Egly, U. (eds.) SAT 2014. LNCS, vol. 8561, pp. 243–251. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_19

    Chapter  Google Scholar 

  8. Fröhlich, A., Kovásznai, G., Biere, A.: A DPLL algorithm for solving DQBF. In: Pragmatics of SAT (PoS 2012, aff. to SAT 2012) (2012)

    Google Scholar 

  9. Fröhlich, A., Kovásznai, G., Biere, A., Veith, H.: iDQ: instantiation-based DQBF solving. In: Le Berre, D. (ed.) POS-14. Fifth Pragmatics of SAT Workshop, A Workshop of the SAT 2014 Conference, part of FLoC 2014 during the Vienna Summer of Logic, 13 July, 2014, Vienna, Austria, volume 27 of EPiC Series in Computing, pp. 103–116. EasyChair (2014)

    Google Scholar 

  10. Ge-Ernst, A., Scholl, C., Síč, J., Wimmer, R.: Solving dependency quantified Boolean formulas using quantifier localization. Theoretical Computer Science (2021). Submitted. Preprint available as arXiv:1905.04755v2

  11. Ge-Ernst, A., Scholl, C., Wimmer, R.: Localizing quantifiers for DQBF. In: Barrett, C.W., Yang, J. (eds.) 2019 Formal Methods in Computer Aided Design, FMCAD 2019, San Jose, CA, USA, 22–25 October, 2019, pp. 184–192. IEEE (2019)

    Google Scholar 

  12. Gitina, K., Reimer, S., Sauer, M., Wimmer, R., Scholl, C., Becker, B.: Equivalence checking of partial designs using dependency quantified Boolean formulae. In: 2013 IEEE 31st International Conference on Computer Design, ICCD 2013, Asheville, NC, USA, 6–9 October, 2013, pp. 396–403. IEEE Computer Society (2013)

    Google Scholar 

  13. Gitina, K., Wimmer, R., Reimer, S., Sauer, M., Scholl, C., Becker, B.:. Solving DQBF through quantifier elimination. In: Nebel, W., Atienza, D. (eds.) Proceedings of the 2015 Design, Automation and Test in Europe Conference and Exhibition, DATE 2015, Grenoble, France, 9–13 March, 2015, pp. 1617–1622. ACM (2015)

    Google Scholar 

  14. Harrison, J.: Handbook of Practical Logic and Automated Reasoning. Cambridge University Press (2009)

    Google Scholar 

  15. Jonáš, M., Strejček, J.: Solving quantified bit-vector formulas using binary decision diagrams. In: Creignou, N., Le Berre, D. (eds.) SAT 2016. LNCS, vol. 9710, pp. 267–283. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_17

    Chapter  Google Scholar 

  16. Jonáš, M., Strejček, J.: Q3B: an efficient BDD-based SMT solver for quantified bit-vectors. In: Dillig, I., Tasiran, S. (eds.) CAV 2019. LNCS, vol. 11562, pp. 64–73. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-25543-5_4

    Chapter  Google Scholar 

  17. Jordan, C., Klieber, W., Seidl, M.: Non-CNF QBF solving with QCIR. Beyond NP. In: AAAI Workshop (2016)

    Google Scholar 

  18. Korovin, K.: iProver – an instantiation-based theorem prover for first-order logic (system description). In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 292–298. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-71070-7_24

    Chapter  Google Scholar 

  19. Kovásznai, G.: What is the state-of-the-art in DQBF solving. In: MaCS-16. Joint Conference on Mathematics and Computer Science (2016)

    Google Scholar 

  20. Mishchenko, A., Chatterjee, S., Brayton, R.: FRAIGs: a unifying representation for logic synthesis and verification. EECS Dept., UC Berkeley, Technical report (2005)

    Google Scholar 

  21. Olivo, O., Emerson, E.A.: A more efficient BDD-based QBF solver. In: Lee, J. (ed.) CP 2011. LNCS, vol. 6876, pp. 675–690. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-23786-7_51

    Chapter  Google Scholar 

  22. Peterson, G., Reif, J., Azhar, S.: Lower bounds for multiplayer noncooperative games of incomplete information. Comput. Math. Appl. 41(7), 957–992 (2001)

    Article  MathSciNet  Google Scholar 

  23. Pulina, L., Seidl, M.: QBF evaluation 2018 (2018)

    Google Scholar 

  24. Pulina, L., Seidl, M., Shukla, A.: QBF evaluation 2019 (2019)

    Google Scholar 

  25. Pulina, L., Seidl, M., Shukla, A.: QBF evaluation 2020 (2020)

    Google Scholar 

  26. Rudell, R.: Dynamic variable ordering for ordered binary decision diagrams. In: Proceedings of 1993 International Conference on Computer Aided Design (ICCAD), pp. 42–47 (1993)

    Google Scholar 

  27. Scholl, C., Becker, B.: Checking equivalence for partial implementations. In: Proceedings of the 38th Design Automation Conference (IEEE Cat. No.01CH37232), pp. 238–243 (2001)

    Google Scholar 

  28. Scholl, C., Wimmer, R.: Dependency quantified Boolean formulas: an overview of solution methods and applications. In: Beyersdorff, O., Wintersteiger, C.M. (eds.) SAT 2018. LNCS, vol. 10929, pp. 3–16. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-94144-8_1

    Chapter  Google Scholar 

  29. Schubert, T., Lewis, M., Becker, B.: Antom - solver description (2010)

    Google Scholar 

  30. Slivovsky, F.: Interpolation-based semantic gate extraction and its applications to QBF preprocessing. In: Lahiri, S.K., Wang, C. (eds.) CAV 2020. LNCS, vol. 12224, pp. 508–528. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-53288-8_24

    Chapter  Google Scholar 

  31. Somenzi, F.: CUDD: CU decision diagram package release 3.0.0 (2015)

    Google Scholar 

  32. Síč, J.: Satisfiability of DQBF using binary decision diagrams. Master’s thesis, Masaryk University, Faculty of Informatics (2020)

    Google Scholar 

  33. Tentrup, L., Rabe, M.N.: Clausal abstraction for DQBF. In: Janota, M., Lynce, I. (eds.) SAT 2019. LNCS, vol. 11628, pp. 388–405. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-24258-9_27

    Chapter  Google Scholar 

  34. Wimmer, R., Karrenbauer, A., Becker, R., Scholl, C., Becker, B.: From DQBF to QBF by dependency elimination. In: Gaspers, S., Walsh, T. (eds.) SAT 2017. LNCS, vol. 10491, pp. 326–343. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66263-3_21

    Chapter  Google Scholar 

  35. Wimmer, R., Scholl, C., Becker, B.: The (D)QBF preprocessor HQSpre - underlying theory and its implementation. J. Satisfiability Boolean Model. Comput. 11, 3–52 (2019)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Brno University of Technology, FIT, Brno, Czech Republic

    Juraj Síč

  2. Masaryk University, Brno, Czech Republic

    Jan Strejček

Authors
  1. Juraj Síč
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jan Strejček
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Juraj Síč .

Editor information

Editors and Affiliations

  1. Laboratoire MIS, University of Picardie Jules Verne, Amiens, France

    Chu-Min Li

  2. IIIA-CSIC, Spanish National Research Council (CSIC), Bellaterra, Barcelona, Spain

    Felip Manyà

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Síč, J., Strejček, J. (2021). DQBDD: An Efficient BDD-Based DQBF Solver. In: Li, CM., Manyà, F. (eds) Theory and Applications of Satisfiability Testing – SAT 2021. SAT 2021. Lecture Notes in Computer Science(), vol 12831. Springer, Cham. https://doi.org/10.1007/978-3-030-80223-3_36

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-80223-3_36

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-80222-6

  • Online ISBN: 978-3-030-80223-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation