Skip to main content
SpringerLink
Log in

A Resolution-Style Proof System for DQBF

  • Conference paper
  • First Online:
Book cover Theory and Applications of Satisfiability Testing – SAT 2017 (SAT 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10491))

Abstract

This paper presents a sound and complete proof system for Dependency Quantified Boolean Formulas (DQBF) using resolution, universal reduction, and a new proof rule that we call fork extension. This opens new avenues for the development of efficient algorithms for DQBF.

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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.

    The concept is loosely connected to information forks in reactive synthesis of distributed systems [10].

References

  1. Balabanov, V., Chiang, H.J.K., Jiang, J.H.R.: Henkin quantifiers and Boolean formulae: a certification perspective of DQBF. Theor. Comput. Sci. 523, 86–100 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  2. Beyersdorff, O., Chew, L., Schmidt, R.A., Suda, M.: Lifting QBF resolution calculi to DQBF. In: Creignou, N., Le Berre, D. (eds.) SAT 2016. LNCS, vol. 9710, pp. 490–499. Springer, Cham (2016). doi:10.1007/978-3-319-40970-2_30

    Google Scholar 

  3. Biere, A.: Resolve and expand. In: Hoos, H.H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 59–70. Springer, Heidelberg (2005). doi:10.1007/11527695_5

    Chapter  Google Scholar 

  4. Biere, A., Lonsing, F., Seidl, M.: Blocked clause elimination for QBF. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS (LNAI), vol. 6803, pp. 101–115. Springer, Heidelberg (2011). doi:10.1007/978-3-642-22438-6_10

    Chapter  Google Scholar 

  5. Bruttomesso, R., Cimatti, A., Franzén, A., Griggio, A., Santuari, A., Sebastiani, R.: To Ackermann-ize or not to Ackermann-ize? On efficiently handling uninterpreted function symbols in \(\mathit{SMT}(\cal{EUF} \cup \cal{T})\). In: Hermann, M., Voronkov, A. (eds.) LPAR 2006. LNCS, vol. 4246, pp. 557–571. Springer, Heidelberg (2006). doi:10.1007/11916277_38

    Chapter  Google Scholar 

  6. Buning, H.K., Karpinski, M., Flogel, A.: Resolution for quantified boolean formulas. Inf. Comput. 117(1), 12–18 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  7. Davis, M., Putnam, H.: A computing procedure for quantification theory. J. ACM (JACM) 7(3), 201–215 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  8. Faymonville, P., Finkbeiner, B., Rabe, M.N., Tentrup, L.: 3 encodings of reactive synthesis. In: Proceedings of QUANTIFY, pp. 20–22 (2015)

    Google Scholar 

  9. 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). doi:10.1007/978-3-662-54577-5_20

    Chapter  Google Scholar 

  10. Finkbeiner, B., Schewe, S.: Uniform distributed synthesis. In: Proceedings of LICS, Washington, DC, USA, pp. 321–330. IEEE Computer Society (2005)

    Google Scholar 

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

    Google Scholar 

  12. Fröhlich, A., Kovásznai, G., Biere, A.: A DPLL algorithm for solving DQBF. In: Proceedings of Pragmatics of SAT 2012 (2012)

    Google Scholar 

  13. Fröhlich, A., Kovásznai, G., Biere, A., Veith, H.: iDQ: instantiation-based DQBF solving. In: Proceedings of Pragmatics of SAT, pp. 103–116 (2014)

    Google Scholar 

  14. Gitina, K., Reimer, S., Sauer, M., Wimmer, R., Scholl, C., Becker, B.: Equivalence checking of partial designs using dependency quantified Boolean formulae. In: Proceedings of ICCD, pp. 396–403, October 2013

    Google Scholar 

  15. Gitina, K., Wimmer, R., Reimer, S., Sauer, M., Scholl, C., Becker, B.: Solving DQBF through quantifier elimination. In: Proceedings of DATE (2015)

    Google Scholar 

  16. Giunchiglia, E., Narizzano, M., Pulina, L., Tacchella, A.: Quantified Boolean formulas satisfiability library (QBFLIB) (2005). www.qbflib.org

  17. Henkin, L.: Some remarks on infinitely long formulas. J. Symb. Logic 30, 167–183 (1961)

    MathSciNet  MATH  Google Scholar 

  18. Janota, M., Marques-Silva, J.: Solving QBF by clause selection. In: Proceedings of IJCAI, pp. 325–331. AAAI Press (2015)

    Google Scholar 

  19. 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). doi:10.1007/978-3-642-21581-0_19

    Chapter  Google Scholar 

  20. Lonsing, F., Biere, A.: DepQBF: a dependency-aware QBF solver. JSAT 7(2–3), 71–76 (2010)

    Google Scholar 

  21. 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  MATH  Google Scholar 

  22. Peterson, G.L., Reif, J.H.: Multiple-person alternation. In: Proceedings of FOCS, pp. 348–363. IEEE (1979)

    Google Scholar 

  23. Rabe, M.N., Seshia, S.A.: Incremental determinization. In: Creignou, N., Le Berre, D. (eds.) SAT 2016. LNCS, vol. 9710, pp. 375–392. Springer, Cham (2016). doi:10.1007/978-3-319-40970-2_23

    Google Scholar 

  24. Rabe, M.N., Leander Tentrup, C.: A certifying QBF solver. In: Proceedings of FMCAD, pp. 136–143 (2015)

    Google Scholar 

  25. Siekmann, J., Wrightson, G.: Automation of Reasoning: 2: Classical Papers on Computational Logic 1967–1970. Springer, Heidelberg (1983). doi:10.1007/978-3-642-81955-1

    MATH  Google Scholar 

  26. Silva, J.P.M., Sakallah, K.A.: GRASP - a new search algorithm for satisfiability. In: Proceedings of CAD, pp. 220–227. IEEE (1997)

    Google Scholar 

  27. 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). doi:10.1007/978-3-319-40970-2_24

    Google Scholar 

  28. Tentrup, L.: On expansion and resolution in CEGAR based QBF solving. In: Majumdar, R., Kunčak, V. (eds.) CAV 2017. LNCS, vol. 10427, pp. 475–494. Springer, Cham (2017)

    Google Scholar 

  29. Tseitin, G.S.: On the complexity of derivation in propositional calculus. Stud. Constr. Math. Math. Logic 2, 115–125 (1968). Reprinted in [2]: 10–13

    Google Scholar 

  30. Gelder, A.: Contributions to the theory of practical quantified Boolean formula solving. In: Milano, M. (ed.) CP 2012. LNCS, pp. 647–663. Springer, Heidelberg (2012). doi:10.1007/978-3-642-33558-7_47

    Chapter  Google Scholar 

  31. Wimmer, R., Gitina, K., Nist, J., Scholl, C., Becker, B.: Preprocessing for DQBF. In: Heule, M., Weaver, S. (eds.) SAT 2015. LNCS, vol. 9340, pp. 173–190. Springer, Cham (2015). doi:10.1007/978-3-319-24318-4_13

    Chapter  Google Scholar 

  32. Wimmer, R., Reimer, S., Marin, P., Becker, B.: HQSpre-an effective preprocessor for QBF and DQBF. In: Proceedings of TACAS (2017)

    Google Scholar 

  33. Zhang, L., Malik, S.: Conflict driven learning in a quantified Boolean satisfiability solver. In: Proceedings of ICCAD, pp. 442–449, November 2002

    Google Scholar 

Download references

Acknowledgements

The author expresses his gratitude to Armin Biere, Benjamin Caulfield, Daniel J. Fremont, Martina Seidl, Sanjit A. Seshia, Martin Suda, Leander Tentrup, and Ralf Wimmer for supportive comments and detailed discussions on this work.

This work was supported in part by NSF grants CCF-1139138, CNS-1528108, and CNS-1646208, and by TerraSwarm, one of six centers of STARnet, a Semiconductor Research Corporation program sponsored by MARCO and DARPA.

Author information

Authors and Affiliations

  1. University of California, Berkeley, Berkeley, USA

    Markus N. Rabe

Authors
  1. Markus N. Rabe
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Markus N. Rabe .

Editor information

Editors and Affiliations

  1. UNSW Sydney, Sydney, New South Wales, Australia

    Serge Gaspers

  2. University of New South Wales , Sydney, New South Wales, Australia

    Toby Walsh

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Rabe, M.N. (2017). A Resolution-Style Proof System for DQBF. In: Gaspers, S., Walsh, T. (eds) Theory and Applications of Satisfiability Testing – SAT 2017. SAT 2017. Lecture Notes in Computer Science(), vol 10491. Springer, Cham. https://doi.org/10.1007/978-3-319-66263-3_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-66263-3_20

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66262-6

  • Online ISBN: 978-3-319-66263-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation