Abstract

We consider the problem of incrementally solving a sequence of quantified Boolean formulae (QBF). Incremental solving aims at using information learned from one formula in the process of solving the next formulae in the sequence. Based on a general overview of the problem and related challenges, we present an approach to incremental QBF solving which is application-independent and hence applicable to QBF encodings of arbitrary problems. We implemented this approach in our incremental search-based QBF solver DepQBF and report on implementation details. Experimental results illustrate the potential benefits of incremental solving in QBF-based workflows.

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References

  1. 1.
    Audemard, G., Lagniez, J.M., Simon, L.: Improving Glucose for Incremental SAT Solving with Assumptions: Application to MUS Extraction. In: Järvisalo, M., Van Gelder, A. (eds.) SAT 2013. LNCS, vol. 7962, pp. 309–317. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  2. 2.
    Balabanov, V., Jiang, J.R.: Unified QBF certification and its applications. Formal Methods in System Design 41(1), 45–65 (2012)CrossRefMATHGoogle Scholar
  3. 3.
    Becker, B., Ehlers, R., Lewis, M.D.T., Marin, P.: ALLQBF Solving by Computational Learning. In: Chakraborty, S., Mukund, M. (eds.) ATVA 2012. LNCS, vol. 7561, pp. 370–384. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  4. 4.
    Benedetti, M., Mangassarian, H.: QBF-Based Formal Verification: Experience and Perspectives. JSAT 5, 133–191 (2008)MathSciNetGoogle Scholar
  5. 5.
    Biere, A.: PicoSAT Essentials. JSAT 4(2-4), 75–97 (2008)MATHGoogle Scholar
  6. 6.
    Bloem, R., Könighofer, R., Seidl, M.: SAT-Based Synthesis Methods for Safety Specs. In: McMillan, K.L., Rival, X. (eds.) VMCAI 2014. LNCS, vol. 8318, pp. 1–20. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  7. 7.
    Büning, H.K., Karpinski, M., Flögel, A.: Resolution for Quantified Boolean Formulas. Inf. Comput. 117(1), 12–18 (1995)CrossRefMATHGoogle Scholar
  8. 8.
    Cadoli, M., Schaerf, M., Giovanardi, A., Giovanardi, M.: An Algorithm to Evaluate Quantified Boolean Formulae and Its Experimental Evaluation. J. Autom. Reasoning 28(2), 101–142 (2002)CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Cashmore, M., Fox, M., Giunchiglia, E.: Planning as Quantified Boolean Formula. In: Raedt, L.D., Bessière, C., Dubois, D., Doherty, P., Frasconi, P., Heintz, F., Lucas, P.J.F. (eds.) ECAI. Frontiers in Artificial Intelligence and Applications, pp. 217–222. IOS Press (2012)Google Scholar
  10. 10.
    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)CrossRefGoogle Scholar
  11. 11.
    Eén, N., Sörensson, N.: Temporal Induction by Incremental SAT Solving. Electr. Notes Theor. Comput. Sci. 89(4), 543–560 (2003)CrossRefGoogle Scholar
  12. 12.
    Egly, U., Kronegger, M., Lonsing, F., Pfandler, A.: Conformant Planning as a Case Study of Incremental QBF Solving. CoRR abs/1405.7253 (2014)Google Scholar
  13. 13.
    Giunchiglia, E., Narizzano, M., Tacchella, A.: Clause/Term Resolution and Learning in the Evaluation of Quantified Boolean Formulas. J. Artif. Intell. Res. (JAIR). 26, 371–416 (2006)Google Scholar
  14. 14.
    Goultiaeva, A., Van Gelder, A., Bacchus, F.: A Uniform Approach for Generating Proofs and Strategies for Both True and False QBF Formulas. In: Walsh, T. (ed.) IJCAI, pp. 546–553. IJCAI/AAAI (2011)Google Scholar
  15. 15.
    Goultiaeva, A., Bacchus, F.: Recovering and Utilizing Partial Duality in QBF. In: Järvisalo, M., Van Gelder, A. (eds.) SAT 2013. LNCS, vol. 7962, pp. 83–99. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  16. 16.
    Goultiaeva, A., Seidl, M., Biere, A.: Bridging the Gap between Dual Propagation and CNF-based QBF Solving. In: Macii, E. (ed.) DATE, pp. 811–814. EDA Consortium. ACM DL, San Jose (2013)Google Scholar
  17. 17.
    Hillebrecht, S., Kochte, M.A., Erb, D., Wunderlich, H.J., Becker, B.: Accurate QBF-Based Test Pattern Generation in Presence of Unknown Values. In: Macii, E. (ed.) DATE, pp. 436–441. EDA Consortium, ACM DL, San Jose, CA, USA (2013)Google Scholar
  18. 18.
    Janota, M., Grigore, R., Marques-Silva, J.: On QBF Proofs and Preprocessing. In: McMillan, K., Middeldorp, A., Voronkov, A. (eds.) LPAR-19 2013. LNCS, vol. 8312, pp. 473–489. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  19. 19.
    Klieber, W., Sapra, S., Gao, S., Clarke, E.M.: 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)CrossRefGoogle Scholar
  20. 20.
    Lagniez, J.M., Biere, A.: Factoring Out Assumptions to Speed Up MUS Extraction. In: Järvisalo, M., Van Gelder, A. (eds.) SAT 2013. LNCS, vol. 7962, pp. 276–292. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  21. 21.
    Letz, R.: Lemma and Model Caching in Decision Procedures for Quantified Boolean Formulas. In: Egly, U., Fermüller, C. (eds.) TABLEAUX 2002. LNCS (LNAI), vol. 2381, pp. 160–175. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  22. 22.
    Lonsing, F., Biere, A.: Integrating Dependency Schemes in Search-Based QBF Solvers. In: Strichman, O., Szeider, S. (eds.) SAT 2010. LNCS, vol. 6175, pp. 158–171. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  23. 23.
    Lonsing, F., Egly, U.: Incremental QBF Solving by DepQBF (Extended Abstract). In: Hong, H., Yap, C. (eds.) ICMS 2014. LNCS, vol. 8592, pp. 307–314. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  24. 24.
    Lonsing, F., Egly, U., Van Gelder, A.: Efficient Clause Learning for Quantified Boolean Formulas via QBF Pseudo Unit Propagation. In: Järvisalo, M., Van Gelder, A. (eds.) SAT 2013. LNCS, vol. 7962, pp. 100–115. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  25. 25.
    Mangassarian, H., Veneris, A.G., Benedetti, M.: Robust QBF Encodings for Sequential Circuits with Applications to Verification, Debug, and Test. IEEE Trans. Computers 59(7), 981–994 (2010)CrossRefMathSciNetGoogle Scholar
  26. 26.
    Marin, P., Miller, C., Becker, B.: Incremental QBF Preprocessing for Partial Design Verification - (Poster Presentation). In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 473–474. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  27. 27.
    Marin, P., Miller, C., Lewis, M.D.T., Becker, B.: Verification of Partial Designs using Incremental QBF Solving. In: Rosenstiel, W., Thiele, L. (eds.) DATE, pp. 623–628. IEEE (2012)Google Scholar
  28. 28.
    Nadel, A., Ryvchin, V.: Efficient SAT Solving under Assumptions. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 242–255. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  29. 29.
    Niemetz, A., Preiner, M., Lonsing, F., Seidl, M., Biere, A.: Resolution-Based Certificate Extraction for QBF - (Tool Presentation). In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 430–435. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  30. 30.
    Samulowitz, H., Davies, J., Bacchus, F.: Preprocessing QBF. In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, pp. 514–529. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  31. 31.
    Seidl, M., Könighofer, R.: Partial witnesses from preprocessed quantified Boolean formulas. In: DATE, pp. 1–6. IEEE (2014)Google Scholar
  32. 32.
    Silva, J.P.M., Lynce, I., Malik, S.: Conflict-Driven Clause Learning SAT Solvers. In: Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.) Handbook of Satisfiability, FAIA, vol. 185, pp. 131–153. IOS Press (2009)Google Scholar
  33. 33.
    Staber, S., Bloem, R.: Fault Localization and Correction with QBF. In: Marques-Silva, J., Sakallah, K.A. (eds.) SAT 2007. LNCS, vol. 4501, pp. 355–368. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  34. 34.
    Sülflow, A., Fey, G., Drechsler, R.: Using QBF to Increase Accuracy of SAT-Based Debugging. In: ISCAS, pp. 641–644. IEEE (2010)Google Scholar
  35. 35.
    Van Gelder, A.: Primal and Dual Encoding from Applications into Quantified Boolean Formulas. In: Schulte, C. (ed.) CP 2013. LNCS, vol. 8124, pp. 694–707. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  36. 36.
    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)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Florian Lonsing
    • 1
  • Uwe Egly
    • 1
  1. 1.Institute of Information Systems, Knowledge-Based Systems GroupVienna University of TechnologyViennaAustria

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