Incremental QBF Solving by DepQBF

  • Florian Lonsing
  • Uwe Egly
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8592)


The logic of quantified Boolean formulae (QBF) extends propositional logic by explicit existential and universal quantification of the variables. We present the search-based QBF solver DepQBF which allows to solve a sequence of QBFs incrementally. The goal is to exploit information which was learned when solving previous formulae in the process of solving the next formula in a sequence. We illustrate incremental QBF solving and potential usage scenarios by examples. Incremental QBF solving has the potential to considerably improve QBF-based workflows in many application domains.


quantified Boolean formulae QBF search-based solving Q-resolution clause learning cube learning incremental solving 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Biere, A., Cimatti, A., Clarke, E., Zhu, Y.: Symbolic Model Checking without BDDs. In: Cleaveland, W.R. (ed.) TACAS 1999. LNCS, vol. 1579, pp. 193–207. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  2. 2.
    Bubeck, U., Kleine Büning, H.: Encoding Nested Boolean Functions as Quantified Boolean Formulas. JSAT 8(1/2), 101–116 (2012)Google Scholar
  3. 3.
    Kleine Büning, H., Karpinski, M., Flögel, A.: Resolution for Quantified Boolean Formulas. Inf. Comput. 117(1), 12–18 (1995)CrossRefzbMATHGoogle Scholar
  4. 4.
    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)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Davis, M., Logemann, G., Loveland, D.: A Machine Program for Theorem-proving. Commun. ACM 5(7), 394–397 (1962)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Eén, N., Sörensson, N.: Temporal Induction by Incremental SAT Solving. Electr. Notes Theor. Comput. Sci. 89(4), 543–560 (2003)CrossRefGoogle Scholar
  7. 7.
    Egly, U., Kronegger, M., Lonsing, F., Pfandler, A.: Conformant Planning as a Case Study of Incremental QBF Solving. CoRR (submitted, 2014)Google Scholar
  8. 8.
    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)zbMATHMathSciNetGoogle Scholar
  9. 9.
    Janota, M., Grigore, R., Marques-Silva, J.: On QBF Proofs and Preprocessing. In: McMillan, K., Middeldorp, A., Voronkov, A. (eds.) LPAR-19. LNCS, vol. 8312, pp. 473–489. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  10. 10.
    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
  11. 11.
    Lonsing, F., Biere, A.: DepQBF: A Dependency-Aware QBF Solver. JSAT 7(2-3), 71–76 (2010)Google Scholar
  12. 12.
    Lonsing, F., Egly, U.: Incremental QBF Solving. CoRR, abs/1402.2410 (2014)Google Scholar
  13. 13.
    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
  14. 14.
    Marin, P., Miller, C., Lewis, M.D.T., Becker, B.: Verification of Partial Designs using Incremental QBF Solving. In: Proc. DATE. IEEE (2012)Google Scholar
  15. 15.
    Marques Silva, J.P., Lynce, I., Malik, S.: Conflict-Driven Clause Learning SAT Solvers. In: Handbook of Satisfiability. FAIA, vol. 185. IOS Press (2009)Google Scholar
  16. 16.
    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-Verlag Berlin Heidelberg 2014

Authors and Affiliations

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

Personalised recommendations