QBF Encoding of Temporal Properties and QBF-Based Verification

  • Wenhui Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8562)


SAT and QBF solving techniques have applications in various areas. One area of the applications of SAT-solving is formal verification of temporal properties of transition system models. Because of the restriction on the structure of formulas, complicated verification problems cannot be naturally represented with SAT-formulas succinctly. This paper investigates QBF-applications in this area, aiming at the verification of branching-time temporal logic properties of transition system models. The focus of this paper is on temporal logic properties specified by the extended computation tree logic that allows some sort of fairness, and the main contribution of this paper is a bounded semantics for the extended computation tree logic. A QBF encoding of the temporal logic is then developed from the definition of the bounded semantics, and an implementation of QBF-based verification follows from the QBF encoding. Experimental evaluation of the feasibility and the computational properties of such a QBF-based verification algorithm is reported.


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/ETAPS 1999. LNCS, vol. 1579, pp. 193–207. Springer, Heidelberg (1999)Google Scholar
  2. 2.
    Biere, A., Cimmatti, A., Clarke, E., Strichman, O., Zhu, Y.: Bounded Model Checking. Advances in Computers, vol. 58. Academic Press (2003)Google Scholar
  3. 3.
    Burch, J.R., Clarke, E.M., McMillan, K.L., Dill, D.L., Hwang, J.: Symbolic model checking: 1020 states and beyond. LICS, pp. 428–439 (1990)Google Scholar
  4. 4.
    Cimatti, A., Clarke, E.M., Giunchiglia, F., Roveri, M.: NUSMV: A New Symbolic Model Verifier. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 495–499. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  5. 5.
    Clarke, E.M., Grumberg, O., Peled, D.: Model Checking. The MIT Press (1999)Google Scholar
  6. 6.
    Duan, Z., Tian, C., Yang, M., He, J.: Bounded Model Checking for Propositional Projection Temporal Logic. In: Du, D.-Z., Zhang, G. (eds.) COCOON 2013. LNCS, vol. 7936, pp. 591–602. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  7. 7.
    Emerson, E.A., Clarke, E.M.: Using Branching-time Temporal Logics to Synthesize Synchronization Skeletons. Sci. of Comp. Prog. 2(3), 241–266 (1982)CrossRefzbMATHGoogle Scholar
  8. 8.
    Emerson, E.A., Halpern, J.Y.: “Sometimes” and “Not Never” revisited: on branching versus linear time temporal logic. J. ACM 33(1), 151–178 (1986)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Goultiaeva, A., Van Gelder, A., Bacchus, F.: A Uniform Approach for Generating Proofs and Strategies for Both True and False QBF Formulas. In: IJCAI 2011, pp. 546–553 (2011)Google Scholar
  10. 10.
    Hoffmann, J., Gomes, C.P., Selman, B., Kautz, H.A.: SAT Encodings of State-Space Reachability Problems in Numeric Domains. In: IJCAI 2007, pp. 1918–1923 (2007)Google Scholar
  11. 11.
    Holzmann, G.J.: The model checker Spin. IEEE Transactions on Software Engineering 23(5), 279–295 (1997)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Kemper, S.: SAT-based verification for timed component connectors. Sci. Comput. Program. 77(7-8), 779–798 (2012)CrossRefzbMATHGoogle Scholar
  13. 13.
    Kontchakov, R., Pulina, L., Sattler, U., Schneider, T., Selmer, P., Wolter, F., Zakharyaschev, M.: Minimal Module Extraction from DL-Lite Ontologies Using QBF Solvers. In: IJCAI 2009, pp. 836–841 (2009)Google Scholar
  14. 14.
    Penczek, W., Wozna, B., Zbrzezny, A.: Bounded Model Checking for the Universal Fragment of CTL. Fundamenta Informaticae 51, 135–156 (2002)zbMATHMathSciNetGoogle Scholar
  15. 15.
    Wozna, B.: ATCL* properties and Bounded Model Checking. Fundam. Inform. 63(1), 65–87 (2004)zbMATHMathSciNetGoogle Scholar
  16. 16.
    McMillan, K.L.: Symbolic Model Checking. Kluwer Academic Publisher (1993)Google Scholar
  17. 17.
    Peled, D.A.: Software Reliability Methods. Springer (2001)Google Scholar
  18. 18.
    Peterson, G.L.: Myths About the Mutual Exclusion Problem. Information Processing Letters 12(3), 115–116 (1981)CrossRefzbMATHGoogle Scholar
  19. 19.
    Zhang, W.: Bounded Semantics of CTL and SAT-based Verification. In: Breitman, K., Cavalcanti, A. (eds.) ICFEM 2009. LNCS, vol. 5885, pp. 286–305. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  20. 20.
    Zhang, W.: Bounded Semantics of CTL. Institute of Software, Chinese Academy of Sciences. Technical Report ISCAS-LCS-10-16 (2010)Google Scholar
  21. 21.
    Zhang, W.: VERDS modeling language,

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Wenhui Zhang
    • 1
  1. 1.State Key Laboratory of Computer Science, Institute of SoftwareChinese Academy of SciencesBeijingChina

Personalised recommendations