Advertisement

Don’t Know in the μ-Calculus

  • Orna Grumberg
  • Martin Lange
  • Martin Leucker
  • Sharon Shoham
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3385)

Abstract

This work presents game-based model checking for abstract models with respect to specifications in μ-calculus, interpreted over a 3-valued semantics. If the model checking result is indefinite (don’t know), the abstract model is refined, based on an analysis of the cause for this result. For finite concrete models our abstraction-refinement is fully automatic and guaranteed to terminate with a definite result true or false.

Keywords

Model Check Abstract Model Winning Strategy Kripke Structure Game Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Burch, J.R., Clarke, E.M., McMillan, K.L., Dill, D.L., Hwang, L.J.: Symbolic model checking: 1020 states and beyond. Information and Computation 98(2), 142–170 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Clarke, E., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  3. 3.
    Clarke, E., Grumberg, O., Peled, D.: Model Checking. MIT press, Cambridge (1999)Google Scholar
  4. 4.
    Clarke, E., Gupta, A., Kukula, J., Strichman, O.: SAT based abstraction-refinement using ILP and machine leraning techniques. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, p. 265. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  5. 5.
    Cleaveland, R.: Tableau-based model checking in the propositional mu-calculus. Acta Inf. 27, 725–747 (1990)zbMATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Dams, D., Gerth, R., Grumberg, O.: Abstract interpretation of reactive systems. ACM Transactions on Programming Languages and Systems 19(2) (March 1997)Google Scholar
  7. 7.
    Emerson, E.A., Jutla, C.S.: Tree automata, μ-calculus and determinacy. In: Proc. 32th Symp. on Foundations of Computer Science (FOCS 1991), pp. 368–377. IEEE Computer Society Press, Los Alamitos (1991)Google Scholar
  8. 8.
    Emerson, E.A., Lei, C.-L.: Efficient model checking in fragments of the propositional mu-calculus. In: Logic in Computer Science, LICS (1986)Google Scholar
  9. 9.
    Godefroid, P., Jagadeesan, R.: Automatic abstraction using generalized model checking. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 137–150. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  10. 10.
    Godefroid, P., Jagadeesan, R.: On the expressiveness of 3-valued models. In: Zuck, L.D., Attie, P.C., Cortesi, A., Mukhopadhyay, S. (eds.) VMCAI 2003. LNCS, vol. 2575, pp. 206–222. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  11. 11.
    Huth, M., Jagadeesan, R., Schmidt, D.: Modal transition systems: A foundation for three-valued program analysis. In: Sands, D. (ed.) ESOP 2001. LNCS, vol. 2028, pp. 155–169. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  12. 12.
    Kozen, D.: Results on the Propositional μ-calculus. TCS 27, 333–354 (1983)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Lee, W., Pardo, A., Jang, J.-Y., Hachtel, G.D., Somenzi, F.: Tearing based automatic abstraction for CTL model checking. In: ICCAD, pp. 76–81 (1996)Google Scholar
  14. 14.
    Loiseaux, C., Graf, S., Sifakis, J., Bouajjani, A., Bensalem, S.: Property preserving abstractions for the verification of concurrent systems. Formal Methods in System Design 6, 11–45 (1995)zbMATHCrossRefGoogle Scholar
  15. 15.
    Long, D., Browne, A., Clark, E., Jha, S., Marrero, W.: An improved algorithm for the evaluation of fixpoint expressions. In: Dill, D.L. (ed.) CAV 1994. LNCS, vol. 818, pp. 338–350. Springer, Heidelberg (1994)Google Scholar
  16. 16.
    Pardo, A., Hachtel, G.D.: Automatic abstraction techniques for propositional mu-calculus model checking. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254. Springer, Heidelberg (1997)Google Scholar
  17. 17.
    Pardo, A., Hachtel, G.D.: Incremental CTL model checking using BDD subsetting. In: Design Automation Conference (DAC), pp. 457–462 (1998)Google Scholar
  18. 18.
    Shoham, S., Grumberg, O.: A game-based framework for CTL counterexamples and 3-valued abstraction-refinemnet. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 275–287. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  19. 19.
    Stirling, C.: Local model checking games. In: Lee, I., Smolka, S.A. (eds.) CONCUR 1995. LNCS, vol. 962, pp. 1–11. Springer, Heidelberg (1995)Google Scholar
  20. 20.
    Stirling, C., Walker, D.J.: Local model checking in the modal mu-calculus. In: Díaz, J., Orejas, F. (eds.) TAPSOFT 1989 and CCIPL 1989. LNCS, vol. 352. Springer, Heidelberg (1989)Google Scholar
  21. 21.
    Tarski, A.: A lattice-theoretical fixpoint theorem and its application. Pacific J.Math. 5, 285–309 (1955)zbMATHMathSciNetGoogle Scholar
  22. 22.
    Winskel, G.: Model checking in the modal ν-calculus. In: International Colloquium on Automata, Languages, and Programming, ICALP (1989)Google Scholar
  23. 23.
    Zielonka, W.: Infinite games on finitely coloured graphs with applications to automata on infinite trees. Theoretical Computer Science 200(1–2), 135–183 (1998)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Orna Grumberg
    • 1
  • Martin Lange
    • 2
  • Martin Leucker
    • 3
  • Sharon Shoham
    • 1
  1. 1.Computer Science DepartmentThe TechnionHaifaIsrael
  2. 2.Institut für InformatikUniversity of MunichGermany
  3. 3.Institut für InformatikTechnical University of MunichGermany

Personalised recommendations