On Modal Refinement and Consistency

  • Kim G. Larsen
  • Ulrik Nyman
  • Andrzej Wąsowski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4703)

Abstract

Almost 20 years after the original conception, we revisit several fundamental question about modal transition systems. First, we demonstrate the incompleteness of the standard modal refinement using a counterexample due to Hüttel. Deciding any refinement, complete with respect to the standard notions of implementation, is shown to be computationally hard (co-NP hard). Second, we consider four forms of consistency (existence of implementations) for modal specifications. We characterize each operationally, giving algorithms for deciding, and for synthesizing implementations, together with their complexities.

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References

  1. 1.
    Larsen, K.G., Thomsen, B.: A modal process logic. In: LICS, IEEE Computer Society Press, Los Alamitos (1988)Google Scholar
  2. 2.
    Huth, M., Jagadeesan, R., Schmidt, D.: Modal transition systems: A foundation for three-valued program analysis. In: Sands, D. (ed.) ESOP 2001 and ETAPS 2001. LNCS, vol. 2028, Springer, Heidelberg (2001)Google Scholar
  3. 3.
    Schmidt, D.: From trace sets to modal-transition systems by stepwise abstract interpretation (2001)Google Scholar
  4. 4.
    Godefroid, P., Huth, M., Jagadeesan, R.: Abstraction-based model checking using modal transition systems. In: Larsen, K.G., Nielsen, M. (eds.) CONCUR 2001. LNCS, vol. 2154, p. 426. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  5. 5.
    Børjesson, A., Larsen, K.G., Skou, A.: Generality in design and compositional verification using tav. In: FORTE 1992 Proceedings, The Netherlands, pp. 449–464. North-Holland Publishing Co., Amsterdam (1993)Google Scholar
  6. 6.
    Larsen, K.G., Steffen, B., Weise, C.: A constraint oriented proof methodology based on modal transition systems. In: Tools and Algorithms for Construction and Analysis of Systems, pp. 17–40 (1995)Google Scholar
  7. 7.
    Bruns, G.: An industrial application of modal process logic. Sci. Comput. Program. 29(1-2), 3–22 (1997)CrossRefGoogle Scholar
  8. 8.
    Larsen, K.G., Xinxin, L.: Equation solving using modal transition systems. In: LICS. Fifth Annual IEEE Symposium on Logics in Computer Science, Philadelphia, PA, USA, 4–7 June 1990, pp. 108–117. IEEE Computer Society Press, Los Alamitos (1990)Google Scholar
  9. 9.
    Larsen, K.G., Nyman, U., Wąsowski, A.: Modal i/o automata for interface and product line theories. In: Nicola, R.D. (ed.) ESOP 2007. Programming Languages and Systems. LNCS, vol. 4421, pp. 64–79. Springer, Heidelberg (2007)Google Scholar
  10. 10.
    Fischbein, D., Uchitel, S., Braberman, V.: A foundation for behavioural conformance in software product line architectures. In: ROSATEA 2006 Proceedings, pp. 39–48. ACM Press, New York (2006)CrossRefGoogle Scholar
  11. 11.
    Uchitel, S., Chechik, M.: Merging partial behavioural models. In: Taylor, R.N., Dwyer, M.B. (eds.) SIGSOFT FSE, pp. 43–52. ACM Press, New York (2004)Google Scholar
  12. 12.
    Brunet, G., Chechik, M., Uchitel, S.: Properties of behavioural model merging. In: Misra, J., Nipkow, T., Sekerinski, E. (eds.) FM 2006. LNCS, vol. 4085, pp. 98–114. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  13. 13.
    Weise, C., Lenzkes, D.: Weak refinement for modal hybrid systems. In: Maler, O. (ed.) HART 1997. LNCS, vol. 1201, pp. 316–330. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  14. 14.
    Larsen, K.G.: Modal specifications. In: Sifakis, J. (ed.) Automatic Verification Methods for Finite State Systems. LNCS, vol. 407, pp. 232–246. Springer, Heidelberg (1990)Google Scholar
  15. 15.
    Cerans, K., Godskesen, J.C., Larsen, K.G.: Timed modal specification - theory and tools. In: Courcoubetis, C. (ed.) CAV 1993. LNCS, vol. 697, pp. 253–267. Springer, Heidelberg (1993)Google Scholar
  16. 16.
    Larsen, K.G., Steffen, B., Weise, C.: Fischer’s protocol revisited: a simple proof using modal constraints. In: Alur, R., Sontag, E.D., Henzinger, T.A. (eds.) Hybrid Systems III. LNCS, vol. 1066, pp. 604–615. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  17. 17.
    Fecher, H., Huth, M.: Ranked predicate abstraction for branching time: Complete incremental, and precise. In: Graf, S., Zhang, W. (eds.) ATVA 2006. LNCS, vol. 4218, pp. 322–336. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  18. 18.
    Schmidt, H., Fecher, H.: Comparing disjunctive modal transition systems with a one-selecting variant (submitted for publication) (2007)Google Scholar
  19. 19.
    Hüttel, H., Larsen, K.G.: The use of static constructs in a modal process logic. In: LFCS. The 1st International Symposium on Logical Foundations of Computer Science (1989)Google Scholar
  20. 20.
    Dams, D.: Abstract Interpretation and Partition Refinement for Model Checking. PhD thesis, Eindhoven University of Technology (July 1996)Google Scholar
  21. 21.
    Henessy, M., Milner, R.: Algebraic laws for nondeterminism and concurrency. Journal of the ACM, 137–161 (1985)Google Scholar
  22. 22.
    Larsen, K.G.: A context dependent bisimulation between processes. Theoretical Computer Science 49 (1987)Google Scholar
  23. 23.
    Park, D.: Concurrency and automata on infinite sequences. In: Proceedings of 5th GI Conference, vol. 104 (1981)Google Scholar
  24. 24.
    Milner, R.: Calculi for synchrony and asynchrony. Theoretical Computer Science 25 (1983)Google Scholar
  25. 25.
    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
  26. 26.
    Hüttel, H.: Operational and denotational properties of modal process logic. Master’s thesis, Computer Science Department. Aalborg University (1988)Google Scholar
  27. 27.
    Xinxin, L.: Specification and Decomposition in Concurrency. PhD thesis, Department of Mathematics and Comnputer Science, Aalborg University (April 1992)Google Scholar
  28. 28.
    Alur, R., Henzinger, T.A., Kupferman, O., Vardi, M.: Alternating refinement relations. In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 163–178. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  29. 29.
    Alfaro, L., Henzinger, T.A.: Interface automata. In: FSE. Proceedings of the Ninth Annual Symposium on Foundations of Software Engineering, Vienna, Austria, pp. 109–120 (september 2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Kim G. Larsen
    • 1
  • Ulrik Nyman
    • 1
  • Andrzej Wąsowski
    • 1
  1. 1.Department of Computer Science, Aalborg UniversityDenmark

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