A Compositional Approach on Modal Specifications for Timed Systems

  • Nathalie Bertrand
  • Axel Legay
  • Sophie Pinchinat
  • Jean-Baptiste Raclet
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5885)


On the one hand, modal specifications are classic, convenient, and expressive mathematical objects to represent interfaces of component-based systems. On the other hand, time is a crucial aspect of systems for practical applications, e.g. in the area of embedded systems. And yet, only few results exist on the design of timed component-based systems. In this paper, we propose a timed extension of modal specifications, together with fundamental operations (conjunction, product, and quotient) that enable to reason in a compositional way about timed system. The specifications are given as modal event-clock automata, where clock resets are easy to handle. We develop an entire theory that promotes efficient incremental design techniques.


Region Graph Compositional Approach Inconsistent State Interface Theory Interface Automaton 
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.


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  1. 1.
    Alur, R., Dill, D.L.: A theory of timed automata. Theoretical Computer Science 126(2), 183–235 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Alur, R., Fix, L., Henzinger, T.A.: Event-clock automata: A determinizable class of timed automata. Theoretical Computer Science 211, 1–13 (1999)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-time temporal logic. Journal of the ACM 49(5), 672–713 (2002)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Alur, R., Henzinger, T.A., Kupferman, O., Vardi, M.Y.: Alternating refinement relations. In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 163–178. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  5. 5.
    Antonik, A., Huth, M., Larsen, K.G., Nyman, U., Wasowski, A.: 20 years of modal and mixed specifications. Bulletin of European Association of Theoretical Computer Science 1(94) (2008)Google Scholar
  6. 6.
    Arnold, A., Nivat, M.: Metric interpretations of infinite trees and semantics of non deterministic recursive programs. Theoretical Computer Science 11, 181–205 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Arnold, A., Vincent, A., Walukiewicz, I.: Games for synthesis of controllers with partial observation. Theoretical Computer Science 303(1), 7–34 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Bertrand, N., Legay, A., Pinchinat, S., Raclet, J.-B.: A compositional approach on modal specifications for timed systems. Technical report, INRIA 7039 (September 2009)Google Scholar
  9. 9.
    Bertrand, N., Pinchinat, S., Raclet, J.-B.: Refinement and consistency of timed modal specifications. In: Proceedings of the 3rd International Conference on Language and Automata Theory and Applications (LATA 2009). LNCS, vol. 5457, pp. 152–163. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  10. 10.
    Kārlis Čerāns, Jens Chr. Godskesen, and Kim G. Larsen. Timed modal specification - theory and tools. In Proceedings of the 5th International Conference on Computer Aided Verification (CAV’93), volume 697 of Lecture Notes in Computer Science, pages 253–267. Springer, 1993. 679Google Scholar
  11. 11.
    Chatain, T., David, A., Larsen, K.G.: Playing games with timed games. In: Proceedings of the 3rd IFAC Conference on Analysis and Design of Hybrid Systems, ADHS 2009 (to appear, 2009)Google Scholar
  12. 12.
    de Alfaro, L., Henzinger, T.A.: Interface automata. In: Proceedings of the 9th ACM SIGSOFT International Symposium on Foundations of Software Engineering (FSE 2001), pp. 109–120 (2001)Google Scholar
  13. 13.
    de Alfaro, L., Henzinger, T.A., Stoelinga, M.: Timed interfaces. In: Sangiovanni-Vincentelli, A.L., Sifakis, J. (eds.) EMSOFT 2002. LNCS, vol. 2491, pp. 108–122. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  14. 14.
    Doyen, L., Henzinger, T.A., Jobstmann, B., Petrov, T.: Interface theories with component reuse. In: Proceedings of the 8th International Conference on Embedded Software (EMSOFT 2008), pp. 79–88. ACM Press, New York (2008)CrossRefGoogle Scholar
  15. 15.
    Feuillade, G., Pinchinat, S.: Modal specifications for the control theory of discrete-event systems. Discrete Event Dynamic Systems 17(2), 181–205 (2007)CrossRefMathSciNetGoogle Scholar
  16. 16.
    Henzinger, T.A., Sifakis, J.: The embedded systems design challenge. In: Misra, J., Nipkow, T., Sekerinski, E. (eds.) FM 2006. LNCS, vol. 4085, pp. 1–15. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  17. 17.
    Jonsson, B., Larsen, K.G.: On the complexity of equation solving in process algebra. In: Proceedings of the International Joint Conference on Theory and Practice of Software Development (TAPSOFT 1991), pp. 381–396. Springer, Heidelberg (1991)Google Scholar
  18. 18.
    Larsen, K.G.: Modal specifications. In: Sifakis, J. (ed.) CAV 1989. LNCS, vol. 407, pp. 232–246. Springer, Heidelberg (1990)Google Scholar
  19. 19.
    Larsen, K.G., Nyman, U., Wasowski, A.: Modal i/o automata for interface and product line theories. In: De Nicola, R. (ed.) ESOP 2007. LNCS, vol. 4421, pp. 64–79. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  20. 20.
    Larsen, K.G., Nyman, U., Wasowski, A.: On modal refinement and consistency. In: Caires, L., Vasconcelos, V.T. (eds.) CONCUR 2007. LNCS, vol. 4703, pp. 105–119. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  21. 21.
    Lynch, N., Tuttle, M.R.: An introduction to Input/Output automata. CWI-quarterly 2(3) (1989)Google Scholar
  22. 22.
    Raclet, J.-B.: Quotient de spécifications pour la réutilisation de composants. PhD thesis, Université de Rennes I, december, In French (2007)Google Scholar
  23. 23.
    Raclet, J.-B.: Residual for component specifications. In: Proceedings of the 4th International Workshop on Formal Aspects of Component Software, FACS 2007 (2007)Google Scholar
  24. 24.
    Raclet, J.-B., Badouel, E., Benveniste, A., Caillaud, B., Passerone, R.: Why are modalities good for interface theories? In: Proceedings of the 9th International Conference on Application of Concurrency to System Design (ACSD 2009), pp. 127–199. IEEE Computer Society Press, Los Alamitos (2009)Google Scholar
  25. 25.
    The UPPAAL tool,

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Nathalie Bertrand
    • 1
  • Axel Legay
    • 1
  • Sophie Pinchinat
    • 2
  • Jean-Baptiste Raclet
    • 3
  1. 1.INRIA RennesFrance
  2. 2.IRISA & Université Rennes 1France
  3. 3.INRIA Rhône-AlpesFrance

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