Timed Temporal Logics for Abstracting Transient States

  • Houda Bel Mokadem
  • Béatrice Bérard
  • Patricia Bouyer
  • François Laroussinie
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4218)


In previous work, the timed logic TCTL was extended with an “almost everywhere” Until modality which abstracts negligible sets of positions (i.e. with a null duration) along a run of a timed automaton. We propose here an extension of this logic with more powerful modalities, in order to specify properties abstracting transient states, which are events that last for less than k time units. Our main result is that model-checking is still decidable and PSPACE-complete for this extension. On the other hand, a second semantics is defined, in which we consider the total duration where the property does not hold along a run. In this case, we prove that model-checking is undecidable.


Model Check Temporal Logic Transient State Atomic Proposition Hybrid 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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alur, R., Courcoubetis, C., Dill, D.: Model-checking in dense real-time. Information and Computation 104(1), 2–34 (1993)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Alur, R., Courcoubetis, C., Halbwachs, N., Henzinger, T.A., Ho, P.-H., Nicollin, X., Olivero, A., Sifakis, J., Yovine, S.: The algorithmic analysis of hybrid systems. Theoretical Computer Science 138(1), 3–34 (1995)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Alur, R., Courcoubetis, C., Henzinger, T.A.: Computing accumulated delays in real-time systems. Formal Methods in System Design 11(2), 137–156 (1997)CrossRefGoogle Scholar
  4. 4.
    Alur, R., Dill, D.: A theory of timed automata. Theoretical Computer Science 126(2), 183–235 (1994)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Alur, R., Feder, T., Henzinger, Th.A.: The benefits of relaxing punctuality. J. ACM 43(1), 116–146 (1996)MATHMathSciNetGoogle Scholar
  6. 6.
    Alur, R., Henzinger, Th.A.: Logics and models of real-time: a survey. In: Huizing, C., de Bakker, J.W., Rozenberg, G., de Roever, W.-P. (eds.) REX 1991. LNCS, vol. 600, pp. 74–106. Springer, Heidelberg (1992)CrossRefGoogle Scholar
  7. 7.
    Alur, R., La Torre, S., Pappas, G.J.: Optimal paths in weighted timed automata. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 49–62. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  8. 8.
    Behrmann, G., Fehnker, A., Hune, Th., Larsen, K.G., Pettersson, P., Romijn, J., Vaandrager, F.: Minimum-cost reachability for priced timed automata. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 147–161. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  9. 9.
    Belmokadem, H., Bérard, B., Bouyer, P., Laroussinie, F.: A New Modality for Almost Everywhere Propeties in Timed Automata. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653, pp. 110–124. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  10. 10.
    Bouyer, P., Brihaye, T., Markey, N.: Improved Undecidability Results on Priced Timed Automata. Information Processing Letters 98(5), 188–194 (2006)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Bouyer, P., Brinksma, E., Larsen, K.G.: Staying alive as cheaply as possible. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 203–218. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  12. 12.
    Brihaye, T., Bruyère, V., Raskin, J.-F.: Model-checking for weighted timed automata. In: Lakhnech, Y., Yovine, S. (eds.) FORMATS 2004 and FTRTFT 2004. LNCS, vol. 3253, pp. 277–292. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  13. 13.
    Bruyère, V., Dall’Olio, E., Raskin, J.-F.: Durations, parametric model-checking in timed automata with presburger arithmetic. In: Alt, H., Habib, M. (eds.) STACS 2003. LNCS, vol. 2607, pp. 687–698. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  14. 14.
    Chaochen, Z., Hoare, C., Ravn, A.: A calculus of duration. Information Processing Letters 40(5), 269–276 (1991)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Henzinger, T.A., Ho, P.-H., Wong-Toi, H.: HyTech: A model-checker for hybrid systems. Journal of Software Tools for Technology Transfer 1(1–2), 110–122 (1997)MATHCrossRefGoogle Scholar
  16. 16.
    Henzinger, Th.A.: The theory of hybrid automata. In: Proc. 11th IEEE Symp. Logic in Computer Science (LICS 1996), New Brunswick, NJ, USA, July 1996, pp. 278–292. IEEE Comp. Soc. Press, Los Alamitos (1996)Google Scholar
  17. 17.
    Henzinger, Th.A., Nicollin, X., Sifakis, J., Yovine, S.: Symbolic model-checking for real-time systems. Information and Computation 111(2), 193–244 (1994)MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Kesten, Y., Pnueli, A., Sifakis, J., Yovine, S.: Decidable integration graphs. Information and Computation 150(2), 209–243 (1999)MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Koymans, R.: Specifying real-time properties with metric temporal logic. Real-Time Systems 2(4), 255–299 (1990)CrossRefGoogle Scholar
  20. 20.
    Larsen, K.G., Pettersson, P., Yi, W.: Uppaal in a nutshell. Journal of Software Tools for Technology Transfer 1(1–2), 134–152 (1997)MATHCrossRefGoogle Scholar
  21. 21.
    Ouaknine, J., Worrell, J.: On the decidability of Metric Temporal Logic. In: Proc. 20th IEEE Symp. Logic in Computer Science (LICS 2005), Chicago, IL, USA, June 2005, pp. 188–197. IEEE Computer Society Press, Los Alamitos (2005)CrossRefGoogle Scholar
  22. 22.
    Yovine, S.: Kronos: A verification tool for real-time systems. Journal of Software Tools for Technology Transfer 1(1–2), 123–133 (1997)MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Houda Bel Mokadem
    • 1
  • Béatrice Bérard
    • 2
  • Patricia Bouyer
    • 1
  • François Laroussinie
    • 1
  1. 1.LSVCNRS & ENS de CachanFrance
  2. 2.LAMSADECNRS & Université Paris-DauphineFrance

Personalised recommendations