Advertisement

Memory Event Clocks

  • James Jerson Ortiz
  • Axel Legay
  • Pierre-Yves Schobbens
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6246)

Abstract

We introduce logics and automata based on memory event clocks. A memory clock is not really reset: instead, a new clock is created, while the old one is still accessible by indexing. We can thus constrain not only the time since the last reset (which was the main limitation in event clocks), but also since previous resets. When we introduce these clocks in the linear temporal logic of the reals, we create Recursive Memory Event Clocks Temporal Logic (RMECTL). It turns out to have the same expressiveness as the Temporal Logic with Counting (TLC) of Hirshfeld and Rabinovich. We then examine automata with recursive memory event clocks (RMECA). Recursive event clocks are reset by simpler RMECA, hence the name “recursive”. In contrast, we show that for RMECA, memory clocks do not add expressiveness, but only concision. The original RECA define thus a fully decidable, robust and expressive level of real-time expressiveness.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Alur, R., Feder, T., Henzinger, T.A.: The benefits of relaxing punctuality. J. ACM 43(1), 116–146 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Alur, R., Fix, L., Henzinger, T.A.: A determinizable class of timed automata. In: Dill, D.L. (ed.) CAV 1994. LNCS, vol. 818, pp. 1–13. Springer, Heidelberg (1994)Google Scholar
  4. 4.
    Alur, R., Henzinger, T.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
  5. 5.
    Alur, R., Henzinger, T.A.: Real-time logics: Complexity and expressiveness. Inf. Comput. 104(1), 35–77 (1994)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Annichini, A., Bouajjani, A., Sighireanu, M.: Trex: A tool for reachability analysis of complex systems. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 368–372. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  7. 7.
    Baier, C., Bertrand, N., Bouyer, P., Brihaye, T.: When are timed automata determinizable? In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5556, pp. 43–54. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  8. 8.
    Bouyer, P., Chevalier, F., Markey, N.: On the expressiveness of TPTL and MTL. In: Sarukkai, S., Sen, S. (eds.) FSTTCS 2005. LNCS, vol. 3821, pp. 432–443. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  9. 9.
    Bozga, M., Daws, C., Maler, O., Olivero, A., Tripakis, S., Yovine, S.: Kronos: A model-checking tool for real-time systems. In: Vardi, M.Y. (ed.) CAV 1998. LNCS, vol. 1427, pp. 546–550. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  10. 10.
    Gabbay, D.M., Hodkinson, I.M.: An axiomatization of the temporal logic with until and since over the real numbers. J. Log. Comput. 1(2), 229–259 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Henzinger, T.A., Raskin, J.-F., Schobbens, P.-Y.: The regular real-time languages. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 580–591. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  12. 12.
    Hirshfeld, Y., Rabinovich, A.M.: A framework for decidable metrical logics. In: Wiedermann, J., Van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, pp. 422–432. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  13. 13.
    Hirshfeld, Y., Rabinovich, A.M.: An expressive temporal logic for real time. In: Královič, R., Urzyczyn, P. (eds.) MFCS 2006. LNCS, vol. 4162, pp. 492–504. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  14. 14.
    Hirshfeld, Y., Rabinovich, A.M.: Expressiveness of metric modalities for continuous time. In: Grigoriev, D., Harrison, J., Hirsch, E.A. (eds.) CSR 2006. LNCS, vol. 3967, pp. 211–220. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  15. 15.
    Ouaknine, J., Worrell, J.: On the language inclusion problem for timed automata: Closing a decidability gap. In: LICS, pp. 54–63. IEEE Computer Society, Los Alamitos (2004)Google Scholar
  16. 16.
    Ouaknine, J., Worrell, J.: Some recent results in metric temporal logic. In: Cassez, F., Jard, C. (eds.) FORMATS 2008. LNCS, vol. 5215, pp. 1–13. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  17. 17.
    Parys, P., Walukiewicz, I.: Weak alternating timed automata. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5556, pp. 273–284. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  18. 18.
    Rabinovich, A.: Complexity of metric temporal logics with counting and the Pnueli modalities. In: Cassez, F., Jard, C. (eds.) FORMATS 2008. LNCS, vol. 5215, pp. 93–108. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  19. 19.
    Raskin, J.-F.: Logics, Automata and Classical Theories for Deciding Real Time. Phd thesis, FUNDP University, Belgium (1999)Google Scholar
  20. 20.
    Raskin, J.-F., Schobbens, P.-Y.: State clock logic: A decidable real-time logic. In: Maler, O. (ed.) HART 1997. LNCS, vol. 1201, pp. 33–47. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  21. 21.
    The UPPAAL tool, http://www.uppaal.com/

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • James Jerson Ortiz
    • 1
  • Axel Legay
    • 2
    • 3
  • Pierre-Yves Schobbens
    • 1
  1. 1.Computer Science FacultyUniversity of Namur 
  2. 2.INRIA/IRISARennes
  3. 3.Institut MontefioreUniversity of Liège 

Personalised recommendations