Decision Problems for Lower/Upper Bound Parametric Timed Automata

  • Laura Bozzelli
  • Salvatore La Torre
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4596)

Abstract

We investigate a class of parametric timed automata, called lower bound/upper bound (L/U) automata, where each parameter occurs in the timing constraints either as a lower bound or as un upper bound. For such automata, we show that checking if for a parameter valuation (resp., all parameter valuations) there is an infinite accepting run is Pspace-complete. We extend these results by allowing the specification of constraints on parameters as a linear system. We show that the considered decision problems are still Pspace-complete, if the lower bound parameters are not compared to the upper bound parameters in the linear system, and are undecidable in general. Finally, we consider a parametric extension of Open image in new window , and prove that the related satisfiability and model checking (w.r.t. L/U automata) problems are Pspace-complete.

Keywords

Model Check Decision Problem Linear Constraint Linear Expression Parametric Extension 
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.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alur, R., Courcoubetis, C., Dill, D.L.: Model-checking in dense real-time. Information and Computation 104(1), 2–34 (1993)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Alur, R., Dill, D.: A theory of timed automata. Theoretical Computer Science 126(2), 183–235 (1994)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Alur, R., Etessami, K., La Torre, S., Peled, D.: Parametric temporal logic for model measuring. ACM Transactions on Computational Logic 2(3), 388–407 (2001)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Alur, R., Feder, T., Henzinger, Th.A.: The benefits of relaxing punctuality. Journal of the ACM 43(1), 116–146 (1996)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Alur, R., Henzinger, T.A., Vardi, M.Y.: Parametric real-time reasoning. In: STOC 1993. Proc. of the 25th ACM Symposium on Theory of Computing, pp. 592–601. ACM Press, New York (1993)CrossRefGoogle Scholar
  6. 6.
    Alur, R., Madhusudan, P.: Decision problems for timed automata: a survey. In: Bernardo, M., Corradini, F. (eds.) Formal Methods for the Design of Real-Time Systems. LNCS, vol. 3185, pp. 1–24. Springer, Heidelberg (2004)Google Scholar
  7. 7.
    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)Google Scholar
  8. 8.
    Bruyère, V., Raskin, J.F.: Real-time model-checking: Parameters everywhere. In: Pandya, P.K., Radhakrishnan, J. (eds.) FST TCS 2003. LNCS, vol. 2914, pp. 100–111. Springer, Heidelberg (2003)Google Scholar
  9. 9.
    Emerson, E.A., Trefler, R.: Parametric Quantitative Temporal Reasoning. In: LICS 1999. Proc. 14th Ann. Symp. Logic in Computer Science, pp. 336–343. IEEE Computer Society Press, Los Alamitos (1999)Google Scholar
  10. 10.
    Henzinger, T., Kopke, P., Puri, A., Varaiya, P.: What’s decidable about hybrid automata. Journal of Computer and System Sciences 57, 94–124 (1998)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Hune, T., Romijn, J., Stoelinga, M., Vaandrager, F.: Linear parametric model checking of timed automata. Journal of Logic and Algebraic Programming 52,53, 183–220 (2002)CrossRefMathSciNetGoogle Scholar
  12. 12.
    IEEE Computer Society. IEEE Standard for a High Performance Serial Bus. Std 1394-1995 (August 1996)Google Scholar
  13. 13.
    Lamport, L.: A Fast Mutual Exclusion Algorithm. ACM Transactions Computer Systems 5(1), 1–11 (1987)CrossRefGoogle Scholar
  14. 14.
    Pnueli, A.: The temporal logic of programs. In: Proc. of the 18th IEEE Symposium on Foundations of Computer Science, pp. 46–77. IEEE Computer Society Press, Los Alamitos (1977)Google Scholar
  15. 15.
    Pottier, L.: Minimal solutions of linear diophantine systems: bounds and algorithms. In: Book, R.V. (ed.) Rewriting Techniques and Applications. LNCS, vol. 488, pp. 162–173. Springer, Heidelberg (1991)Google Scholar
  16. 16.
    Wang, F.: Parametric timing analysis for real-time systems. Information and Computation 130(2), 131–150 (1996)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Laura Bozzelli
    • 1
  • Salvatore La Torre
    • 2
  1. 1.Università di Napoli Federico II , Via Cintia, 80126 - NapoliItaly
  2. 2.Università degli Studi di Salerno, Via Ponte Don Melillo - 84084 FiscianoItaly

Personalised recommendations