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 
, and prove that the related satisfiability and model checking (w.r.t. L/U automata) problems are Pspace-complete.
This research was partially supported by the MIUR grant ex-60% 2005-2006 Università di Salerno, and the European Commission via FP6 program under contracts FP6-1596 AEOLUS.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alur, R., Courcoubetis, C., Dill, D.L.: Model-checking in dense real-time. Information and Computation 104(1), 2–34 (1993)
Alur, R., Dill, D.: A theory of timed automata. Theoretical Computer Science 126(2), 183–235 (1994)
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)
Alur, R., Feder, T., Henzinger, Th.A.: The benefits of relaxing punctuality. Journal of the ACM 43(1), 116–146 (1996)
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)
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)
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)
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)
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)
Henzinger, T., Kopke, P., Puri, A., Varaiya, P.: What’s decidable about hybrid automata. Journal of Computer and System Sciences 57, 94–124 (1998)
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)
IEEE Computer Society. IEEE Standard for a High Performance Serial Bus. Std 1394-1995 (August 1996)
Lamport, L.: A Fast Mutual Exclusion Algorithm. ACM Transactions Computer Systems 5(1), 1–11 (1987)
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)
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)
Wang, F.: Parametric timing analysis for real-time systems. Information and Computation 130(2), 131–150 (1996)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bozzelli, L., La Torre, S. (2007). Decision Problems for Lower/Upper Bound Parametric Timed Automata. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds) Automata, Languages and Programming. ICALP 2007. Lecture Notes in Computer Science, vol 4596. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73420-8_79
Download citation
DOI: https://doi.org/10.1007/978-3-540-73420-8_79
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73419-2
Online ISBN: 978-3-540-73420-8
eBook Packages: Computer ScienceComputer Science (R0)