Abstract
We consider the problem of model-checking a parametric extension of the logic TCTL over timed automata and establish its decidability. Given a timed automaton, we show that the set of durations of runs starting from a region and ending in another region is definable in the arithmetic of Presburger (when the time domain is discrete) or in the theory of the reals (when the time domain is dense). With this logical definition, we show that the parametric model-checking problem for the logic TCTL can easily be solved. More generally, we are able to effectively characterize the values of the parameters that satisfy the parametric TCTL formula.
Keywords
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.
Supported by the FRFC project “Centre Fédéré en Vérification” funded by the Belgian National Science Fundation (FNRS) under grant nr 2.4530.02
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
R. Alur, C. Courcoubetis, and D.L. Dill. Model checking for real-time systems. In Proceedings of the Fifth Annual Symposium on Logic in Computer Science, pages 414–425. IEEE Computer Society Press, 1990.
R. Alur and D.L. Dill. A theory of timed automata. Theoretical Computer Science, 126:183–235, 1994.
R. Alur, T.A. Henzinger, and M.Y. Vardi. Parametric real-time reasoning. In Proceedings of the 25th Annual Symposium on Theory of Computing, pages 592–601. ACM Press, 1993.
Rajeev Alur, Kousha Etessami, Salvatore La Torre, and Doron Peled. Parametric temporal logic for “model measuring”. Lecture Notes in Computer Science, 1644:159–173, 1999.
Bernard Boigelot, Sébastien Jodogne, and Pierre Wolper. On the use of weak automata for deciding linear arithmetic with integer and real variables. In Proc. International Joint Conference on Automated Reasoning, volume 2083, pages 611–625. Springer-Verlag, 2001.
V. Bruyère, E. Dall’olio, and J.-F. Raskin. Durations, parametric model-checking in timed automata with Presburger arithmetic. Technical Report CFV-2002-1, Centre Fédéré en Vérification (Belgique), 2002. http://www.ulb.ac.be/di/ssd/cfv/TechReps/TechRep CFV 2002 1.ps.
H. Comon and Y. Jurski. Timed automata and the theory of real numbers. In Proc. 10th Int. Conf. Concurrency Theory (CONCUR’99), Eindhoven, The Netherlands, Aug. 1999, volume 1664of Lecture Notes in Computer Science, pages 242–257. Springer, 1999.
E. Allen Emerson and Richard J. Trefler. Parametric quantitative temporal reasoning. In Logic in Computer Science, pages 336–343, 1999.
Jeanne Ferrante and Charles W. Racko.. The computational complexity of logical theories. Number 718 in Lecture Notes in Mathematics. Springer-Verlag, 1979.
T.A. Henzinger. It’s about time: Real-time logics reviewed. In D. Sangiorgi and R. de Simone, editors, CONCUR 98: Concurrency Theory, Lecture Notes in Computer Science 1466, pages 439–454. Springer-Verlag, 1998.
Farn Wang. Timing behavior analysis for real-time systems. In In Proceedings of the Tenth IEEE Symposium on Logic in Computer Science, pages 112–122, 1995.
Farn Wang and Pao-Ann Hsiung. Parametric analysis of computer systems. In Algebraic Methodology and Software Technology, pages 539–553, 1997.
Volker Weispfenning. Mixed real-integer linear quantifier elimination. In ISSAC: Proceedings of the ACM SIGSAM International Symposium on Symbolic and Algebraic Computation, 1999.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bruyère, V., Dall’Olio, E., Raskin, JF. (2003). Durations, Parametric Model-Checking in Timed Automata with Presburger Arithmetic. In: Alt, H., Habib, M. (eds) STACS 2003. STACS 2003. Lecture Notes in Computer Science, vol 2607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36494-3_60
Download citation
DOI: https://doi.org/10.1007/3-540-36494-3_60
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-00623-7
Online ISBN: 978-3-540-36494-8
eBook Packages: Springer Book Archive