Abstract
We deal with a parametric version of timed game automata (PGA), where clocks can be compared to parameters, and parameter synthesis. As usual, parametrization leads to undecidability of the most interesting problems, such as reachability game. It is not surprising then that the symbolic exploration of the state-space often does not terminate. It is known that the undecidability remains even when severely restricting the form of the parametric constraints. Since in classical timed automata, real-valued clocks are always compared to integers for all practical purposes, we solve undecidability and termination issues by computing parameters as bounded integers. We give a symbolic algorithm that computes the set of winning states for a given PGA and the corresponding set of bounded integer parameter valuations as symbolic constraints between parameters. We argue the relevance of this approach and demonstrate its practical usability with a small case-study.
This work was partially funded by the ANR national research program ImpRo (ANR-2010-BLAN-0317).
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., Dill, D.: A theory of timed automata. Theoretical Computer Science 126(2), 183–235 (1994)
Alur, R., Henzinger, T.A., Vardi, M.Y.: Parametric real-time reasoning. In: ACM Symposium on Theory of Computing, pp. 592–601 (1993)
André, E., Chatain, T., Encrenaz, E., Fribourg, L.: An inverse method for parametric timed automata. In: RP Workshop on Reachability Problems, vol. 223, pp. 29–46. Liverpool, U.K (2008)
Asarin, E., Maler, O., Pnueli, A., Sifakis, J.: Controller synthesis for timed automata. In: Proc. IFAC SSSC. Elsevier (1998)
Behrmann, G., Cougnard, A., David, A., Fleury, E., Larsen, K.G., Lime, D.: UPPAAL-tiga: Time for playing games! In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 121–125. Springer, Heidelberg (2007)
Bozzelli, L., Torre, S.L.: Decision problems for lower/upper bound parametric timed automata. Formal Methods in System Design 35(2), 121–151 (2009)
Bruyère, V., Raskin, J.-F.: Real-time model-checking: Parameters everywhere. Logical Methods in Computer Science 3(1), 1–30 (2007)
Cassez, F., David, A., Fleury, E., Larsen, K.G., Lime, D.: Efficient on-the-fly algorithms for the analysis of timed games. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653, pp. 66–80. Springer, Heidelberg (2005)
Cassez, F., Jessen, J.J., Larsen, K.G., Raskin, J.-F., Reynier, P.-A.: Automatic synthesis of robust and optimal controllers – an industrial case study. In: Majumdar, R., Tabuada, P. (eds.) HSCC 2009. LNCS, vol. 5469, pp. 90–104. Springer, Heidelberg (2009)
Henzinger, T.A., Nicollin, X., Sifakis, J., Yovine, S.: Symbolic model checking for real-time systems. Inform. and Computation 111(2), 193–244 (1994)
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)
Jovanović, A., Faucou, S., Lime, D., Roux, O.H.: Real-time control with parametric timed reachability games. In: Proc. of WODES 2012, pp. 323–330. IFAC (October 2012)
Jovanović, A., Lime, D., Roux, O.H.: Integer parameter synthesis for timed automata. In: Piterman, N., Smolka, S.A. (eds.) TACAS 2013. LNCS, vol. 7795, pp. 401–415. Springer, Heidelberg (2013)
Jurdziński, M., Trivedi, A.: Reachability-time games on timed automata. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 838–849. Springer, Heidelberg (2007)
Maler, O., Pnueli, A., Sifakis, J.: On the synthesis of discrete controllers for timed systems. In: Mayr, E.W., Puech, C. (eds.) STACS 1995. LNCS, vol. 900, pp. 229–242. Springer, Heidelberg (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this paper
Cite this paper
Jovanović, A., Lime, D., Roux, O.H. (2013). Synthesis of Bounded Integer Parameters for Parametric Timed Reachability Games. In: Van Hung, D., Ogawa, M. (eds) Automated Technology for Verification and Analysis. Lecture Notes in Computer Science, vol 8172. Springer, Cham. https://doi.org/10.1007/978-3-319-02444-8_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-02444-8_8
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02443-1
Online ISBN: 978-3-319-02444-8
eBook Packages: Computer ScienceComputer Science (R0)