Abstract
Solving games played on timed automata is a well-known problem and has led to tools and industrial case studies. In these games, the first player (Controller) chooses delays and actions and the second player (Perturbator) resolves the non-determinism of actions. However, the model of timed automata suffers from mathematical idealizations such as infinite precision of clocks and instantaneous synchronization of actions. To address this issue, we extend the theory of timed games in two directions. First, we study the synthesis of robust strategies for Controller which should be tolerant to adversarially chosen clock imprecisions. Second, we address the case of a stochastic perturbation model where both clock imprecisions and the non-determinism are resolved randomly. These notions of robustness guarantee the implementability of synthesized controllers. We provide characterizations of the resulting games for Büchi conditions, and prove the EXPTIME-completeness of the corresponding decision problems.
This work was partly supported by ANR projects ECSPER (ANR-2009-JCJC-0069) and ImpRo (ANR-2010-BLAN-0317), European project Cassting (FP7-ICT-601148), and ERC starting grant inVEST (FP7-279499), and ARC Project : Game Theory for the Automatic Synthesis of Computer Systems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Alur, R., Dill, D.L.: A theory of timed automata. Theoretical Computer Science 126(2), 183–235 (1994)
Asarin, E., Maler, O., Pnueli, A., Sifakis, J.: Controller synthesis for timed automata. In: SSC 1998, pp. 469–474. Elsevier Science (1998)
Basset, N., Asarin, E.: Thin and thick timed regular languages. In: Fahrenberg, U., Tripakis, S. (eds.) FORMATS 2011. LNCS, vol. 6919, pp. 113–128. Springer, Heidelberg (2011)
Beauquier, D.: On probabilistic timed automata. Theor. Comput. Sci. 292(1), 65–84 (2003)
Bengtsson, J., Yi, W.: Timed automata: Semantics, algorithms and tools. In: Desel, J., Reisig, W., Rozenberg, G. (eds.) ACPN 2003. LNCS, vol. 3098, pp. 87–124. Springer, Heidelberg (2004)
Berthomieu, B., Menasche, M.: An enumerative approach for analyzing time Petri nets. In: WCC 1983, pp. 41–46. North-Holland/IFIP (September 1983)
Bouyer, P., Markey, N., Reynier, P.-A.: Robust analysis of timed automata via channel machines. In: Amadio, R.M. (ed.) FOSSACS 2008. LNCS, vol. 4962, pp. 157–171. Springer, Heidelberg (2008)
Bouyer, P., Markey, N., Sankur, O.: Robust reachability in timed automata: A game-based approach. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds.) ICALP 2012, Part II. LNCS, vol. 7392, pp. 128–140. Springer, Heidelberg (2012)
Bouyer, P., Markey, N., Sankur, O.: Robustness in timed automata. In: Abdulla, P.A., Potapov, I. (eds.) RP 2013. LNCS, vol. 8169, pp. 1–18. Springer, Heidelberg (2013)
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)
Chatterjee, K., Henzinger, T.A., Prabhu, V.S.: Timed parity games: Complexity and robustness. Logical Methods in Computer Science 7(4) (2011)
De Wulf, M., Doyen, L., Markey, N., Raskin, J.-F.: Robust safety of timed automata. Formal Methods in System Design 33(1-3), 45–84 (2008)
Dill, D.L.: Timing assumptions and verification of finite-state concurrent systems. In: Sifakis, J. (ed.) AVMFSS 1989. LNCS, vol. 407, pp. 197–212. Springer, Heidelberg (1990)
Forejt, V., Kwiatkowska, M., Norman, G., Trivedi, A.: Expected reachability-time games. In: Chatterjee, K., Henzinger, T.A. (eds.) FORMATS 2010. LNCS, vol. 6246, pp. 122–136. Springer, Heidelberg (2010)
Henzinger, T.A., Sifakis, J.: The embedded systems design challenge. In: Misra, J., Nipkow, T., Sekerinski, E. (eds.) FM 2006. LNCS, vol. 4085, pp. 1–15. Springer, Heidelberg (2006)
Jensen, H.E.: Model checking probabilistic real time systems. In: Proc. 7th Nordic Workshop on Programming Theory, pp. 247–261. Citeseer (1996)
Kwiatkowska, M., Norman, G., Segala, R., Sproston, J.: Automatic verification of real-time systems with discrete probability distributions. Theor. Comput. Sci. 282(1), 101–150 (2002)
Oualhadj, Y., Reynier, P.-A., Sankur, O.: Probabilistic Robust Timed Games. Technical report (June 2014), http://hal.archives-ouvertes.fr/hal-01010813
Puri, A.: Dynamical properties of timed automata. Discrete Event Dynamic Systems 10(1-2), 87–113 (2000)
Putterman, M.L.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. John Wiley and Sons, New York (1994)
Sankur, O., Bouyer, P., Markey, N.: Shrinking timed automata. In: FSTTCS 2011. LIPIcs, vol. 13, pp. 375–386. Leibniz-Zentrum für Informatik (2011)
Sankur, O., Bouyer, P., Markey, N., Reynier, P.-A.: Robust controller synthesis in timed automata. In: D’Argenio, P.R., Melgratti, H. (eds.) CONCUR 2013 – Concurrency Theory. LNCS, vol. 8052, pp. 546–560. Springer, Heidelberg (2013)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Oualhadj, Y., Reynier, PA., Sankur, O. (2014). Probabilistic Robust Timed Games. In: Baldan, P., Gorla, D. (eds) CONCUR 2014 – Concurrency Theory. CONCUR 2014. Lecture Notes in Computer Science, vol 8704. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44584-6_15
Download citation
DOI: https://doi.org/10.1007/978-3-662-44584-6_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-44583-9
Online ISBN: 978-3-662-44584-6
eBook Packages: Computer ScienceComputer Science (R0)