Abstract
We address the problem of alternating simulation refinement for concurrent timed games (TG). We show that checking timed alternating simulation between TG is EXPTIME-complete, and provide a logical characterization of this preorder in terms of a meaningful fragment of a new logic, TAMTL*. TAMTL* is an action-based timed extension of standard alternating-time temporal logic ATL*, which allows to quantify over strategies where the designated coalition of players is not responsible for blocking time. While for full TAMTL*, model-checking TG is undecidable, we show that for its fragment TAMTL, corresponding to the timed version of ATL, the problem is instead decidable and in EXPTIME.
Similar content being viewed by others
References
Aceto L., Jeffrey A.: A complete axiomatization of timed bisimulation for a class of timed regular behaviours. Theor. Comput. Sci. 152(2), 251–268 (1995)
Alur R., Courcoubetis C., Dill D.L.: Model-checking in dense real-time. Inf. Comput. 104(1), 2–34 (1993)
Alur R., Dill D.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994)
Alur R., Henzinger T.A., Kupferman O.: Alternating-time temporal logic. J. ACM 49(5), 672–713 (2002)
Alur R., Henzinger T.A., Kupferman O., Vardi M.Y.: Alternating refinement relations. In: Proceedings of the 9th CONCUR, LNCS 1466, pp. 163–178 (1998)
Brihye T., Laroussinie F., Markey N., Oreiby G.: Timed concurrent game structures. In: Proceedings of the 18th CONCUR, LNCS 4703, pp. 445–459 (2007)
Bulychev P., Chatain T., David A., Larsen K.G.: Efficient on-the-fly algorithm for checking alternating timed simulation. In: Proceedings of the 7th FORMATS, LNCS 5813, pp. 73–87 (2009)
Čerāns K.: Decidability of bisimulation equivalences for parallel timer processes. In: Proceedings of the 4th CAV,LNCS 663, pp. 302–315 (1992)
de Alfaro L., Dias da Silva L., Faella M., Legay A., Roy P., Sorea M.: Sociable interfaces. In: Proceedings of the 5th FROCOS, LNCS 3717, pp. 81–105 (2005)
de Alfaro L., Faella M., Henzinger T.A., Majumdar R., Stoelinga M.: The element of surprise in timed games. In: 14th CONCUR, LNCS 2761, pp. 142–156 (2003)
de Alfaro L., Henzinger T.A.: Interface automata. In: Proceedings of the 9th FSE, ACM, pp. 109–120 (2001)
D’Souza D., Prabhakar P.: On the expressiveness of MTL in the pointwise and continuous semantics. Int. J. Softw. Tools Technol. Transf. 9(1), 1–4 (2007)
Emerson E.A., Halpern J.Y.: Sometimes and not never revisited: on branching versus linear time. J. ACM 33(1), 151–178 (1986)
Henzinger T.A., Prabhu V.S.: Timed alternating-time temporal logic. In: Proceedings of the 4th FORMATS, LNCS 4202, pp. 1–17 (2006)
Jurdzinski M., Laroussinie F., Sproston J.: Model checking probabilistic timed automata with one or two clocks. In: Proceedings of the 13th TACAS, LNCS 4424, pp. 170–184 (2007)
Koymans R.: Specifying real-time properties with metric temporal logic. Real-Time Syst. 2(4), 255–299 (1990)
Laroussinie F., Schnoebelen Ph.: The state explosion problem from trace to bisimulation equivalence. In: Proceedings of the 3rd FOSSACS, LNCS 1784, pp. 192–207 (2000)
Milner R.: A complete axiomatisation for observational congruence of finite-state behaviors. Inf. Comput. 81(2), 227–247 (1989)
Ouaknine J. Worrell J.L: On metric temporal logic and faulty turing machines. In: Proceedings of the 9th FOSSACS, LNCS 3921, pp. 217–230 (2006)
Ouaknine J., Worrell J.: On the decidability of metric temporal logic. In: Proceedings of the 20th LICS, pp. 188–197. IEEE Computer Society Press (2005)
Tasiran S., Alur R., Kurshan R.P., Brayton R.K.: Verifying abstractions of timed systems. In: Proceedings of the 7th CONCUR, LNCS 1119, pp. 546–562 (1996)
Thomas, W.: Automata on infinite objects. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science: Formal Models and Sematics, vol. B, pp. 133–192 (1990)
Author information
Authors and Affiliations
Corresponding author
Additional information
A preliminary version of the paper appears in Proceedings of the 29th International Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS’09), IIT Kanpur, India, December 15–17, 2009. Leibniz International Proceedings in Informatics (LIPIcs).
Rights and permissions
About this article
Cite this article
Bozzelli, L., Legay, A. & Pinchinat, S. On timed alternating simulation for concurrent timed games. Acta Informatica 49, 249–279 (2012). https://doi.org/10.1007/s00236-012-0158-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00236-012-0158-y