Timed Alternating-Time Temporal Logic

  • Thomas A. Henzinger
  • Vinayak S. Prabhu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4202)

Abstract

We add freeze quantifiers to the game logic ATL in order to specify real-time objectives for games played on timed structures. We define the semantics of the resulting logic TATL by restricting the players to physically meaningful strategies, which do not prevent time from diverging. We show that TATL can be model checked over timed automaton games. We also specify timed optimization problems for physically meaningful strategies, and we show that for timed automaton games, the optimal answers can be approximated to within any degree of precision.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Adler, B., de Alfaro, L., Faella, M.: Average reward timed games. In: Pettersson, P., Yi, W. (eds.) FORMATS 2005. LNCS, vol. 3829, pp. 65–80. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  2. 2.
    Alur, R., Bernadsky, M., Madhusudan, P.: Optimal reachability for weighted timed games. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 122–133. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  3. 3.
    Alur, R., Courcoubetis, C., Dill, D.L.: Model-checking in dense real-time. Inf. and Comp. 104(1), 2–34 (1993)CrossRefMathSciNetMATHGoogle Scholar
  4. 4.
    Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994)CrossRefMathSciNetMATHGoogle Scholar
  5. 5.
    Alur, R., Henzinger, T.A.: A really temporal logic. Journal of the ACM 41, 181–204 (1994)CrossRefMathSciNetMATHGoogle Scholar
  6. 6.
    Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-time temporal logic. Journal of the ACM 49, 672–713 (2002)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Asarin, E., Maler, O.: As soon as possible: Time optimal control for timed automata. In: Vaandrager, F.W., van Schuppen, J.H. (eds.) HSCC 1999. LNCS, vol. 1569, pp. 19–30. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  8. 8.
    Bouyer, P., Cassez, F., Fleury, E., Larsen, K.G.: Optimal strategies in priced timed game automata. In: Lodaya, K., Mahajan, M. (eds.) FSTTCS 2004. LNCS, vol. 3328, pp. 148–160. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    Bouyer, P., D’Souza, D., Madhusudan, P., Petit, A.: Timed control with partial observability. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 180–192. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  10. 10.
    Brihaye, T., Bruyère, V., Raskin, J.F.: On optimal timed strategies. In: Pettersson, P., Yi, W. (eds.) FORMATS 2005. LNCS, vol. 3829, pp. 49–64. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  11. 11.
    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)CrossRefGoogle Scholar
  12. 12.
    Courcoubetis, C., Yannakakis, M.: Minimum and maximum delay problems in real-time systems. Formal Methods in System Design 1(4), 385–415 (1992)CrossRefMATHGoogle Scholar
  13. 13.
    de Alfaro, L., Faella, M., Henzinger, T.A., Majumdar, R., Stoelinga, M.: The element of surprise in timed games. In: Amadio, R.M., Lugiez, D. (eds.) CONCUR 2003. LNCS, vol. 2761, pp. 144–158. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  14. 14.
    D’Souza, D., Madhusudan, P.: Timed control synthesis for external specifications. In: Alt, H., Ferreira, A. (eds.) STACS 2002. LNCS, vol. 2285, pp. 571–582. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  15. 15.
    Faella, M., La Torre, S., Murano, A.: Automata-theoretic decision of timed games. In: Cortesi, A. (ed.) VMCAI 2002. LNCS, vol. 2294, pp. 94–108. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  16. 16.
    Faella, M., La Torre, S., Murano, A.: Dense real-time games. In: LICS 2002, pp. 167–176. IEEE Computer Society, Los Alamitos (2002)Google Scholar
  17. 17.
    Henzinger, T.A., Kopke, P.W.: Discrete-time control for rectangular hybrid automata. Theoretical Computer Science 221, 369–392 (1999)CrossRefMathSciNetMATHGoogle Scholar
  18. 18.
    Henzinger, T.A., Nicollin, X., Sifakis, J., Yovine, S.: Symbolic model checking for real-time systems. Information and Computation 111, 193–244 (1994)CrossRefMathSciNetMATHGoogle Scholar
  19. 19.
    Laroussinie, F., Markey, N., Oreiby, G.: Model checking timed ATL for durational concurrent game structures. In: Asarin, E., Bouyer, P. (eds.) FORMATS 2006. LNCS, vol. 4202, pp. 245–259. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  20. 20.
    Maler, O., Pnueli, A., Sifakis, J.: On the synthesis of discrete controllers for timed systems (an extended abstract). In: Mayr, E.W., Puech, C. (eds.) STACS 1995. LNCS, vol. 900, pp. 229–242. Springer, Heidelberg (1995)Google Scholar
  21. 21.
    Pnueli, A., Asarin, E., Maler, O., Sifakis, J.: Controller synthesis for timed automata. In: Proc. System Structure and Control. Elsevier, Amsterdam (1998)Google Scholar
  22. 22.
    Wong-Toi, H., Hoffmann, G.: The control of dense real-time discrete event systems. In: Proc. of 30th Conf. Decision and Control, pp. 1527–1528 (1991)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Thomas A. Henzinger
    • 1
  • Vinayak S. Prabhu
    • 2
  1. 1.Department of Computer and Communication Sciences, EPFL 
  2. 2.Department of Electrical Engineering and Computer SciencesUC Berkeley

Personalised recommendations