Efficient On-the-Fly Algorithms for the Analysis of Timed Games

  • Franck Cassez
  • Alexandre David
  • Emmanuel Fleury
  • Kim G. Larsen
  • Didier Lime
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3653)


In this paper, we propose the first efficient on-the-fly algorithm for solving games based on timed game automata with respect to reachability and safety properties

The algorithm we propose is a symbolic extension of the on-the-fly algorithm suggested by Liu & Smolka [15] for linear-time model-checking of finite-state systems. Being on-the-fly, the symbolic algorithm may terminate long before having explored the entire state-space. Also the individual steps of the algorithm are carried out efficiently by the use of so-called zones as the underlying data structure.

Various optimizations of the basic symbolic algorithm are proposed as well as methods for obtaining time-optimal winning strategies (for reachability games). Extensive evaluation of an experimental implementation of the algorithm yields very encouraging performance results.


Winning Strategy Symbolic State Controller Synthesis Quotient Graph Time Automaton 
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.


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  1. 1.
    Altisen, K., Tripakis, S.: Tools for controller synthesis of timed systems. In: Proc. 2nd Work. on Real-Time Tools (RT-TOOLS 2002), Proc. published as Technical Report 2002-025, Uppsala University, Sweden (2002)Google Scholar
  2. 2.
    Alur, R., Dill, D.: A theory of timed automata. Theoretical Computer Science 126(2), 183–235 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Alur, R., La Torre, S., Pappas, G.J.: Optimal Paths in Weighted Timed Automata. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 49–62. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  4. 4.
    Andersen, H.R.: Model Checking and Boolean Graphs. Theoretical Computer Science 126(1), 3–30 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    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
  6. 6.
    Asarin, E., Maler, O., Pnueli, A., Sifakis, J.: Controller Synthesis for Timed Automata. In: Proc. IFAC Symp. on System Structure & Control, pp. 469–474. Elsevier Science, Amsterdam (1998)Google Scholar
  7. 7.
    Behrmann, G.: Distributed reachability analysis in timed automata. Journal of Software Tools for Technology Transfer (STTT) 7(1), 19–30 (2005)CrossRefGoogle Scholar
  8. 8.
    Bozga, M., Daws, C., Maler, O., Olivero, A., Tripakis, S., Yovine, S.: Kronos: a Model-Checking Tool for Real-Time Systems. In: Y. Vardi, M. (ed.) CAV 1998. LNCS, vol. 1427, pp. 546–550. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  9. 9.
    De Alfaro, L., Henzinger, T.A., Majumdar, R.: Symbolic algorithms for infinite-state games. In: Larsen, K.G., Nielsen, M. (eds.) CONCUR 2001. LNCS, vol. 2154, pp. 536–550. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  10. 10.
    Holzmann, G.J.: The SPIN Model Checker. Addison-Wesley, Reading (2003)Google Scholar
  11. 11.
    La Torre, S., Mukhopadhyay, S., Murano, A.: Optimal-Reachability and Control for Acyclic Weighted Timed Automata. In: Proc. 2nd IFIP Conf. on Theoretical Computer Science (TCS 2002), vol. 223, pp. 485–497. Kluwer, Norwell (2002)Google Scholar
  12. 12.
    Larsen, K.G.: Efficient Local Correctness Checking. In: Proc. of Conf. of Computer Assisted Verification (CAV 1992). LNCS, vol. 663, pp. 30–43. Springer, Heidelberg (1992)Google Scholar
  13. 13.
    Larsen, K.G., Pettersson, P., Yi, W.: Uppaal in a Nutshell. Journal of Software Tools for Technology Transfer (STTT) 1(1-2), 134–152 (1997)zbMATHCrossRefGoogle Scholar
  14. 14.
    Lewerentz, C., Lindner, T.: Production Cell: A Comparative Study in Formal Specification and Verification. In: Jähnichen, S., Broy, M. (eds.) KORSO 1995. LNCS, vol. 1009, pp. 388–416. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  15. 15.
    Liu, X., Smolka, S.: Simple Linear-Time Algorithm for Minimal Fixed Points. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 53–66. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  16. 16.
    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)Google Scholar
  17. 17.
    Melcher, H., Winkelmann, K.: Controller Synthesis for the “Production Cell” Case Study. In: Proc. of 2nd Work. on Formal Methods in Software Practice, pp. 24–36. ACM Press, New York (1998)CrossRefGoogle Scholar
  18. 18.
    Rasmussen, J., Larsen, K.G., Subramani, K.: Resource-optimal scheduling using priced timed automata. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 220–235. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  19. 19.
    Thomas, W.: On the Synthesis of Strategies in Infinite Games. In: Mayr, E.W., Puech, C. (eds.) STACS 1995. LNCS, vol. 900, pp. 1–13. Springer, Heidelberg (1995) (invited talk)Google Scholar
  20. 20.
    Tripakis, S., Altisen, K.: On-the-Fly Controller Synthesis for Discrete and Timed Systems. In: Wing, J.M., Woodcock, J.C.P., Davies, J. (eds.) FM 1999. LNCS, vol. 1708, pp. 233–252. Springer, Heidelberg (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Franck Cassez
    • 1
  • Alexandre David
    • 2
  • Emmanuel Fleury
    • 2
  • Kim G. Larsen
    • 2
  • Didier Lime
    • 2
  1. 1.IRCCyN, UMR 6597, CNRSFrance
  2. 2.Computer Science Department, CISS (Center for Embedded Software Systems)Aalborg UniversityDenmark

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