Predictability of Event Occurrences in Timed Systems

  • Franck Cassez
  • Alban Grastien
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8053)


We address the problem of predicting events’ occurrences in partially observable timed systems modelled by timed automata. Our contribution is many-fold: 1) we give a definition of bounded predictability, namely k-predictability, that takes into account the minimum delay between the prediction and the actual event’s occurrence; 2) we show that 0-predictability is equivalent to the original notion of predictability of S. Genc and S. Lafortune; 3) we provide a necessary and sufficient condition for k-predictability (which is very similar to k-diagnosability) and give a simple algorithm to check k-predictability; 4) we address the problem of predictability of events’ occurrences in timed automata and show that the problem is PSPACE-complete.


Fault Diagnosis Observable Event Time System Event Occurrence Discrete Event System 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Sampath, M., Sengupta, R., Lafortune, S., Sinnamohideen, K., Teneketzis, D.: Diagnosability of discrete event systems. IEEE Trans. on Auto. Cont. 40(9) (1995)Google Scholar
  2. 2.
    Yoo, T.S., Lafortune, S.: Polynomial-time verification of diagnosability of partially-observed discrete-event systems. IEEE Trans. on Auto. Cont. 47(9), 1491–1495 (2002)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Jiang, S., Huang, Z., Chandra, V., Kumar, R.: A polynomial algorithm for testing diagnosability of discrete event systems. IEEE Trans. on Auto. Cont. 46(8) (2001)Google Scholar
  4. 4.
    Alur, R., Dill, D.: A theory of timed automata. Theoretical Computer Science 126, 183–235 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Genc, S., Lafortune, S.: Predictability of event occurrences in partially-observed discrete-event systems. Automatica 45(2), 301–311 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Genc, S., Lafortune, S.: Predictability in discrete-event systems under partial observation. In: IFAC Symp. on Fault Detection, Supervision and Safety of Technical Processes, Beijing, China. IEEE (2006)Google Scholar
  7. 7.
    Jéron, T., Marchand, H., Genc, S., Lafortune, S.: Predictability of sequence patterns in discrete event systems. In: IFAC WC, Seoul, Korea, pp. 537–543 (2008)Google Scholar
  8. 8.
    Brandán Briones, L., Madalinski, A.: Bounded predictability for faulty discrete event systems. In: 30th Int. Conf. of the Chilean Computer Science Society (2011)Google Scholar
  9. 9.
    Tripakis, S.: Fault diagnosis for timed automata. In: Damm, W., Olderog, E.-R. (eds.) FTRTFT 2002. LNCS, vol. 2469, pp. 205–224. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  10. 10.
    Bouyer, P., Chevalier, F., D’Souza, D.: Fault diagnosis using timed automata. In: Sassone, V. (ed.) FOSSACS 2005. LNCS, vol. 3441, pp. 219–233. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  11. 11.
    Larsen, K.G., Pettersson, P., Yi, W.: Uppaal in a nutshell. STTT 1(1-2), 134–152 (1997)zbMATHCrossRefGoogle Scholar
  12. 12.
    Cassez, F., Grastien, A.: Predictability of Event Occurrences in Timed Systems. CoRR/abs arXiv:1306.0662 [cs.SY] (2013),
  13. 13.
    Behrmann, G., Fehnker, A., Hune, T., Larsen, K.G., Pettersson, P., Romijn, J., Vaandrager, F.: Minimum-cost reachability for priced timed automata. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 147–161. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  14. 14.
    Courcoubetis, C., Yannakakis, M.: Minimum and maximum delay problems in real-time systems. Formal Methods in System Design 1(4), 385–415 (1992)zbMATHCrossRefGoogle Scholar
  15. 15.
    De Wulf, M., Doyen, L., Raskin, J.-F.: Almost ASAP semantics: From timed models to timed implementations. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 296–310. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  16. 16.
    Cassez, F., Henzinger, T.A., Raskin, J.-F.: A Comparison of Control Problems for Timed and Hybrid Systems. In: Tomlin, C.J., Greenstreet, M.R. (eds.) HSCC 2002. LNCS, vol. 2289, pp. 134–148. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  17. 17.
    Cassez, F., Tripakis, S.: Fault diagnosis with static and dynamic diagnosers. Fundamenta Informaticae 88(4), 497–540 (2008)MathSciNetzbMATHGoogle Scholar
  18. 18.
    Cassez, F., Dubreil, J., Marchand, H.: Synthesis of opaque systems with static and dynamic masks. Formal Methods in System Design 40(1), 88–115 (2012)zbMATHCrossRefGoogle Scholar
  19. 19.
    Cassez, F., Tripakis, S., Altisen, K.: Sensor minimization problems with static or dynamic observers for fault diagnosis. In: ACSD 2007, pp. 90–99. IEEE Comp. Soc. (2007)Google Scholar
  20. 20.
    Cassez, F., Dubreil, J., Marchand, H.: Dynamic observers for the synthesis of opaque systems. In: Liu, Z., Ravn, A.P. (eds.) ATVA 2009. LNCS, vol. 5799, pp. 352–367. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  21. 21.
    Cassez, F., Tripakis, S., Altisen, K.: Synthesis of optimal-cost dynamic observers for fault diagnosis of discrete-event systems. In: TASE 2007, pp. 316–325. IEEE Comp. Soc. (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Franck Cassez
    • 1
  • Alban Grastien
    • 2
  1. 1.NICTA and UNSWAustralia
  2. 2.NICTA and ANUAustralia

Personalised recommendations