Removing All Silent Transitions from Timed Automata

  • Cătălin Dima
  • Ruggero Lanotte
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5813)


We show that all ε-transitions can be removed from timed automata if we allow transitions to be labeled with periodic clock constraints and with periodic clock updates. This utilizes a representation of the reachability relation in timed automata in a generalization of Difference Logic with periodic constraints. We also show that periodic updates are necessary for the removal of ε-transitions.


Difference Logic Relational Symbol Time Automaton Silent Transition Partial Order Reduction 
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.
    Alur, R., Dill, D.: A theory of timed automata. Theoretical Computer Science 126, 183–235 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Asarin, E.: Challenges in timed languages. Bulletin of EATCS 83 (2004)Google Scholar
  3. 3.
    Asarin, E., Degorre, A.: Volume and entropy of regular timed languages. HAL Archive no. hal-00369812 (2009)Google Scholar
  4. 4.
    Bellmann, R.: Dynamic Programming. Princeton University Press, Princeton (1957)zbMATHGoogle Scholar
  5. 5.
    Bengtsson, J.E., Jonsson, B., Lilius, J., Yi, W.: Partial order reductions for timed systems. In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 485–500. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  6. 6.
    Bérard, B., Diekert, V., Gastin, P., Petit, A.: Characterization of the expressive power of silent transitions in timed automata. Fundamenta Informaticae 36, 145–182 (1998)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Bouyer, P., Dufourd, C., Fleury, E., Petit, A.: Are timed automata updatable? In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 464–479. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  8. 8.
    Bouyer, P., Dufourd, C., Fleury, É., Petit, A.: Expressiveness of updatable timed automata. In: Nielsen, M., Rovan, B. (eds.) MFCS 2000. LNCS, vol. 1893, pp. 232–242. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  9. 9.
    Bouyer, P., Haddad, S., Reynier, P.-A.: Undecidability results for timed automata with silent transitions. Fundamenta Informaticae 92, 1–25 (2009)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Choffrut, C., Goldwurm, M.: Timed automata with periodic clock constraints. Journal of Automata, Languages and Combinatorics 5, 371–404 (2000)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Comon, H., Jurski, Y.: Timed automata and the theory of real numbers. In: Baeten, J.C.M., Mauw, S. (eds.) CONCUR 1999. LNCS, vol. 1664, pp. 242–257. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  12. 12.
    Dima, C.: An algebraic theory of real-time formal languages. PhD thesis, Université Joseph Fourier Grenoble, France (2001)Google Scholar
  13. 13.
    Dima, C.: Computing reachability relations in timed automata. In: Proceedings of the 17th IEEE Symposium on Logic in Computer Science (LICS 2002), pp. 177–186 (2002)Google Scholar
  14. 14.
    Dima, C.: A nonarchimedian discretization for timed languages. In: Larsen, K.G., Niebert, P. (eds.) FORMATS 2003. LNCS, vol. 2791, pp. 161–181. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  15. 15.
    Dima, C.: A class of automata for computing reachability relations in timed systems. In: Clarke, E., Tiplea, F.L. (eds.) Proceedings of the NATO Advanced Research Workshop on Verification of Infinite State Systems with Applications to Security (VISSAS 2005). NATO ARW Series (to appear, 2005)Google Scholar
  16. 16.
    Dima, C., Lanotte, R.: Removing all silent transitions from timed automata. Technical Report TR-LACL-2009-6, LACL (2009)Google Scholar
  17. 17.
    Jurski, Y.: Expression de la relation binaire d’accessibilité pour les automates à compteurs plats et les automates temporisés. PhD thesis, École Normale Supérieure de Cachan, France (1999)Google Scholar
  18. 18.
    Mahfoudh, M., Niebert, P., Asarin, E., Maler, O.: A satisfiability checker for difference logic. In: Proceedings of SAT 2002, pp. 222–230 (2002)Google Scholar
  19. 19.
    Ouaknine, J., Worrell, J.: Revisiting digitization, robustness, and decidability for timed automata. In: Proceedings of LICS 2003, pp. 198–207. IEEE Computer Society Press, Los Alamitos (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Cătălin Dima
    • 1
  • Ruggero Lanotte
    • 2
  1. 1.LACL, Université Paris 12Créteil CedexFrance
  2. 2.DSCPI, Università dell’InsubriaComoItaly

Personalised recommendations