We present an algorithm for finding the minimal number of clocks of a given timed automaton recognizing the language described by a so-called bounded timed regular expressionw. This algorithm is based on the partition of the timed projection of w into so-called delay cells. Using this decomposition, we give a method to compute practically this number for w. We then apply this technique to prove that for some n-clock timed automation we need an additional clock to encode urgency.


Timed automaton timed regular expression minimal number of clocks n-clock timed language urgency 


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  1. 1.
    Adélaïde, M., Pagetti, C.: When the minimal number of clocks is computable. Technical Report 1329-04, Labri/CNRS, Bordeaux (2004),
  2. 2.
    Alur, R., Dill, D.: A theory of timed automata. Theoretical Computer Science B 126, 183–235 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Alur, R., Grosu, R., Hur, Y., Kumar, V., Lee, I.: Modular specification of hybrid systems in CHARON. In: Lynch, N.A., Krogh, B.H. (eds.) HSCC 2000. LNCS, vol. 1790, pp. 6–19. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  4. 4.
    Alur, R., Henzinger, T.A.: Back to the future: Towards a theory of timed regular languages. In: IEEE Symposium on Foundations of Computer Science, pp. 177–186 (1992)Google Scholar
  5. 5.
    Arnold, A., Griffault, A., Point, G., Rauzy, A.: The AltaRica formalism for describing concurrent systems. Fundamenta Informaticae 40, 109–124 (2000)MathSciNetGoogle Scholar
  6. 6.
    Asarin, E., Caspi, P., Maler, O.: Timed regular expressions. Journal of the ACM 49(2), 172–206 (2002)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Bornot, S., Sifakis, J.: An algebraic framework for urgency. Information and Computation 163(1), 172–202 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Bornot, S., Sifakis, J., Tripakis, S.: Modeling urgency in timed systems. In: de Roever, W.-P., Langmaack, H., Pnueli, A. (eds.) COMPOS 1997. LNCS, vol. 1536, pp. 103–129. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  9. 9.
    Bouyer, P., Petit, A.: A Kleene/Bchi-like theorem for clock languages. Journal of Automata, Languages and Combinatorics 7, 167–186 (2001)MathSciNetGoogle Scholar
  10. 10.
    Cassez, F., Pagetti, C., Roux, O.: A timed extension for AltaRica. To appear in Fundamenta Informaticae (2004)Google Scholar
  11. 11.
    Chandru, V., Rao, M.R.: 175 years of Linear Programming, part 1. The French Connection. The Journal of Science Education (1998)Google Scholar
  12. 12.
    Daws, C., Yovine, S.: Reducing the number of clock variables of timed automata. In: 7th IEEE Real Time Systems Symposium, RTSS 1996, Washington, DC, USA, pp. 73–81. IEEE Computer Society Press, Los Alamitos (1996)CrossRefGoogle Scholar
  13. 13.
    Labroue, A.: Conditions de vivacité dans les automates temporisés. Technical Report LSV-98-7, Lab. Specification and Verification, ENS de Cachan (1998)Google Scholar
  14. 14.
    Larsen, K., Larsson, F., Pettersson, P.: Efficient verification of real-time systems: Compact data structure and state-space reduction. Real-Time Systems — The International 25, 255–275 (2003)zbMATHCrossRefGoogle Scholar
  15. 15.
    Larsen, K.G., Pettersson, P., Yi, W.: Compositional and Symbolic Model-Checking of Real-Time Systems. In: Proc. of the 16th IEEE Real-Time Systems Symposium, pp. 76–87. IEEE Computer Society Press, Los Alamitos (1995)CrossRefGoogle Scholar
  16. 16.
    Lugiez, D., Niebert, P., Zennou, S.: A Partial Order Semantics Approach to the Clock Explosion Problem of Timed Automata. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 296–311. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  17. 17.
    Maler, O., Pnueli, A.: On Recognizable Timed Languages. In: Walukiewicz, I. (ed.) FOSSACS 2004. LNCS, vol. 2987, pp. 348–362. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  18. 18.
    Sifakis, J., Yovine, S.: Compositional specification of timed systems. In: Puech, C., Reischuk, R. (eds.) STACS 1996. LNCS, vol. 1046, pp. 347–359. Springer, Heidelberg (1996)Google Scholar
  19. 19.
    Tripakis, S.: Folk Theorems on the Determinization and Minimization of Timed Automata. In: FORMATS (2003)Google Scholar
  20. 20.
    Wilke, T.: Automaten und Logiken zur Beschreibung zeitabhängiger Systeme. PhD thesis, Inst. f. Informatik u. Prakt. Math., CAU Kiel (1994)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Michaël Adélaïde
    • 1
  • Claire Pagetti
    • 1
  1. 1.Labri (UMR 5800), Domaine UniversitaireTalenceFrance

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