On the Determinization of Timed Systems

  • Patricia Bouyer
  • Samy Jaziri
  • Nicolas Markey
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10419)


We introduce a new formalism called automata over a timed domain which provides an adequate framework for the determinization of timed systems. In this formalism, determinization w.r.t. timed language is always possible at the cost of changing the timed domain. We give a condition for determinizability of automata over a timed domain without changing the timed domain, which allows us to recover several known determinizable classes of timed systems, such as strongly-non-zeno timed automata, integer-reset timed automata, perturbed timed automata, etc. Moreover in the case of timed automata this condition encompasses most determinizability conditions from the literature.


  1. [AD94]
    Alur, R., Dill, D.L.: A theory of timed automata. Theoret. Comput. Sci. 126(2), 183–235 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  2. [AFH94]
    Alur, R., Fix, L., Henzinger, T.A.: A determinizable class of timed automata. In: Dill, D.L. (ed.) CAV 1994. LNCS, vol. 818, pp. 1–13. Springer, Heidelberg (1994). doi: 10.1007/3-540-58179-0_39 CrossRefGoogle Scholar
  3. [ALM05]
    Alur, R., Torre, S., Madhusudan, P.: Perturbed timed automata. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 70–85. Springer, Heidelberg (2005). doi: 10.1007/978-3-540-31954-2_5 CrossRefGoogle Scholar
  4. [AMPS98]
    Asarin, E., Maler, O., Pnueli, A., Sifakis, J.: Controller synthesis for timed automata. In: SSC 1998, pp. 469–474. Elsevier (1998)Google Scholar
  5. [BBBB09]
    Baier, C., Bertrand, N., Bouyer, P., Brihaye, T.: When are timed automata determinizable? In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5556, pp. 43–54. Springer, Heidelberg (2009). doi: 10.1007/978-3-642-02930-1_4 CrossRefGoogle Scholar
  6. [BDFP04]
    Bouyer, P., Dufourd, C., Fleury, E., Petit, A.: Updatable timed automata. Theoret. Comput. Sci. 321(2–3), 291–345 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  7. [BL12]
    Bojańczyk, M., Lasota, S.: A machine-independent characterization of timed languages. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds.) ICALP 2012. LNCS, vol. 7392, pp. 92–103. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-31585-5_12 CrossRefGoogle Scholar
  8. [BSJK15]
    Bertrand, N., Stainer, A., Jéron, T., Krichen, M.: A game approach to determinize timed automata. Formal Meth. Syst. Des. 46(1), 42–80 (2015)CrossRefzbMATHGoogle Scholar
  9. [DM02]
    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). doi: 10.1007/3-540-45841-7_47 CrossRefGoogle Scholar
  10. [DT04]
    D’Souza, D., Tabareau, N.: On timed automata with input-determined guards. In: Lakhnech, Y., Yovine, S. (eds.) FORMATS/FTRTFT -2004. LNCS, vol. 3253, pp. 68–83. Springer, Heidelberg (2004). doi: 10.1007/978-3-540-30206-3_7 CrossRefGoogle Scholar
  11. [Fin06]
    Finkel, O.: Undecidable problems about timed automata. In: Asarin, E., Bouyer, P. (eds.) FORMATS 2006. LNCS, vol. 4202, pp. 187–199. Springer, Heidelberg (2006). doi: 10.1007/11867340_14 CrossRefGoogle Scholar
  12. [KT09]
    Krichen, M., Tripakis, S.: Conformance testing for real-time systems. Formal Meth. Syst. Des. 34(3), 238–304 (2009)CrossRefzbMATHGoogle Scholar
  13. [OW04]
    Ouaknine, J., Worrell, J.: On the language inclusion problem for timed automata: closing a decidability gap. In: LICS 2004, pp. 54–63. IEEE Computer Society Press (2004)Google Scholar
  14. [Tri06]
    Tripakis, S.: Folk theorems on the determinization and minimization of timed automata. Inf. Process. Lett. 99(6), 222–226 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  15. [VPKM08]
    Suman, P.V., Pandya, P.K., Krishna, S.N., Manasa, L.: Timed automata with integer resets: language inclusion and expressiveness. In: Cassez, F., Jard, C. (eds.) FORMATS 2008. LNCS, vol. 5215, pp. 78–92. Springer, Heidelberg (2008). doi: 10.1007/978-3-540-85778-5_7 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.LSV – CNRS & ENS Paris-SaclayCachanFrance
  2. 2.IRISA – CNRS & INRIA & Univ. Rennes 1RennesFrance

Personalised recommendations