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Abstract

A notion of alternating timed automata is proposed. It is shown that such automata with only one clock have decidable emptiness problem. This gives a new class of timed languages which is closed under boolean operations and which has an effective presentation. We prove that the complexity of the emptiness problem for alternating timed automata with one clock is non-primitive recursive. The proof gives also the same lower bound for the universality problem for nondeterministic timed automata with one clock thereby answering a question asked in a recent paper by Ouaknine and Worrell.

Keywords

Boolean Operation Transition Rule Channel System Label Transition System Reachability Problem 
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.

References

  1. 1.
    Abdulla, P., Čer\(\bar{a}\)ns, K., Jonsson, B., Tsay, Y.: General decidability theorems for infinite state systems. In: LICS 1996, p. 313–323 (1996)Google Scholar
  2. 2.
    Alur, R., Dill, D.L.: A theory of timed automata. Theoretical Computer Science 126, 183–235 (1994)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Alur, R., Bernadsky, M., Madhusudan, P.: Optimal reachability for weighted timed games. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 122–133. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  4. 4.
    Alur, R., Fix, L., Henzinger, T.: Event-clock automata: A determinizable class of timed automata. Theoretical Computer Science 204, 253–273 (1999)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Asarin, E., Maler, O., Pnueli, A., Sifakis, J.: Controller synthesis for timed automata. In: Proc. IFAC Symp. System Structure and Control, pp. 469–474 (1998)Google Scholar
  6. 6.
    Bouyer, P., Cassez, F., Fleury, E., Larsen, K.G.: Optimal strategies in priced timed game automata. In: Lodaya, K., Mahajan, M. (eds.) FSTTCS 2004. LNCS, vol. 3328, pp. 148–160. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  7. 7.
    Bouyer, P., D’Souza, D., Madhusudan, P., Petit, A.: Timed control with partial observability. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 180–192. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  8. 8.
    Brand, D., Zafiropulo, P.: On communicating finite-state machines. J. ACM 30(2), 323–342 (1983)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Bérard, B., Diekert, V., Gastin, P., Petit, A.: Characterization of the expressive power of silent transitions in timed automata. Fundamenta Informaticae 36(2), 145–182 (1998)MathSciNetMATHGoogle Scholar
  10. 10.
    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
  11. 11.
    Dickhöfer, M., Wilke, T.: Timed alternating tree automata: the automata-theoretic solution to the TCTL model checking problem. In: Wiedermann, J., Van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, pp. 281–290. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  12. 12.
    Dima, C.: Real-time automata and the Kleene algebra of sets of real numbers. In: Nagl, M. (ed.) IPSEN 1996. LNCS, vol. 1170, pp. 279–289. Springer, Heidelberg (1996)Google Scholar
  13. 13.
    Finkel, A., Schnoebelen, P.: Well structured transition systems everywhere? Theoretical Computer Science 256(1-2), 63–92 (2001)MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Higman, G.: Ordering by divisibility in abstract algebras. Proc. London Math. Soc. 2(7), 326–336 (1952)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Laroussinie, F., Markey, N., Schnoebelen, P.: Model checking timed automata with one or two clocks. In: Gardner, P., Yoshida, N. (eds.) CONCUR 2004. LNCS, vol. 3170, pp. 387–401. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  16. 16.
    Ouaknine, J., Worrell, J.: On the language inclusion problem for timed automata: Closing a decidability gap. In: LICS 2004, pp. 54–63 (2004)Google Scholar
  17. 17.
    Schnoebelen, P.: Verifying lossy channel systems has nonprimitive recursive complexity. Information Processing Letters 83(5), 251–261 (2002)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Sławomir Lasota
    • 1
  • Igor Walukiewicz
    • 2
  1. 1.Institute of InformaticsWarsaw UniversityWarszawa
  2. 2.LaBRIUniversité Bordeaux-1Talence cedexFrance

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