On MITL and Alternating Timed Automata over Infinite Words

  • Thomas Brihaye
  • Morgane Estiévenart
  • Gilles Geeraerts
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8711)

Abstract

One clock alternating timed automata (OCATA) have been introduced as natural extension of (one clock) timed automata to express the semantics of MTL [15]. In this paper, we consider the application of OCATA to the problems of model-checking and satisfiability for MITL (a syntactic fragment of MTL), interpreted over infinite words. Our approach is based on the interval semantics (recently introduced in [5] in the case of finite words) extended to infinite words. We propose region-based and zone-based algorithms, based on this semantics, for MITL model-checking and satisfiability. We report on the performance of a prototype tool implementing those algorithms.

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References

  1. 1.
    Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Abdulla, P.A., Deneux, J., Ouaknine, J., Quaas, K., Worrell, J.: Universality Analysis for One-Clock Timed Automata. Fundam. Inform. 89(4), 419–450 (2008)MATHMathSciNetGoogle Scholar
  3. 3.
    Alur, R., Feder, T., Henzinger, T.A.: The benefits of relaxing punctuality. J. ACM 43(1), 116–146 (1996)CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Bouyer, P.: Timed Automata may cause some troubles. Research Report LSV-02-9, Lab. Spécification et Vérification, CNRS & ENS de Cachan, France (2002)Google Scholar
  5. 5.
    Brihaye, T., Estiévenart, M., Geeraerts, G.: On MITL and Alternating Timed Automata. In: Braberman, V., Fribourg, L. (eds.) FORMATS 2013. LNCS, vol. 8053, pp. 47–61. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  6. 6.
    Brihaye, T., Estiévenart, M., Geeraerts, G.: On MITL and Alternating Timed Automata over infinite words. Technical report arXiv.org., http://arxiv.org/abs/1406.4395
  7. 7.
    Clarke, E.M., Grumberg, O., Peled, D.: Model checking. MIT Press (2001)Google Scholar
  8. 8.
    Daws, C., Yovine, S.: Reducing the number of clock variables of timed automata. Real-Time Systems, 73–81 (1996)Google Scholar
  9. 9.
    Geeraerts, G., Kalyon, G., Le Gall, T., Maquet, N., Raskin, J.-F.: Lattice-Valued Binary Decision Diagrams. In: Bouajjani, A., Chin, W.-N. (eds.) ATVA 2010. LNCS, vol. 6252, pp. 158–172. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  10. 10.
    Gastin, P., Oddoux, D.: Fast LTL to Büchi Automata Translation. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 53–65. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  11. 11.
    Koymans, R.: Specifying real-time properties with metric temporal logic. Real-Time Systems 2(4), 255–299 (1990)CrossRefGoogle Scholar
  12. 12.
    Kupferman, O., Vardi, M.Y.: Weak alternating automata are not that weak. ACM Trans. Comput. Log. 2(3), 408–429 (2001)CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Maquet, N.: New Algorithms and Data Structures for the Emptiness Problem of Alternating Automata. PhD thesis, Université Libre de Bruxelles (2011)Google Scholar
  14. 14.
    Miyano, S., Hayashi, T.: Alternating Finite Automata on omega-Words. Theor. Comput. Sci. 32, 321–330 (1984)CrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    Ouaknine, J., Worrell, J.: On the decidability of metric temporal logic. In: LICS 2005, pp. 188–197. IEEE (2005)Google Scholar
  16. 16.
    Ouaknine, J., Worrell, J.: On the decidability and complexity of metric temporal logic over finite words. Logical Methods in Computer Science 3(1) (2007)Google Scholar
  17. 17.
    Parys, P., Walukiewicz, I.: Weak Alternating Timed Automata. Logical Methods in Computer Science 8(3) (2012)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Thomas Brihaye
    • 1
  • Morgane Estiévenart
    • 1
  • Gilles Geeraerts
    • 2
  1. 1.Université de MonsBelgium
  2. 2.Université libre de BruxellesBelgium

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