Advertisement

Coarse Abstractions Make Zeno Behaviours Difficult to Detect

  • Frédéric Herbreteau
  • B. Srivathsan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6901)

Abstract

An infinite run of a timed automaton is Zeno if it spans only a finite amount of time. Such runs are considered unfeasible and hence it is important to detect them, or dually, find runs that are non-Zeno. Over the years important improvements have been obtained in checking reachability properties for timed automata. We show that some of these very efficient optimizations make testing for Zeno runs costly. In particular we show NP-completeness for the LU-extrapolation of Behrmann et al. We analyze the source of this complexity in detail and give general conditions on extrapolation operators that guarantee a (low) polynomial complexity of Zenoness checking. We propose a slight weakening of the LU-extrapolation that satisfies these conditions.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alur, R., Dill, D.L.: A theory of timed automata. Theoretical Computer Science 126(2), 183–235 (1994)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Behrmann, G., Bouyer, P., Larsen, K.G., Pelanek, R.: Lower and upper bounds in zone-based abstractions of timed automata. Int. Journal on Software Tools for Technology Transfer 8(3), 204–215 (2006)CrossRefMATHGoogle Scholar
  3. 3.
    Behrmann, G., David, A., Larsen, K.G., Haakansson, J., Pettersson, P., Yi, W., Hendriks, M.: Uppaal 4.0. In: QEST, pp. 125–126. IEEE Computer Society, Los Alamitos (2006)Google Scholar
  4. 4.
    Bouyer, P.: Forward analysis of updatable timed automata. Formal Methods in System Design 24(3), 281–320 (2004)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Bowman, H., Gómez, R.: How to stop time stopping. Formal Aspects of Computing 18(4), 459–493 (2006)CrossRefMATHGoogle Scholar
  6. 6.
    Bozga, M., Daws, C., Maler, O., Olivero, A., Tripakis, S., Yovine, S.: Kronos: A model-checking tool for real-time systems. In: Vardi, M.Y. (ed.) CAV 1998. LNCS, vol. 1427, pp. 546–550. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  7. 7.
    Dill, D.: Timing assumptions and verification of finite-state concurrent systems. In: Sifakis, J. (ed.) AVMFSS 1989. LNCS, vol. 407, pp. 197–212. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  8. 8.
    Gómez, R., Bowman, H.: Efficient detection of zeno runs in timed automata. In: Raskin, J.-F., Thiagarajan, P.S. (eds.) FORMATS 2007. LNCS, vol. 4763, pp. 195–210. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  9. 9.
    Herbreteau, F., Srivathsan, B.: Coarse abstractions make zeno behaviours difficult to detect. CoRR abs/1106.1850 (2011); Extended version with proofsGoogle Scholar
  10. 10.
    Herbreteau, F., Srivathsan, B., Walukiewicz, I.: Efficient Emptiness Check for Timed Büchi Automata. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 148–161. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  11. 11.
    Li, G.: Checking timed Büchi automata emptiness using LU-abstractions. In: Ouaknine, J., Vaandrager, F.W. (eds.) FORMATS 2009. LNCS, vol. 5813, pp. 228–242. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  12. 12.
    Tripakis, S.: Verifying progress in timed systems. In: Katoen, J.-P. (ed.) AMAST-ARTS 1999, ARTS 1999, and AMAST-WS 1999. LNCS, vol. 1601, pp. 299–314. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  13. 13.
    Tripakis, S.: Checking timed Büchi emptiness on simulation graphs. ACM Trans. on Computational Logic 10(3) (2009)Google Scholar
  14. 14.
    Tripakis, S., Yovine, S., Bouajjani, A.: Checking timed Büchi automata emptiness efficiently. Formal Methods in System Design 26(3), 267–292 (2005)CrossRefMATHGoogle Scholar
  15. 15.
    Wang, F.: Redlib for the formal verification of embedded systems. In: ISoLA, pp. 341–346. IEEE, Los Alamitos (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Frédéric Herbreteau
    • 1
  • B. Srivathsan
    • 1
  1. 1.IPB, Université Bordeaux 1, CNRS, LaBRI UMR5800Université de BordeauxTalenceFrance

Personalised recommendations