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Robustness of Time Petri Nets under Guard Enlargement

  • S. Akshay
  • Loïc Hélouët
  • Claude Jard
  • Pierre-Alain Reynier
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7550)

Abstract

Robustness of timed systems aims at studying whether infinitesimal perturbations in clock values can result in new discrete behaviors. A model is robust if the set of discrete behaviors is preserved under arbitrarily small (but positive) perturbations. We tackle this problem for Time Petri Nets (TPNs for short) by considering the model of parametric guard enlargement which allows time-intervals constraining the firing of transitions in TPNs to be enlarged by a (positive) parameter.

We show that TPNs are not robust in general and checking if they are robust with respect to standard properties (such as boundedness, safety) is undecidable. We then extend the marking class timed automaton construction for TPNs to a parametric setting, and prove that it is compatible with guard enlargements. We apply this result to the (undecidable) class of TPNs which are robustly bounded (i.e., whose finite set of reachable markings remains finite under infinitesimal perturbations): we provide two decidable robustly bounded subclasses, and show that one can effectively build a timed automaton which is timed bisimilar even in presence of perturbations. This allows us to apply existing results for timed automata to these TPNs and show further robustness properties.

Keywords

Discrete Move Time Automaton Time Automaton Robustness Problem Reachable Marking 
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.

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References

  1. 1.
    Alur, R., Dill, D.: A theory of timed automata. TCS 126(2), 183–235 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Berthomieu, B., Diaz, M.: Modeling and verification of time dependent systems using time Petri nets. IEEE Trans. in Software Engineering 17(3), 259–273 (1991)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bouyer, P., Markey, N., Reynier, P.-A.: Robust Model-Checking of Linear-Time Properties in Timed Automata. In: Correa, J.R., Hevia, A., Kiwi, M. (eds.) LATIN 2006. LNCS, vol. 3887, pp. 238–249. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  4. 4.
    Bouyer, P., Markey, N., Reynier, P.-A.: Robust Analysis of Timed Automata via Channel Machines. In: Amadio, R.M. (ed.) FOSSACS 2008. LNCS, vol. 4962, pp. 157–171. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  5. 5.
    Bouyer, P., Markey, N., Sankur, O.: Robust Model-Checking of Timed Automata via Pumping in Channel Machines. In: Fahrenberg, U., Tripakis, S. (eds.) FORMATS 2011. LNCS, vol. 6919, pp. 97–112. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  6. 6.
    Cassez, F., Roux, O.H.: Structural translation from time petri nets to timed automata. Journal of Systems and Software 79(10), 1456–1468 (2006)CrossRefGoogle Scholar
  7. 7.
    D’Aprile, D., Donatelli, S., Sangnier, A., Sproston, J.: From Time Petri Nets to Timed Automata: An Untimed Approach. In: Grumberg, O., Huth, M. (eds.) TACAS 2007. LNCS, vol. 4424, pp. 216–230. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  8. 8.
    De Wulf, M., Doyen, L., Markey, N., Raskin, J.-F.: Robust safety of timed automata. Formal Methods in System Design 33(1-3), 45–84 (2008)zbMATHCrossRefGoogle Scholar
  9. 9.
    De Wulf, M., Doyen, L., Raskin, J.-F.: Systematic Implementation of Real-Time Models. In: Fitzgerald, J.S., Hayes, I.J., Tarlecki, A. (eds.) FM 2005. LNCS, vol. 3582, pp. 139–156. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  10. 10.
    Gardey, G., Roux, O.H., Roux, O.F.: Using Zone Graph Method for Computing the State Space of a Time Petri Net. In: Larsen, K.G., Niebert, P. (eds.) FORMATS 2003. LNCS, vol. 2791, pp. 246–259. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  11. 11.
    Karp, R., Miller, R.: Parallel program chemata. JCSS 3, 147–195 (1969)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Lime, D., Roux, O.H.: Model checking of time petri nets using the state class timed automaton. Discrete Event Dynamic Systems 16(2), 179–205 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Merlin, P.M.: A Study of the Recoverability of Computing Systems. PhD thesis, University of California, Irvine, CA, USA (1974)Google Scholar
  14. 14.
    Puri, A.: Dynamical properties of timed automata. DEDS 10(1-2), 87–113 (2000)zbMATHGoogle Scholar
  15. 15.
    Sankur, O.: Untimed Language Preservation in Timed Systems. In: Murlak, F., Sankowski, P. (eds.) MFCS 2011. LNCS, vol. 6907, pp. 556–567. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  16. 16.
    Swaminathan, M., Fränzle, M., Katoen, J.-P.: The Surprising Robustness of (Closed) Timed Automata against Clock-Drift. In: Ausiello, G., Karhumäki, J., Mauri, G., Ong, L. (eds.) TCS 2008. IFIP, vol. 273, pp. 537–553. Springer, Boston (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • S. Akshay
    • 1
    • 2
  • Loïc Hélouët
    • 1
  • Claude Jard
    • 1
    • 2
  • Pierre-Alain Reynier
    • 3
  1. 1.INRIA/IRISA RennesFrance
  2. 2.ENS Cachan BretagneRennesFrance
  3. 3.CNRS, LIF, UMRAix-Marseille UniversitéMarseilleFrance

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