Parametric Timed Broadcast Protocols

  • Étienne AndréEmail author
  • Benoit Delahaye
  • Paulin Fournier
  • Didier Lime
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11388)


In this paper we consider state reachability in networks composed of many identical processes running a parametric timed broadcast protocol (PTBP). PTBP are a new model extending both broadcast protocols and parametric timed automata. This work is, up to our knowledge, the first to consider the combination of both a parametric network size and timing parameters in clock guard constraints. Since the communication topology is of utmost importance in broadcast protocols, we investigate reachability problems in both clique semantics where every message reaches every processes, and in reconfigurable semantics where the set of receivers is chosen non-deterministically. In addition, we investigate the decidability status depending on whether the timing parameters in guards appear only as upper bounds in guards, as lower bounds or when the set of parameters is partitioned in lower-bound and upper-bound parameters.



The authors warmly thank Nathalie Bertrand for fruitful discussions on the topic of this paper.


  1. 1.
    Abdulla, P.A., Delzanno, G., Rezine, O., Sangnier, A., Traverso, R.: On the verification of timed ad hoc networks. In: Fahrenberg, U., Tripakis, S. (eds.) FORMATS 2011. LNCS, vol. 6919, pp. 256–270. Springer, Heidelberg (2011). Scholar
  2. 2.
    Abdulla, P.A., Delzanno, G., Rezine, O., Sangnier, A., Traverso, R.: Parameterized verification of time-sensitive models of ad hoc network protocols. Theor. Comput. Sci. 612, 1–22 (2016)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Abdulla, P.A., Deneux, J., Mahata, P.: Multi-clock timed networks. In: LiCS, pp. 345–354. IEEE Computer Society (2004)Google Scholar
  4. 4.
    Abdulla, P.A., Jonsson, B.: Model checking of systems with many identical timed processes. Theor. Comput. Sci. 290(1), 241–264 (2003)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Alur, R., Henzinger, T.A., Vardi, M.Y.: Parametric real-time reasoning. In: Kosaraju, S.R., Johnson, D.S., Aggarwal, A. (eds.) STOC, pp. 592–601. ACM (1993)Google Scholar
  7. 7.
    André, É.: What’s decidable about parametric timed automata? Int. J. Softw. Tools Technol. Transf. (2018, to appear)Google Scholar
  8. 8.
    André, É., Delahaye, B., Fournier, P., Lime, D.: Parametric timed broadcast protocols (long version) (2018).
  9. 9.
    André, É., Knapik, M., Penczek, W., Petrucci, L.: Controlling actions and time in parametric timed automata. In: Desel, J., Yakovlev, A. (eds.) ACSD, pp. 45–54. IEEE Computer Society (2016)Google Scholar
  10. 10.
    André, É., Lime, D.: Liveness in L/U-parametric timed automata. In: Legay, A., Schneider, K. (eds.) ACSD, pp. 9–18. IEEE (2017)Google Scholar
  11. 11.
    Beneš, N., Bezděk, P., Larsen, K.G., Srba, J.: Language emptiness of continuous-time parametric timed automata. In: Halldórsson, M.M., Iwama, K., Kobayashi, N., Speckmann, B. (eds.) ICALP 2015. LNCS, vol. 9135, pp. 69–81. Springer, Heidelberg (2015). Scholar
  12. 12.
    Bouajjani, A., Jonsson, B., Nilsson, M., Touili, T.: Regular model checking. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 403–418. Springer, Heidelberg (2000). Scholar
  13. 13.
    D’Argenio, P.R., Katoen, J.-P., Ruys, T.C., Tretmans, J.: The bounded retransmission protocol must be on time! In: Brinksma, E. (ed.) TACAS 1997. LNCS, vol. 1217, pp. 416–431. Springer, Heidelberg (1997). Scholar
  14. 14.
    Delzanno, G., Ganty, P.: Automatic verification of time sensitive cryptographic protocols. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 342–356. Springer, Heidelberg (2004). Scholar
  15. 15.
    Delzanno, G., Sangnier, A., Traverso, R., Zavattaro, G.: On the complexity of parameterized reachability in reconfigurable broadcast networks. In: FSTTCS. LIPIcs, vol. 18, pp. 289–300. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2012)Google Scholar
  16. 16.
    Delzanno, G., Sangnier, A., Zavattaro, G.: Parameterized verification of ad hoc networks. In: Gastin, P., Laroussinie, F. (eds.) CONCUR 2010. LNCS, vol. 6269, pp. 313–327. Springer, Heidelberg (2010). Scholar
  17. 17.
    Delzanno, G., Sangnier, A., Zavattaro, G.: On the power of cliques in the parameterized verification of ad hoc networks. In: Hofmann, M. (ed.) FoSSaCS 2011. LNCS, vol. 6604, pp. 441–455. Springer, Heidelberg (2011). Scholar
  18. 18.
    Delzanno, G., Sangnier, A., Zavattaro, G.: Parameterized verification of safety properties in ad hoc network protocols. arXiv preprint arXiv:1108.1864 (2011)
  19. 19.
    Fournier, P.: Parameterized verification of networks of many identical processes. Ph.D. thesis, Rennes 1 (2015)Google Scholar
  20. 20.
    Hune, T., Romijn, J., Stoelinga, M., Vaandrager, F.W.: Linear parametric model checking of timed automata. J. Log. Algebr. Program. 52–53, 183–220 (2002)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Jovanović, A., Lime, D., Roux, O.H.: Integer parameter synthesis for timed automata. IEEE Trans. Softw. Eng. 41(5), 445–461 (2015)CrossRefGoogle Scholar
  22. 22.
    Li, L., Sun, J., Liu, Y., Dong, J.S.: Verifying parameterized timed security protocols. In: Bjørner, N., de Boer, F. (eds.) FM 2015. LNCS, vol. 9109, pp. 342–359. Springer, Cham (2015). Scholar
  23. 23.
    Miller, J.S.: Decidability and complexity results for timed automata and semi-linear hybrid automata. In: Lynch, N., Krogh, B.H. (eds.) HSCC 2000. LNCS, vol. 1790, pp. 296–310. Springer, Heidelberg (2000). Scholar
  24. 24.
    Minsky, M.L.: Computation: Finite and Infinite Machines. Prentice-Hall Inc., Upper Saddle River (1967)zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Étienne André
    • 1
    • 2
    • 3
    Email author
  • Benoit Delahaye
    • 4
  • Paulin Fournier
    • 4
  • Didier Lime
    • 5
  1. 1.Université Paris 13, LIPN, CNRS, UMR 7030VilletaneuseFrance
  2. 2.JFLI, CNRSTokyoJapan
  3. 3.National Institute of InformaticsTokyoJapan
  4. 4.Université de Nantes, LS2N UMR CNRS 6004NantesFrance
  5. 5.École Centrale de Nantes, LS2N UMR CNRS 6004NantesFrance

Personalised recommendations