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Iterative Bounded Synthesis for Efficient Cycle Detection in Parametric Timed Automata

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 12651)

Abstract

We study semi-algorithms to synthesise the constraints under which a Parametric Timed Automaton satisfies some liveness requirement. The algorithms traverse a possibly infinite parametric zone graph, searching for accepting cycles. We provide new search and pruning algorithms, leading to successful termination for many examples. We demonstrate the success and efficiency of these algorithms on a benchmark. We also illustrate parameter synthesis for the classical Bounded Retransmission Protocol. Finally, we introduce a new notion of completeness in the limit, to investigate if an algorithm enumerates all solutions.

Keywords

  • Parameter Synthesis
  • Liveness Properties
  • IMITATOR

This work is partially supported by projects CNRS-INS2I TrAVAIL, IFD SECReTS and ANR-NRF ProMiS (ANR-19-CE25-0015).

References

  1. Alur, R., Dill, D.L.: A theory of timed automata. Theoretical Computer Science 126(2), 183–235 (1994). https://doi.org/10.1016/0304-3975(94)90010-8

  2. 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, New York, NY, USA (1993). https://doi.org/10.1145/167088.167242

  3. André, É.: What’s decidable about parametric timed automata? International Journal on Software Tools for Technology Transfer (2019). https://doi.org/10.1007/s10009-017-0467-0

  4. André, É.: A benchmark library for parametric timed model checking. In: Artho, C., Ölveczky, P.C. (eds.) FTSCS. Communications in Computer and Information Science, vol. 1008, pp. 75–83. Springer (2019). https://doi.org/10.1007/978-3-030-12988-0_5

  5. André, É., Chatain, Th., Encrenaz, E., Fribourg, L.: An inverse method for parametric timed automata. International Journal of Foundations of Computer Science 20(5), 819–836 (2009). https://doi.org/10.1142/S0129054109006905

  6. André, É., Fribourg, L., Kühne, U., Soulat, R.: IMITATOR 2.5: A tool for analyzing robustness in scheduling problems. In: Giannakopoulou, D., Méry, D. (eds.) FM. Lecture Notes in Computer Science, vol. 7436, pp. 33–36. Springer (2012). https://doi.org/10.1007/978-3-642-32759-9_6

  7. André, É., Fribourg, L., Soulat, R.: Merge and conquer: State merging in parametric timed automata. In: Hung, D.V., Ogawa, M. (eds.) ATVA. Lecture Notes in Computer Science, vol. 8172, pp. 381–396. Springer (Oct 2013). https://doi.org/10.1007/978-3-319-02444-8_27

  8. André, É., Lime, D.: Liveness in L/U-parametric timed automata. In: Legay, A., Schneider, K. (eds.) ACSD. pp. 9–18. IEEE (2017). https://doi.org/10.1109/ACSD.2017.19

  9. André, É., Nguyen, H.G., Petrucci, L., Sun, J.: Parametric model checking timed automata under non-Zenoness assumption. In: Barrett, C., Kahsai, T. (eds.) NFM. Lecture Notes in Computer Science, vol. 10227, pp. 35–51. Springer (2017). https://doi.org/10.1007/978-3-319-57288-8_3

  10. Bagnara, R., M., H.P., Zaffanella, E.: The Parma Polyhedra Library: Toward a complete set of numerical abstractions for the analysis and verification of hardware and software systems. Science of Computer Programming 72(1–2), 3–21 (2008). https://doi.org/10.1016/j.scico.2007.08.001

  11. Bezděk, P., Beneš, N., Barnat, J., Černá, I.: LTL parameter synthesis of parametric timed automata. In: Nicola, R.D., eva Kühn (eds.) SEFM. Lecture Notes in Computer Science, vol. 9763, pp. 172–187. Springer (2016). https://doi.org/10.1007/978-3-319-41591-8_12

  12. Cimatti, A., Griggio, A., Magnago, E.: Proving the existence of fair paths in infinite-state systems. In: Henglein, F., Shoham, S., Vizel, Y. (eds.) VMCAI. Lecture Notes in Computer Science, vol. 12597, pp. 104–126. Springer (2021). https://doi.org/10.1007/978-3-030-67067-2_6

  13. Courcoubetis, C., Vardi, M., Wolper, P., Yannakakis, M.: Memory-efficient algorithms for the verification of temporal properties. Formal Methods in System Design 1(2/3), 275–288 (1992). https://doi.org/10.1007/BF00121128

  14. 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. Lecture Notes in Computer Science, vol. 1217, pp. 416–431. Springer (1997). https://doi.org/10.1007/BFb0035403

  15. Duret-Lutz, A., Lewkowicz, A., Fauchille, A., Michaud, T., Renault, É., Xu, L.: Spot 2.0 — A framework for LTL and \(\omega \)-automata manipulation. In: ATVA. Lecture Notes in Computer Science, vol. 9938, pp. 122–129. Springer (2016). https://doi.org/10.1007/978-3-319-46520-3_8

  16. Groote, J.F., van de Pol, J.: A bounded retransmission protocol for large data packets. In: Wirsing, M., Nivat, M. (eds.) AMAST. Lecture Notes in Computer Science, vol. 1101, pp. 536–550. Springer (1996). https://doi.org/10.1007/BFb0014338

  17. Herbreteau, F., Srivathsan, B.: Efficient on-the-fly emptiness check for timed Büchi automata. In: Bouajjani, A., Chin, W.N. (eds.) ATVA. Lecture Notes in Computer Science, vol. 6252, pp. 218–232. Springer (2010). https://doi.org/10.1007/978-3-642-15643-4_17

  18. Herbreteau, F., Srivathsan, B., Tran, T.T., Walukiewicz, I.: Why liveness for timed automata is hard, and what we can do about it. ACM Transactions on Computational Logic 21(3), 17:1–17:28 (2020). https://doi.org/10.1145/3372310

  19. Hune, T., Romijn, J., Stoelinga, M., Vaandrager, F.W.: Linear parametric model checking of timed automata. Journal of Logic and Algebraic Programming 52-53, 183–220 (2002). https://doi.org/10.1016/S1567-8326(02)00037-1

  20. Jovanović, A., Lime, D., Roux, O.H.: Integer parameter synthesis for real-time systems. IEEE Transactions on Software Engineering 41(5), 445–461 (2015). https://doi.org/10.1109/TSE.2014.2357445

  21. Knapik, M., Penczek, W.: Bounded model checking for parametric timed automata. Transactions on Petri Nets and Other Models of Concurrency 5, 141–159 (2012). https://doi.org/10.1007/978-3-642-29072-5_6

  22. Laarman, A., Olesen, M.C., Dalsgaard, A.E., Larsen, K.G., van de Pol, J.: Multi-core emptiness checking of timed Büchi automata using inclusion abstraction. In: Sharygina, N., Veith, H. (eds.) CAV. Lecture Notes in Computer Science, vol. 8044, pp. 968–983. Springer, Heidelberg, Germany (2013). https://doi.org/10.1007/978-3-642-39799-8_69

  23. Li, G.: Checking timed Büchi automata emptiness using LU-abstractions. In: Ouaknine, J., Vaandrager, F.W. (eds.) FORMATS, Lecture Notes in Computer Science, vol. 5813, pp. 228–242. Springer (2009). https://doi.org/10.1007/978-3-642-04368-0_18

  24. Maler, O., Nickovic, D., Pnueli, A.: From MITL to timed automata. In: Asarin, E., Bouyer, P. (eds.) FORMATS. Lecture Notes in Computer Science, vol. 4202, pp. 274–289. Springer (2006). https://doi.org/10.1007/11867340_20

  25. Nguyen, H.G., Petrucci, L., van de Pol, J.: Layered and collecting NDFS with subsumption for parametric timed automata. In: Lin, A.W., Sun, J. (eds.) ICECCS. pp. 1–9. IEEE Computer Society (2018). https://doi.org/10.1109/ICECCS2018.2018.00009

  26. van de Pol, J., Petrucci, L.: On completeness of liveness synthesis for parametric timed automata (extended abstract, invited talk). In: Roggenbach, M. (ed.) WADT 2020 (2021), to appear

    Google Scholar 

  27. Tripakis, S., Yovine, S., Bouajjani, A.: Checking timed Büchi automata emptiness efficiently. Formal Methods in System Design 26(3), 267–292 (2005). https://doi.org/10.1007/s10703-005-1632-8

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André, É., Arias, J., Petrucci, L., Pol, J.v.d. (2021). Iterative Bounded Synthesis for Efficient Cycle Detection in Parametric Timed Automata. In: Groote, J.F., Larsen, K.G. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2021. Lecture Notes in Computer Science(), vol 12651. Springer, Cham. https://doi.org/10.1007/978-3-030-72016-2_17

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  • DOI: https://doi.org/10.1007/978-3-030-72016-2_17

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