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Zone-Based Verification of Timed Automata: Extrapolations, Simulations and What Next?

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Formal Modeling and Analysis of Timed Systems (FORMATS 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13465))

Abstract

Timed automata have been introduced by Rajeev Alur and David Dill in the early 90’s. In the last decades, timed automata have become the de facto model for the verification of real-time systems. Algorithms for timed automata are based on the traversal of their state-space using zones as a symbolic representation. Since the state-space is infinite, termination relies on finite abstractions that yield a finite representation of the reachable states.

The first solution to get finite abstractions was based on extrapolations of zones, and has been implemented in the industry-strength tool Uppaal . A different approach based on simulations between zones has emerged in the last ten years, and has been implemented in the fully open source tool TChecker. The simulation-based approach has led to new efficient algorithms for reachability and liveness in timed automata, and has also been extended to richer models like weighted timed automata, and timed automata with diagonal constraints and updates.

In this article, we survey the extrapolation and simulation techniques, and discuss some open challenges for the future.

This work was partially funded by ANR project Ticktac (ANR-18-CE40-0015).

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Notes

  1. 1.

    For the partial order \(\le \) defined pointwise.

  2. 2.

    For every \(x \in X\), for every constraint \(x \bowtie c\) appearing in \(\mathcal {A}\), \(K_x \ge c\).

  3. 3.

    For every \(x \in X\), for every constraint \(x < c\) or \(x \le c\) (resp. \(x>d\) or \(x \ge d\)) appearing in \(\mathcal {A}\), \(U_x \ge c\) (resp. \(L_x \ge d\)).

References

  1. Akshay, S., Gastin, P., Govind, R., Srivathsan, B.: Simulations for event-clock automata. In: Proceedings of 33th International Conference on Concurrency Theory (CONCUR 2022). Lecture Notes in Computer Science, Springer, Cham (2022, to appear)

    Google Scholar 

  2. Akshay, S., Gastin, P., Prakash, K.R.: Fast zone-based algorithms for reachability in pushdown timed automata. In: Silva, A., Leino, K.R.M. (eds.) CAV 2021. LNCS, vol. 12759, pp. 619–642. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-81685-8_30

    Chapter  Google Scholar 

  3. Alur, R., Courcoubetis, C., Dill, D.L., Halbwachs, N., Wong-Toi, H.: An implementation of three algorithms for timing verification based on automata emptiness. In: Proceedings of 13th IEEE Real-Time Systems Symposium (RTSS 1992), pp. 157–166. IEEE Computer Society Press (1992)

    Google Scholar 

  4. Alur, R., Dill, D.: Automata for modeling real-time systems. In: Paterson, M.S. (ed.) ICALP 1990. LNCS, vol. 443, pp. 322–335. Springer, Heidelberg (1990). https://doi.org/10.1007/BFb0032042

    Chapter  MATH  Google Scholar 

  5. Alur, R., Dill, D.L.: A theory of timed automata. Theoret. Comput. Sci. 126(2), 183–235 (1994)

    Article  MathSciNet  Google Scholar 

  6. Alur, R., Henzinger, T.A., Vardi, M.Y.: Parametric real-time reasoning. In: Proceedings of 25th Annual ACM Symposium on the Theory of Computing (STOC 1993), pp. 592–601. ACM (1993)

    Google Scholar 

  7. Alur, R., La Torre, S., Pappas, G.J.: Optimal paths in weighted timed automata. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 49–62. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45351-2_8

    Chapter  Google Scholar 

  8. André, É.: IMITATOR 3: synthesis of timing parameters beyond decidability. In: Silva, A., Leino, K.R.M. (eds.) CAV 2021. LNCS, vol. 12759, pp. 552–565. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-81685-8_26

    Chapter  Google Scholar 

  9. Audemard, G., Cimatti, A., Kornilowicz, A., Sebastiani, R.: Bounded model checking for timed systems. In: Peled, D.A., Vardi, M.Y. (eds.) FORTE 2002. LNCS, vol. 2529, pp. 243–259. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-36135-9_16

    Chapter  MATH  Google Scholar 

  10. Behrmann, G., Bouyer, P., Fleury, E., Larsen, K.G.: Static guard analysis in timed automata verification. In: Garavel, H., Hatcliff, J. (eds.) TACAS 2003. LNCS, vol. 2619, pp. 254–270. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36577-X_18

    Chapter  MATH  Google Scholar 

  11. Behrmann, G., Bouyer, P., Larsen, K.G., Pelánek, R.: Lower and upper bounds in zone based abstractions of timed automata. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 312–326. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24730-2_25

    Chapter  MATH  Google Scholar 

  12. Behrmann, G., Bouyer, P., Larsen, K.G., Pelànek, R.: Zone based abstractions for timed automata exploiting lower and upper bounds. Int. J. Softw. Tools Technol. Transf. 8(3), 204–215 (2005)

    Article  Google Scholar 

  13. Behrmann, G., Cougnard, A., David, A., Fleury, E., Larsen, K.G., Lime, D.: UPPAAL-TIGA: time for playing games! In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 121–125. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-73368-3_14

    Chapter  Google Scholar 

  14. Behrmann, G., et al.: Uppaal 4.0. In: Proceedings of 3rd International Conference on Quantitative Evaluation of Systems (QEST 2006), pp. 125–126. IEEE Computer Society Press (2006)

    Google Scholar 

  15. Behrmann, G., et al.: Minimum-cost reachability for priced time automata. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 147–161. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45351-2_15

    Chapter  Google Scholar 

  16. Behrmann, G., Hune, T., Vaandrager, F.: Distributing timed model checking — how the search order matters. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 216–231. Springer, Heidelberg (2000). https://doi.org/10.1007/10722167_19

    Chapter  Google Scholar 

  17. Bengtsson, J., Jonsson, B., Lilius, J., Yi, W.: Partial order reductions for timed systems. In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 485–500. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0055643

    Chapter  Google Scholar 

  18. Bengtsson, J., Larsen, K., Larsson, F., Pettersson, P., Yi, W.: UPPAAL — a tool suite for automatic verification of real-time systems. In: Alur, R., Henzinger, T.A., Sontag, E.D. (eds.) HS 1995. LNCS, vol. 1066, pp. 232–243. Springer, Heidelberg (1996). https://doi.org/10.1007/BFb0020949

    Chapter  Google Scholar 

  19. Bengtsson, J., Yi, W.: Timed automata: semantics, algorithms and tools. In: Desel, J., Reisig, W., Rozenberg, G. (eds.) ACPN 2003. LNCS, vol. 3098, pp. 87–124. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-27755-2_3

    Chapter  MATH  Google Scholar 

  20. Berthomieu, B., Menasche, M.: An enumerative approach for analyzing time Petri nets. In: Proceedings of IFIP 9th World Computer Congress. Information Processing, vol. 83, pp. 41–46. North-Holland/ IFIP (1983)

    Google Scholar 

  21. Beyer, D., Lewerentz, C., Noack, A.: Rabbit: a tool for BDD-based verification of real-time systems. In: Hunt, W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 122–125. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-45069-6_13

    Chapter  Google Scholar 

  22. Bouyer, P.: Untameable timed automata! In: Alt, H., Habib, M. (eds.) STACS 2003. LNCS, vol. 2607, pp. 620–631. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36494-3_54

    Chapter  Google Scholar 

  23. Bouyer, P.: Forward analysis of updatable timed automata. Formal Methods Syst. Des. 24(3), 281–320 (2004)

    Article  Google Scholar 

  24. Bouyer, P., Brihaye, T., Bruyère, V., Raskin, J.F.: On the optimal reachability problem. Formal Methods Syst. Des. 31(2), 135–175 (2007)

    Article  Google Scholar 

  25. Bouyer, P., Brinksma, E., Larsen, K.G.: Optimal infinite scheduling for multi-priced timed automata. Formal Methods Syst. Des. 32(1), 2–23 (2008)

    Article  Google Scholar 

  26. Bouyer, P., Colange, M., Markey, N.: Symbolic optimal reachability in weighted timed automata. In: Chaudhuri, S., Farzan, A. (eds.) CAV 2016. LNCS, vol. 9779, pp. 513–530. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-41528-4_28

    Chapter  Google Scholar 

  27. Bouyer, P., Dufourd, C., Fleury, E., Petit, A.: Updatable timed automata. Theoret. Comput. Sci. 321(2–3), 291–345 (2004)

    Article  MathSciNet  Google Scholar 

  28. Bouyer, P., Fahrenberg, U., Larsen, K.G., Markey, N.: Timed automata with observers under energy constraints. In: Proceedings of 13th International Conference on Hybrid Systems: Computation and Control (HSCC 2010), pp. 61–70. ACM Press (2010)

    Google Scholar 

  29. Bouyer, P., Fahrenberg, U., Larsen, K.G., Markey, N.: Quantitative analysis of real-time systems using priced timed automata. Commun. ACM 54(9), 78–87 (2011)

    Article  Google Scholar 

  30. Bouyer, P., Fahrenberg, U., Larsen, K.G., Markey, N., Srba, J.: Infinite runs in weighted timed automata with energy constraints. In: Cassez, F., Jard, C. (eds.) FORMATS 2008. LNCS, vol. 5215, pp. 33–47. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85778-5_4

    Chapter  MATH  Google Scholar 

  31. Bouyer, P., Laroussinie, F., Reynier, P.-A.: Diagonal constraints in timed automata: forward analysis of timed systems. In: Pettersson, P., Yi, W. (eds.) FORMATS 2005. LNCS, vol. 3829, pp. 112–126. Springer, Heidelberg (2005). https://doi.org/10.1007/11603009_10

    Chapter  MATH  Google Scholar 

  32. Bouyer, P., Larsen, K.G., Markey, N.: Lower-bound constrained runs in weighted timed automata. In: Proceedings of 9th International Conference on Quantitative Evaluation of Systems (QEST 2012), pp. 128–137. IEEE Computer Society Press (2012)

    Google Scholar 

  33. Bouyer, P., Markey, N., Perrin, N., Schlehuber-Caissier, P.: Timed-automata abstraction of switched dynamical systems using control funnels. In: Sankaranarayanan, S., Vicario, E. (eds.) FORMATS 2015. LNCS, vol. 9268, pp. 60–75. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-22975-1_5

    Chapter  MATH  Google Scholar 

  34. Bouyer, P., Markey, N., Perrin, N., Schlehuber-Caissier, P.: Timed-automata abstraction of switched dynamical systems using control invariants. Real-Time Syst. 53(3), 327–353 (2017). https://doi.org/10.1007/s11241-016-9262-3

    Article  MATH  Google Scholar 

  35. Bozga, M., Daws, C., Maler, O., Olivero, A., Tripakis, S., Yovine, S.: Kronos: a model-checking tool for real-time systems. In: Hu, A.J., Vardi, M.Y. (eds.) CAV 1998. LNCS, vol. 1427, pp. 546–550. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0028779

    Chapter  Google Scholar 

  36. Bradley, A.R.: SAT-based model checking without unrolling. In: Jhala, R., Schmidt, D. (eds.) VMCAI 2011. LNCS, vol. 6538, pp. 70–87. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-18275-4_7

    Chapter  Google Scholar 

  37. Bulychev, P.E., et al.: UPPAAL-SMC: statistical model checking for priced timed automata. In: Proceedings of 10th Workshop on Quantitative Aspects of Programming Languages (QAPL 2012). Electronic Proceedings in Theoretical Computer Science, vol. 85, pp. 1–16 (2012). https://doi.org/10.4204/EPTCS.85.1

  38. Cassez, F., David, A., Fleury, E., Larsen, K.G., Lime, D.: Efficient on-the-fly algorithms for the analysis of timed games. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653, pp. 66–80. Springer, Heidelberg (2005). https://doi.org/10.1007/11539452_9

    Chapter  Google Scholar 

  39. Cimatti, A., Griggio, A., Magnago, E., Roveri, M., Tonetta, S.: Extending nuXmv with timed transition systems and timed temporal properties. In: Dillig, I., Tasiran, S. (eds.) CAV 2019. LNCS, vol. 11561, pp. 376–386. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-25540-4_21

    Chapter  Google Scholar 

  40. Cimatti, A., Griggio, A., Mover, S., Tonetta, S.: IC3 modulo theories via implicit predicate abstraction. In: Ábrahám, E., Havelund, K. (eds.) TACAS 2014. LNCS, vol. 8413, pp. 46–61. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54862-8_4

    Chapter  MATH  Google Scholar 

  41. Clarke, E., Grumberg, O., Peled, D.: Model-Checking. MIT Press, Cambridge (1999)

    MATH  Google Scholar 

  42. Damm, W., et al.: Exact and fully symbolic verification of linear hybrid automata with large discrete state spaces. Sci. Comput. Program. 77(10), 1122–1150 (2012). https://doi.org/10.1016/j.scico.2011.07.006, https://www.sciencedirect.com/science/article/pii/S0167642311001523

  43. Dams, D., Gerth, R., Knaack, B., Kuiper, R.: Partial-order reduction techniques for real-time model checking. Formal Aspects Comput. 10(5–6), 469–482 (1998). https://doi.org/10.1007/s001650050028

    Article  MATH  Google Scholar 

  44. David, A., Yi, W.: Modelling and analysis of a commercial field bus protocol. In: Proceedings of 12th Euromicro Conference on Real-Time Systems (ECRTS 2000), pp. 165–172. IEEE Computer Society Press (2000). https://doi.org/10.1109/EMRTS.2000.854004

  45. Daws, C., Tripakis, S.: Model checking of real-time reachability properties using abstractions. In: Steffen, B. (ed.) TACAS 1998. LNCS, vol. 1384, pp. 313–329. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0054180

    Chapter  Google Scholar 

  46. Dill, D.L.: Timing assumptions and verification of finite-state concurrent systems. In: Sifakis, J. (ed.) CAV 1989. LNCS, vol. 407, pp. 197–212. Springer, Heidelberg (1990). https://doi.org/10.1007/3-540-52148-8_17

    Chapter  Google Scholar 

  47. Ehlers, R., Fass, D., Gerke, M., Peter, H.J.: Fully symbolic timed model checking using constraint matrix diagrams. In: Proceedings of 31th IEEE Real-Time Systems Symposium (RTSS 2010), pp. 360–371. IEEE Computer Society Press (2010). https://doi.org/10.1109/RTSS.2010.36

  48. Fersman, E., Krcal, P., Pettersson, P., Yi, W.: Task automata: schedulability, decidability and undecidability. Inf. Comput. 205(8), 1149–1172 (2007)

    Article  MathSciNet  Google Scholar 

  49. Gastin, P., Mukherjee, S., Srivathsan, B.: Reachability in timed automata with diagonal constraints. In: Proceedings of 29th International Conference on Concurrency Theory (CONCUR 2018). LIPIcs, vol. 118, pp. 28:1–28:17. Leibniz-Zentrum für Informatik (2018)

    Google Scholar 

  50. Gastin, P., Mukherjee, S., Srivathsan, B.: Fast algorithms for handling diagonal constraints in timed automata. In: Dillig, I., Tasiran, S. (eds.) CAV 2019. LNCS, vol. 11561, pp. 41–59. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-25540-4_3

    Chapter  Google Scholar 

  51. Gastin, P., Mukherjee, S., Srivathsan, B.: Fast algorithms for handling diagonal constraints in timed automata. CoRR abs/1904.08590 (2019). http://arxiv.org/abs/1904.08590

  52. Gastin, P., Mukherjee, S., Srivathsan, B.: Reachability for updatable timed automata made faster and more effective. In: Proceedings of 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). LIPIcs, vol. 118, pp. 47:1–47:17. Leibniz-Zentrum für Informatik (2020)

    Google Scholar 

  53. Govind, R., Herbreteau, F., Srivathsan, B., Walukiewicz, I.: Revisiting local time semantics for networks of timed automata. In: Proceedings of 30th International Conference on Concurrency Theory (CONCUR 2019). LIPIcs, vol. 140, pp. 16:1–16:15. Leibniz-Zentrum für Informatik (2019)

    Google Scholar 

  54. Govind, R., Herbreteau, F., Srivathsan, B., Walukiewicz, I.: abstrations for the local-time semantics of timed automata: a foundation for partial-order methods. Accepted at LICS (2022)

    Google Scholar 

  55. Hansen, H., Lin, S.-W., Liu, Y., Nguyen, T.K., Sun, J.: Diamonds are a girl’s best friend: partial order reduction for timed automata with abstractions. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 391–406. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-08867-9_26

    Chapter  Google Scholar 

  56. Havelund, K., Skou, A., Larsen, K.G., Lund, K.: Formal modeling and analysis of an audio/video protocol: an industrial case study using UPPAAL. In: Proceedings of 18th IEEE Real-Time Systems Symposium (RTSS 1997), pp. 2–13. IEEE Computer Society Press (1997)

    Google Scholar 

  57. Henzinger, Th.A., Kopke, P.W., Puri, A., Varaiya, P.: What’s decidable about hybrid automata? In: Proceedings of 27th Annual ACM Symposium on the Theory of Computing (STOC 1995), pp. 373–382. ACM (1995)

    Google Scholar 

  58. Henzinger, T.A., Nicollin, X., Sifakis, J., Yovine, S.: Symbolic model-checking for real-time systems. Inf. Comput. 111(2), 193–244 (1994)

    Article  MathSciNet  Google Scholar 

  59. Herbreteau, F., Point, G.: The TChecker tool and librairies. https://github.com/ticktac-project/tchecker

  60. Herbreteau, F., Srivathsan, B., Tran, T.T., Walukiewicz, I.: Why liveness for timed automata is hard, and what we can do about it. In: Proceedings of 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016). LIPIcs, vol. 65, pp. 48:1–48:14. Leibniz-Zentrum für Informatik (2016)

    Google Scholar 

  61. Herbreteau, F., Srivathsan, B., Tran, T.T., Walukiewicz, I.: Why liveness for timed automata is hard, and what we can do about it. ACM Trans. Comput. Logic 21(3), 17:1-17:28 (2020)

    Article  MathSciNet  Google Scholar 

  62. Herbreteau, F., Srivathsan, B., Walukiewicz, I.: Better abstractions for timed automata. In: Proceedings of 27th Annual Symposium on Logic in Computer Science (LICS 2012), pp. 375–384. IEEE Computer Society Press (2012)

    Google Scholar 

  63. Herbreteau, F., Srivathsan, B., Walukiewicz, I.: Lazy abstractions for timed automata. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 990–1005. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39799-8_71

    Chapter  Google Scholar 

  64. Herbreteau, F., Srivathsan, B., Walukiewicz, I.: Better abstractions for timed automata. Inf. Comput. 251, 67–90 (2016)

    Article  MathSciNet  Google Scholar 

  65. Herbreteau, F., Tran, T.-T.: Improving search order for reachability testing in timed automata. In: Sankaranarayanan, S., Vicario, E. (eds.) FORMATS 2015. LNCS, vol. 9268, pp. 124–139. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-22975-1_9

    Chapter  MATH  Google Scholar 

  66. Kindermann, R., Junttila, T., Niemela, I.: Modeling for symbolic analysis of safety instrumented systems with clocks. In: Proceedings of 11th International Conference on Application of Concurrency to System Design (ACSD 2011), pp. 185–194. IEEE Computer Society Press (2011). https://doi.org/10.1109/ACSD.2011.29

  67. Kindermann, R., Junttila, T., Niemelä, I.: SMT-based induction methods for timed systems. In: Jurdziński, M., Ničković, D. (eds.) FORMATS 2012. LNCS, vol. 7595, pp. 171–187. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-33365-1_13

    Chapter  MATH  Google Scholar 

  68. Kwiatkowska, M., Norman, G., Parker, D.: PRISM 4.0: verification of probabilistic real-time systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 585–591. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22110-1_47

    Chapter  Google Scholar 

  69. 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 2013. LNCS, vol. 8044, pp. 968–983. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39799-8_69

    Chapter  Google Scholar 

  70. Larsen, K.G., et al.: As cheap as possible: efficient cost-optimal reachability for priced timed automata. In: Proceedings of 13th International Conference on Computer Aided Verification (CAV 2001). Lecture Notes in Computer Science, vol. 2102, pp. 493–505. Springer (2001)

    Google Scholar 

  71. Larsen, K.G., Mikučionis, M., Muñiz, M., Srba, J.: Urgent partial order reduction for extended timed automata. In: Hung, D.V., Sokolsky, O. (eds.) ATVA 2020. LNCS, vol. 12302, pp. 179–195. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-59152-6_10

    Chapter  Google Scholar 

  72. Larsen, K.G., Pettersson, P., Yi, W.: Compositional and symbolic model-checking of real-time systems. In: Proceedings of 16th IEEE Real-Time Systems Symposium (RTSS 1995), pp. 76–89. IEEE Computer Society Press (1995)

    Google Scholar 

  73. Laxsen, K.G., Pettersson, P., Yi, W.: Diagnostic model-checking for real-time systems. In: Alur, R., Henzinger, T.A., Sontag, E.D. (eds.) HS 1995. LNCS, vol. 1066, pp. 575–586. Springer, Heidelberg (1996). https://doi.org/10.1007/BFb0020977

    Chapter  Google Scholar 

  74. 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). https://doi.org/10.1007/978-3-642-04368-0_18

    Chapter  Google Scholar 

  75. Malinowski, J., Niebert, P.: SAT based bounded model checking with partial order semantics for timed automata. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 405–419. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-12002-2_34

    Chapter  MATH  Google Scholar 

  76. Mercaldo, F., Martinelli, F., Santone, A.: Real-time SCADA attack detection by means of formal methods. In: Proceedings of 28th IEEE International Conference on Enabling Technologies: Infrastructure for Collaborative Enterprises (WETICE 2019), pp. 231–236. IEEE Computer Society Press (2019). https://doi.org/10.1109/WETICE.2019.00057

  77. Mikučionis, M., et al.: Schedulability analysis using UPPAAL: Herschel-Planck case study. In: Margaria, T., Steffen, B. (eds.) ISoLA 2010. LNCS, vol. 6416, pp. 175–190. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-16561-0_21

    Chapter  Google Scholar 

  78. Mukherjee, S.: Reachability in timed automata with diagonal constraints and updates. Ph.D. thesis, Chennai Mathematical Institute, India (2022)

    Google Scholar 

  79. Nguyen, T.K., Sun, J., Liu, Y., Dong, J.S., Liu, Y.: Improved BDD-based discrete analysis of timed systems. In: Giannakopoulou, D., Méry, D. (eds.) FM 2012. LNCS, vol. 7436, pp. 326–340. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32759-9_28

    Chapter  Google Scholar 

  80. Norman, G., Parker, D., Sproston, J.: Model checking for probabilistic timed automata. Formal Methods Syst. Des. 43(2), 164–190 (2013)

    Article  Google Scholar 

  81. Point, G.: TChecker online demonstration. https://tchecker.labri.fr/

  82. Point, G.: UPPAAL-to-TChecker: a tool to translate UPPAAL models into TChecker models. https://github.com/ticktac-project/uppaal-to-tchecker

  83. Ravn, A.P., Srba, J., Vighio, S.: Modelling and verification of web services business activity protocol. In: Abdulla, P.A., Leino, K.R.M. (eds.) TACAS 2011. LNCS, vol. 6605, pp. 357–371. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-19835-9_32

    Chapter  Google Scholar 

  84. Roussanaly, V., Sankur, O., Markey, N.: Abstraction refinement algorithms for timed automata. In: Dillig, I., Tasiran, S. (eds.) CAV 2019. LNCS, vol. 11561, pp. 22–40. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-25540-4_2

    Chapter  Google Scholar 

  85. Sorea, M.: Bounded model checking for timed automata. Electron. Notes Theoret. Comput. Sci. 68(5), 116–134 (2003)

    Article  Google Scholar 

  86. Srivathsan, B.: Abstractions for timed automata. Ph.D. thesis, University of Bordeaux (2012)

    Google Scholar 

  87. Thierry-Mieg, Y.: Symbolic model-checking using ITS-tools. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 231–237. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46681-0_20

    Chapter  Google Scholar 

  88. Tóth, T., Majzik, I.: Lazy reachability checking for timed automata using interpolants. In: Abate, A., Geeraerts, G. (eds.) FORMATS 2017. LNCS, vol. 10419, pp. 264–280. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-65765-3_15

    Chapter  MATH  Google Scholar 

  89. Tripakis, S., Yovine, S.: Analysis of timed systems using time-abstracting bisimulations. Formal Methods Syst. Des. 18(1), 25–68 (2001)

    Article  Google Scholar 

  90. Wang, F.: Symbolic verification of complex real-time systems with clock-restriction diagram. In: Kim, M., Chin, B., Kang, S., Lee, D. (eds.) FORTE 2001. IIFIP, vol. 69, pp. 235–250. Springer, Boston (2002). https://doi.org/10.1007/0-306-47003-9_15

    Chapter  Google Scholar 

  91. Wang, F.: REDLIB for the formal verification of embedded systems. In: Proceedings of 2nd International Symposium on Leveraging Applications of Formal Methods (ISoLA 2006), pp. 341–346. IEEE Computer Society Press (2006)

    Google Scholar 

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Authors and Affiliations

  1. Université Paris-Saclay, CNRS, ENS Paris-Saclay, Laboratoire Méthodes Formelles, Gif-sur-Yvette, 91190, France

    Patricia Bouyer & Paul Gastin

  2. Univ. Bordeaux, CNRS, Bordeaux INP, LaBRI, UMR5800, Talence, 33400, France

    Frédéric Herbreteau

  3. Univ Rennes, Inria, CNRS, Irisa, Rennes, France

    Ocan Sankur

  4. Chennai Mathematical Institute, Chennai, India

    B. Srivathsan

  5. CNRS IRL 2000, ReLaX, Chennai, India

    Paul Gastin & B. Srivathsan

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  1. Patricia Bouyer
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  2. Paul Gastin
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  3. Frédéric Herbreteau
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  4. Ocan Sankur
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  5. B. Srivathsan
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Correspondence to Patricia Bouyer .

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  1. Newcastle University, Newcastle upon Tyne, UK

    Sergiy Bogomolov

  2. University of Birmingham, Birmingham, UK

    David Parker

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Bouyer, P., Gastin, P., Herbreteau, F., Sankur, O., Srivathsan, B. (2022). Zone-Based Verification of Timed Automata: Extrapolations, Simulations and What Next?. In: Bogomolov, S., Parker, D. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2022. Lecture Notes in Computer Science, vol 13465. Springer, Cham. https://doi.org/10.1007/978-3-031-15839-1_2

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