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PAC Learning of Deterministic One-Clock Timed Automata

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Formal Methods and Software Engineering (ICFEM 2020)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12531))

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Abstract

We study the problem of learning deterministic one-clock timed automata in the framework of PAC (probably approximately correct) learning. The use of PAC learning relaxes the assumption of having a teacher that can answer equivalence queries exactly, replacing it with approximate answers from testing on a set of samples. The framework provides correctness guarantees in terms of error and confidence parameters. We further discuss several improvements to the basic PAC algorithm. This includes a special sampling method, and the use of comparator and counterexample minimization to reduce the number of equivalence queries. We implemented a prototype for our learning algorithm, and conducted experiments on learning the TCP protocol as well as a number of randomly generated automata. The results demonstrate the effectiveness of our approach, as well as the importance of the various improvements for learning complex models.

This work has been partially funded by NSFC under grant No. 61972284, No. 61625206, No. 61732001 and No. 61836005, and by the CAS Pioneer Hundred Talents Program under grant No. Y9RC585036.

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References

  1. Aichernig, B.K., Tappler, M.: Efficient active automata learning via mutation testing. J. Autom. Reason. 63(4), 1103–1134 (2019)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  3. Alur, R., Fix, L., Henzinger, T.A.: Event-clock automata: a determinizable class of timed automata. Theor. Comput. Sci. 211(1), 253–274 (1999)

    Article  MathSciNet  Google Scholar 

  4. An, J., Chen, M., Zhan, B., Zhan, N., Zhang, M.: Learning one-clock timed automata (full version). arXiv:1910.10680 (2019)

  5. An, J., Chen, M., Zhan, B., Zhan, N., Zhang, M.: Learning one-clock timed automata. In: Biere, A., Parker, D. (eds.) TACAS 2020. LNCS, vol. 12078, pp. 444–462. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45190-5_25

    Chapter  Google Scholar 

  6. An, J., Wang, L., Zhan, B., Zhan, N., Zhang, M.: Learning real-time automata. Science China Information Sciences, in press. https://doi.org/10.1007/s11432-019-2767-4

  7. Angluin, D.: Learning regular sets from queries and counterexamples. Inf. Comput. 75(2), 87–106 (1987)

    Article  MathSciNet  Google Scholar 

  8. Berg, T., Grinchtein, O., Jonsson, B., Leucker, M., Raffelt, H., Steffen, B.: On the correspondence between conformance testing and regular inference. In: Cerioli, M. (ed.) FASE 2005. LNCS, vol. 3442, pp. 175–189. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-31984-9_14

    Chapter  Google Scholar 

  9. van den Bos, P., Smetsers, R., Vaandrager, F.: Enhancing automata learning by log-based metrics. In: Ábrahám, E., Huisman, M. (eds.) IFM 2016. LNCS, vol. 9681, pp. 295–310. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-33693-0_19

    Chapter  Google Scholar 

  10. Chen, Y.F., et al.: PAC learning-based verification and model synthesis. In: ICSE 2016, pp. 714–724. IEEE (2016)

    Google Scholar 

  11. Chow, T.S.: Testing software design modeled by finite-state machines. IEEE Trans. Softw. Eng. 4(3), 178–187 (1978)

    Article  Google Scholar 

  12. Drews, S., D’Antoni, L.: Learning symbolic automata. In: Legay, A., Margaria, T. (eds.) TACAS 2017. LNCS, vol. 10205, pp. 173–189. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-662-54577-5_10

    Chapter  Google Scholar 

  13. En-Nouaary, A., Dssouli, R., Khendek, F.: Timed WP-method: testing real-time systems. IEEE Trans. Softw. Eng. 28(11), 1023–1038 (2002)

    Article  Google Scholar 

  14. En-Nouaary, A., Dssouli, R., Khendek, F., Elqortobi, A.: Timed test cases generation based on state characterization technique. In: RTSS 1998, pp. 220–229. IEEE (1998)

    Google Scholar 

  15. Fujiwara, S., Bochmann, G.V., Khendek, F., Amalou, M., Ghedamsi, A.: Test selection based on finite state models. IEEE Trans. Softw. Eng. 17(6), 591–603 (1991)

    Article  Google Scholar 

  16. Grinchtein, O., Jonsson, B., Leucker, M.: Learning of event-recording automata. Theor. Comput. Sci. 411(47), 4029–4054 (2010)

    Article  MathSciNet  Google Scholar 

  17. Howar, F., Jonsson, B., Vaandrager, F.: Combining black-box and white-box techniques for learning register automata. In: Steffen, B., Woeginger, G. (eds.) Computing and Software Science. LNCS, vol. 10000, pp. 563–588. Springer, Cham (2019). https://doi.org/10.1007/978-3-319-91908-9_26

    Chapter  Google Scholar 

  18. Lee, D., Yannakakis, M.: Principles and methods of testing finite state machines-a survey. Proc. IEEE 84(8), 1090–1123 (1996)

    Article  Google Scholar 

  19. Lin, S.-W., André, É., Dong, J.S., Sun, J., Liu, Y.: An efficient algorithm for learning event-recording automata. In: Bultan, T., Hsiung, P.-A. (eds.) ATVA 2011. LNCS, vol. 6996, pp. 463–472. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-24372-1_35

    Chapter  Google Scholar 

  20. Maler, O., Mens, I.-E.: Learning regular languages over large alphabets. In: Ábrahám, E., Havelund, K. (eds.) TACAS 2014. LNCS, vol. 8413, pp. 485–499. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54862-8_41

    Chapter  Google Scholar 

  21. Maler, O., Mens, I.-E.: A generic algorithm for learning symbolic automata from membership queries. In: Aceto, L., Bacci, G., Bacci, G., Ingólfsdóttir, A., Legay, A., Mardare, R. (eds.) Models, Algorithms, Logics and Tools. LNCS, vol. 10460, pp. 146–169. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63121-9_8

    Chapter  Google Scholar 

  22. Mediouni, B.L., Nouri, A., Bozga, M., Bensalem, S.: Improved learning for stochastic timed models by state-merging algorithms. In: Barrett, C., Davies, M., Kahsai, T. (eds.) NFM 2017. LNCS, vol. 10227, pp. 178–193. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-57288-8_13

    Chapter  Google Scholar 

  23. Mens, I.: Learning regular languages over large alphabets. (Apprentissage de langages réguliers sur des alphabets de grandes tailles). Ph.D. thesis, Grenoble Alpes University, France (2017). https://tel.archives-ouvertes.fr/tel-01792635

  24. Ouaknine, J., Worrell, J.: On the language inclusion problem for timed automata: closing a decidability gap. In: Proceedings of the 19th IEEE Symposium on Logic in Computer Science, LICS 2004, pp. 54–63. IEEE Computer Society (2004)

    Google Scholar 

  25. Pastore, F., Micucci, D., Mariani, L.: Timed k-Tail: automatic inference of timed automata. In: Proceedings of 10th IEEE International Conference on Software Testing, Verification and Validation, ICST 2017, pp. 401–411. IEEE Computer Society (2017)

    Google Scholar 

  26. Pferscher, A., Aichernig, B., Tappler, M.: From passive to active: learning timed automata efficiently. In: NFM 2020 (2020). https://ti.arc.nasa.gov/events/nfm-2020/

  27. Shen, Y.N., Lombardi, F., Dahbura, A.T.: Protocol conformance testing using multiple UIO sequences. IEEE Trans. Commun. 40(8), 1282–1287 (1992)

    Article  Google Scholar 

  28. Smetsers, R., Volpato, M., Vaandrager, F.W., Verwer, S.: Bigger is not always better: on the quality of hypotheses in active automata learning. In: ICGI 2014, pp. 167–181 (2014). http://proceedings.mlr.press/v34/smetsers14a.html

  29. Tappler, M., Aichernig, B.K., Larsen, K.G., Lorber, F.: Time to learn – learning timed automata from tests. In: André, É., Stoelinga, M. (eds.) FORMATS 2019. LNCS, vol. 11750, pp. 216–235. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-29662-9_13

    Chapter  MATH  Google Scholar 

  30. Vaandrager, F.: Model learning. Commun. ACM 60(2), 86–95 (2017)

    Article  Google Scholar 

  31. Valiant, L.G.: A theory of the learnable. Commun. ACM 27(11), 1134–1142 (1984)

    Article  Google Scholar 

  32. Verwer, S., De Weerdt, M., Witteveen, C.: The efficiency of identifying timed automata and the power of clocks. Inf. Comput. 209(3), 606–625 (2011)

    Article  MathSciNet  Google Scholar 

  33. Verwer, S., de Weerdt, M., Witteveen, C.: Efficiently identifying deterministic real-time automata from labeled data. Mach. Learn. 86(3), 295–333 (2011). https://doi.org/10.1007/s10994-011-5265-4

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Software Engineering, Tongji University, Shanghai, China

    Wei Shen, Jie An & Miaomiao Zhang

  2. State Key Laboratory of Computer Science, Institute of Software, CAS, Beijing, China

    Bohua Zhan, Bai Xue & Naijun Zhan

  3. University of Chinese Academy of Sciences, Beijing, China

    Bohua Zhan, Bai Xue & Naijun Zhan

Authors
  1. Wei Shen
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  2. Jie An
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  3. Bohua Zhan
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  4. Miaomiao Zhang
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  5. Bai Xue
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  6. Naijun Zhan
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Corresponding authors

Correspondence to Bohua Zhan , Miaomiao Zhang or Naijun Zhan .

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Editors and Affiliations

  1. Nanyang Technological University, Singapore, Singapore

    Shang-Wei Lin

  2. School of Information and Communication Technology, Griffith University, Nathan Campus, QLD, Australia

    Zhe Hou

  3. Defence Science and Technology Group, Denver, CO, USA

    Brendan Mahony

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Shen, W., An, J., Zhan, B., Zhang, M., Xue, B., Zhan, N. (2020). PAC Learning of Deterministic One-Clock Timed Automata. In: Lin, SW., Hou, Z., Mahony, B. (eds) Formal Methods and Software Engineering. ICFEM 2020. Lecture Notes in Computer Science(), vol 12531. Springer, Cham. https://doi.org/10.1007/978-3-030-63406-3_8

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  • DOI: https://doi.org/10.1007/978-3-030-63406-3_8

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  • Print ISBN: 978-3-030-63405-6

  • Online ISBN: 978-3-030-63406-3

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