Enhancing Automata Learning by Log-Based Metrics

  • Petra van den BosEmail author
  • Rick Smetsers
  • Frits Vaandrager
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9681)


We study a general class of distance metrics for deterministic Mealy machines. The metrics are induced by weight functions that specify the relative importance of input sequences. By choosing an appropriate weight function we may fine-tune a metric so that it captures some intuitive notion of quality. In particular, we present a metric that is based on the minimal number of inputs that must be provided to obtain a counterexample, starting from states that can be reached by a given set of logs. For any weight function, we may boost the performance of existing model learning algorithms by introducing an extra component, which we call the Comparator. Preliminary experiments show that use of the Comparator yields a significant reduction of the number of inputs required to learn correct models, compared to current state-of-the-art algorithms. In existing automata learning algorithms, the quality of subsequent hypotheses may decrease. Generalising a result of Smetsers et al., we show that the quality of hypotheses that are generated by the Comparator never decreases.


Weight Function Input Sequence Intuitive Notion Conformance Testing Test Query 
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.


  1. 1.
    De Alfaro, L., Faella, M., Stoelinga, M.: Linear and branching system metrics. IEEE Trans. Software Eng. 35(2), 258–273 (2009)CrossRefzbMATHGoogle Scholar
  2. 2.
    Angluin, D.: Learning regular sets from queries and counterexamples. Inf. Comput. 75(2), 87–106 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    De Bakker, J.W., Zucker, J.I.: Processes and the denotational semantics of concurrency. Inf. Control 54(12), 70–120 (1982)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Van den Bos, P.: Enhancing active automata learning by a user log based metric. Master’s thesis, Radboud University Nijmegen (2015)Google Scholar
  5. 5.
    Briones, L.B., Brinksma, E., Stoelinga, M.: A semantic framework for test coverage. In: Graf, S., Zhang, W. (eds.) ATVA 2006. LNCS, vol. 4218, pp. 399–414. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Černý, P., Henzinger, T.A., Radhakrishna, A.: Simulation distances. In: Gastin, P., Laroussinie, F. (eds.) CONCUR 2010. LNCS, vol. 6269, pp. 253–268. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  7. 7.
    de Alfaro, L., Henzinger, T.A., Majumdar, R.: Discounting the future in systems theory. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 1022–1037. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  8. 8.
    de la Higuera, C.: Grammatical Inference. Cambridge University Press, Cambridge (2010)CrossRefzbMATHGoogle Scholar
  9. 9.
    de Ruiter, J., Poll, E.: Protocol state fuzzing of TLS implementations. In: USENIX Security 2015, pp. 193–206. USENIX Association, Washington, D.C., August 2015Google Scholar
  10. 10.
    Dijkstra, E.W.: The humble programmer. CACM 15(10), 859–866 (1972)CrossRefGoogle Scholar
  11. 11.
    Droste, M., Kuich, W., Vogler, H.: Handbook of Weighted Automata, 1st edn. Springer, Heidelberg (2009)CrossRefzbMATHGoogle Scholar
  12. 12.
    Fiterău-Broştean, P., Janssen, R., Vaandrager, F.: Learning fragments of the TCP network protocol. In: Lang, F., Flammini, F. (eds.) FMICS 2014. LNCS, vol. 8718, pp. 78–93. Springer, Heidelberg (2014)Google Scholar
  13. 13.
    Fiterău-Broştean, P., Janssen, R., Vaandrager, F.: Combining model learning and model checking to analyze TCP implementations. Submitted to CAV (2016).
  14. 14.
    Henzinger, T.: Quantitative reactive modeling and verification. Comput. Sci. Res. Dev. 28(4), 331–344 (2013)CrossRefGoogle Scholar
  15. 15.
    Isberner, M.: Foundations of Active Automata Learning: An Algorithmic Perspective. Ph.D. thesis, Technical University of Dortmund (2015)Google Scholar
  16. 16.
    Lee, D., Yannakakis, M.: Principles and methods of testing finite state machines-a survey. Proc. IEEE 84(8), 1090–1123 (1996)CrossRefGoogle Scholar
  17. 17.
    Raffelt, H., Steffen, B., Berg, T., Margaria, T.: LearnLib: a framework for extrapolating behavioral models. STTT 11(5), 393–407 (2009)CrossRefGoogle Scholar
  18. 18.
    Rivest, R.L., Schapire, R.E.: Inference of finite automata using homing sequences. Inf. Comput. 103(2), 299–347 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Schuts, M., Hooman, J., Vaandrager, F.: Refactoring of legacy software using model learning and equivalence checking: an industrial experience report. In: Proceedings of iFM (2016)Google Scholar
  20. 20.
    Smeenk, W.: Applying automata learning to complex industrial software. Master’s thesis, Radboud University Nijmegen, September 2012Google Scholar
  21. 21.
    Smeenk, W., Moerman, J., Vaandrage, F., Jansen, D.N.: Applying Automata Learning to Embedded Control Software. In: Butler, M., Conchon, S., Zaïdi, F. (eds.) ICFEM 2015. LNCS, vol. 9407, pp. 67–83. Springer, Heidelberg (2015). doi: 10.1007/978-3-319-25423-4_5 CrossRefGoogle Scholar
  22. 22.
    Smetsers, R., Moerman, J., Jansen, D.N.: Minimal separating sequences for all Pairs of states. In: Dediu, A.-H., Janoušek, J., Martín-Vide, C., Truthe, B. (eds.) LATA 2016. LNCS, vol. 9618, pp. 181–193. Springer, Heidelberg (2016). doi: 10.1007/978-3-319-30000-9_14 CrossRefGoogle Scholar
  23. 23.
    Smetsers, R., Volpato, M., Vaandrager, F., Verwer, S.: Bigger is not always better: on the quality of hypotheses in active automata learning. In: Proceedings of ICGI, JMLR: W&CP, vol. 34, pp. 167–181 (2014)Google Scholar
  24. 24.
    Sommerville, I.: Software Engineering. Addison-Wesley Publishing Company, Boston (2001)zbMATHGoogle Scholar
  25. 25.
    Steffen, B., Howar, F., Merten, M.: Introduction to Active automata learning from a practical perspective. In: Bernardo, M., Issarny, V. (eds.) SFM 2011. LNCS, vol. 6659, pp. 256–296. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  26. 26.
    Thrane, C., Fahrenberg, U., Larsen, K.G.: Quantitative analysis of weighted transition systems. J. Logic Algebraic Program. 79(7), 689–703 (2010)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Petra van den Bos
    • 1
    Email author
  • Rick Smetsers
    • 1
  • Frits Vaandrager
    • 1
  1. 1.Institute for Computing and Information SciencesRadboud UniversityNijmegenThe Netherlands

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