Automata Learning with On-the-Fly Direct Hypothesis Construction

  • Maik Merten
  • Falk Howar
  • Bernhard Steffen
  • Tiziana Margaria
Part of the Communications in Computer and Information Science book series (CCIS, volume 336)


We present an active automata learning algorithm for Mealy state machines that directly constructs a state machine hypothesis according to observations, while other algorithms generate a state machine as output from information gathered in an observation table. Our DHC algorithm starts with a one-state hypothesis that it successively extends using a direct construction approach. This approach enables direct observation of the automata construction process: the learning algorithm continues to complete its hypothesis, providing intuition to a field of formal methods otherwise dominated by algorithms that largely operate on internal data structures without visible feedback.

The DHC algorithm is competitive in cases where memory is the critical issue, e.g., in embedded networked systems. It is also well-suited as educational tool to teach the underlying well-established theoretical methods in a totally unbiased fashion, without cluttering the view onto the actual idea of the learning process with aspects only relevant to internal bookkeeping.


State Machine Input Symbol Automaton Learn Input Alphabet Membership 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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aarts, F., Jonsson, B., Uijen, J.: Generating Models of Infinite-State Communication Protocols Using Regular Inference with Abstraction. In: Petrenko, A., Simão, A., Maldonado, J.C. (eds.) ICTSS 2010. LNCS, vol. 6435, pp. 188–204. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  2. 2.
    Angluin, D.: Learning Regular Sets from Queries and Counterexamples. Information and Computation 75(2), 87–106 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Dijkstra, E.W.: A note on two problems in connexion with graphs. Numerische Mathematik 1(1), 269–271 (1959)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Howar, F., Bauer, O., Merten, M., Steffen, B., Margaria, T.: The Teachers’ Crowd: The Impact of Distributed Oracles on Active Automata Learning. In: Hähnle, R., et al. (eds.) ISoLA 2011 Workshops. CCIS, vol. 336, pp. 232–247. Springer, Heidelberg (2012)Google Scholar
  5. 5.
    Jabbar, S.: External directed search. KI 21(1), 37–38 (2007)Google Scholar
  6. 6.
    Jabbar, S.: External memory algorithms for state space exploration in model checking and action planning. PhD thesis (2008)Google Scholar
  7. 7.
    Kearns, M.J., Vazirani, U.V.: An Introduction to Computational Learning Theory. MIT Press, Cambridge (1994)Google Scholar
  8. 8.
    Maler, O., Pnueli, A.: On the Learnability of Infinitary Regular Sets. Information and Computation 118(2), 316–326 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Merten, M., Howar, F., Steffen, B., Cassel, S., Jonsson, B.: Demonstrating Learning of Register Automata. In: Flanagan, C., König, B. (eds.) TACAS 2012. LNCS, vol. 7214, pp. 466–471. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  10. 10.
    Merten, M., Steffen, B., Howar, F., Margaria, T.: Next Generation LearnLib. In: Abdulla, P.A., Leino, K.R.M. (eds.) TACAS 2011. LNCS, vol. 6605, pp. 220–223. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  11. 11.
    Nerode, A.: Linear Automaton Transformations. Proceedings of the American Mathematical Society 9(4), 541–544 (1958)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Niese, O.: An Integrated Approach to Testing Complex Systems. PhD thesis, University of Dortmund, Germany (2003)Google Scholar
  13. 13.
    Raffelt, H., Margaria, T., Steffen, B., Merten, M.: Hybrid test of web applications with webtest. In: TAV-WEB 2008: Proceedings of the 2008 Workshop on Testing, Analysis, and Verification of Web Services and Applications, pp. 1–7. ACM, New York (2008)CrossRefGoogle Scholar
  14. 14.
    Raffelt, H., Merten, M., Steffen, B., Margaria, T.: Dynamic testing via automata learning. Int. J. Softw. Tools Technol. Transf. 11(4), 307–324 (2009)CrossRefGoogle Scholar
  15. 15.
    Raffelt, H., Steffen, B., Berg, T., Margaria, T.: LearnLib: a framework for extrapolating behavioral models. Int. J. Softw. Tools Technol. Transf. 11(5), 393–407 (2009)CrossRefGoogle Scholar
  16. 16.
    Rivest, R.L., Schapire, R.E.: Inference of finite automata using homing sequences. Inf. Comput. 103(2), 299–347 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    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
  18. 18.
    Sulewski, D., Edelkamp, S., Kissmann, P.: Exploiting the computational power of the graphics card: Optimal state space planning on the gpu. In: Bacchus, F., Domshlak, C., Edelkamp, S., Helmert, M. (eds.) ICAPS. AAAI (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Maik Merten
    • 1
  • Falk Howar
    • 1
  • Bernhard Steffen
    • 1
  • Tiziana Margaria
    • 2
  1. 1.Chair for Programming SystemsTechnical University DortmundDortmundGermany
  2. 2.Chair for Service and Software EngineeringUniversity PotsdamPotsdamGermany

Personalised recommendations