Skip to main content

Advertisement

SpringerLink
Book cover

International Conference on Tools and Algorithms for the Construction and Analysis of Systems

TACAS 2022: Tools and Algorithms for the Construction and Analysis of Systems pp 223–243Cite as

  1. Home
  2. Tools and Algorithms for the Construction and Analysis of Systems
  3. Conference paper
A New Approach for Active Automata Learning Based on Apartness

A New Approach for Active Automata Learning Based on Apartness

  • Frits Vaandrager  ORCID: orcid.org/0000-0003-3955-191010,
  • Bharat Garhewal  ORCID: orcid.org/0000-0003-4908-286310,
  • Jurriaan Rot10 &
  • …
  • Thorsten Wißmann  ORCID: orcid.org/0000-0001-8993-648610 
  • Conference paper
  • Open Access
  • First Online: 30 March 2022

  • 2310 Accesses

  • 7 Citations

Part of the Lecture Notes in Computer Science book series (LNCS,volume 13243)

Abstract

We present \(L^{\#}\), a new and simple approach to active automata learning. Instead of focusing on equivalence of observations, like the \(L^{*}\) algorithm and its descendants, \(L^{\#}\) takes a different perspective: it tries to establish apartness, a constructive form of inequality. \(L^{\#}\) does not require auxiliary notions such as observation tables or discrimination trees, but operates directly on tree-shaped automata. \(L^{\#}\) has the same asymptotic query and symbol complexities as the best existing learning algorithms, but we show that adaptive distinguishing sequences can be naturally integrated to boost the performance of \(L^{\#}\) in practice. Experiments with a prototype implementation, written in Rust, suggest that \(L^{\#}\) is competitive with existing algorithms.

Keywords

  • \(L^{\#}\) algorithm
  • active automata learning
  • Mealy machine
  • apartness relation
  • adaptive distinguishing sequence
  • observation tree
  • conformance testing

Research supported by NWO TOP project 612.001.852 “Grey-box learning of Interfaces for Refactoring Legacy Software (GIRLS)”.

Download conference paper PDF

References

  1. Aarts, F., Heidarian, F., Kuppens, H., Olsen, P., Vaandrager, F.: Automata learning through counterexample-guided abstraction refinement. In: Giannakopoulou, D., Méry, D. (eds.) Proceedings of 18th International Symposium on Formal Methods (FM 2012). Lecture Notes in Computer Science, vol. 7436, pp. 10–27. Springer (Aug 2012). https://doi.org/10.1007/978-3-642-32759-9_4

  2. Aarts, F., Vaandrager, F.: Learning I/O automata. In: Gastin, P., Laroussinie, F. (eds.) 21st International Conference on Concurrency Theory (CONCUR), 2010, Proceedings. Lecture Notes in Computer Science, vol. 6269, pp. 71–85. Springer (2010)

    Google Scholar 

  3. Abadi, M., Lamport, L.: The existence of refinement mappings. Theor. Comput. Sci. 82(2), 253–284 (1991)

    Google Scholar 

  4. Aichernig, B.K., Mostowski, W., Mousavi, M.R., Tappler, M., Taromirad, M.: Model learning and model-based testing. In: Bennaceur, A., Hähnle, R., Meinke, K. (eds.) Machine Learning for Dynamic Software Analysis: Potentials and Limits - International Dagstuhl Seminar 16172, Dagstuhl Castle, Germany, April 24-27, 2016, Revised Papers. Lecture Notes in Computer Science, vol. 11026, pp. 74–100. Springer (2018)

    Google Scholar 

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

    Google Scholar 

  6. Angluin, D., Eisenstat, S., Fisman, D.: Learning regular languages via alternating automata. In: IJCAI. pp. 3308–3314. AAAI Press (2015)

    Google Scholar 

  7. Argyros, G., D’Antoni, L.: The learnability of symbolic automata. In: Chockler, H., Weissenbacher, G. (eds.) Computer Aided Verification - 30th International Conference, CAV 2018. Proceedings, Part I. Lecture Notes in Computer Science, vol. 10981, pp. 427–445. Springer (2018). https://doi.org/10.1007/978-3-319-96145-3_23

  8. Aslam, K., Cleophas, L., Schiffelers, R.R.H., van den Brand, M.: Interface protocol inference to aid understanding legacy software components. Softw. Syst. Model. 19(6), 1519–1540 (2020). https://doi.org/10.1007/s10270-020-00809-2

  9. Aslam, K., Luo, Y., Schiffelers, R.R.H., van den Brand, M.: Interface protocol inference to aid understanding legacy software components. In: Hebig, R., Berger, T. (eds.) Proceedings of MODELS 2018 Workshops. CEUR Workshop Proceedings, vol. 2245, pp. 6–11. CEUR-WS.org (2018)

    Google Scholar 

  10. Balcázar, J.L., Díaz, J., Gavaldà, R.: Algorithms for learning finite automata from queries: A unified view. In: Du, D., Ko, K. (eds.) Advances in Algorithms, Languages, and Complexity - In Honor of Ronald V. Book. pp. 53–72. Kluwer (1997)

    Google Scholar 

  11. Balle, B., Mohri, M.: Learning weighted automata. In: CAI. Lecture Notes in Computer Science, vol. 9270, pp. 1–21. Springer (2015)

    Google Scholar 

  12. Barlocco, S., Kupke, C., Rot, J.: Coalgebra learning via duality. In: FoSSaCS. Lecture Notes in Computer Science, vol. 11425, pp. 62–79. Springer (2019)

    Google Scholar 

  13. 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.) Proceedings, Fundamental Approaches to Software Engineering, 8th International Conference, FASE 2005. Lecture Notes in Computer Science, vol. 3442, pp. 175–189. Springer (2005)

    Google Scholar 

  14. Bergadano, F., Varricchio, S.: Learning behaviors of automata from multiplicity and equivalence queries. SIAM J. Comput. 25(6), 1268–1280 (Dec 1996). https://doi.org/10.1137/S009753979326091X

  15. Biermann, A.W., Feldman, J.A.: On the synthesis of finite-state machines from samples of their behavior. IEEE Trans. Computers 21(6), 592–597 (1972). https://doi.org/10.1109/TC.1972.5009015

  16. Bollig, B., Habermehl, P., Kern, C., Leucker, M.: Angluin-style learning of NFA. In: IJCAI. pp. 1004–1009 (2009)

    Google Scholar 

  17. Cassel, S., Howar, F., Jonsson, B., Steffen, B.: Active learning for extended finite state machines. Formal Asp. Comput. 28(2), 233–263 (2016)

    Google Scholar 

  18. Colcombet, T., Petrisan, D., Stabile, R.: Learning automata and transducers: A categorical approach. In: CSL. LIPIcs, vol. 183, pp. 15:1–15:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

    Google Scholar 

  19. Dijkstra, E.W.: A note on two problems in connexion with graphs. Numer. Math. 1(1), 269–271 (Dec 1959). https://doi.org/10.1007/BF01386390

  20. Dijkstra, E.W.: Guarded commands, nondeterminacy and formal derivation of programs. Commun. ACM 18(8), 453–457 (Aug 1975). https://doi.org/10.1145/360933.360975

  21. Fiterău-Broştean, P., Howar, F.: Learning-based testing the sliding window behavior of TCP implementations. in FMICS, LNCS 10471, 185–200 (2017)

    Google Scholar 

  22. Fiterău-Broştean, P., Janssen, R., Vaandrager, F.: Combining model learning and model checking to analyze TCP implementations. in CAV, LNCS 9780, 454–471 (2016)

    Google Scholar 

  23. Fiterău-Broştean, P., Lenaerts, T., Poll, E., de Ruiter, J., Vaandrager, F., Verleg, P.: Model learning and model checking of SSH implementations. In: Proceedings of the 24th ACM SIGSOFT International SPIN Symposium on Model Checking of Software. pp. 142–151. SPIN 2017, ACM, New York, NY, USA (2017)

    Google Scholar 

  24. Florêncio, C.C., Verwer, S.: Regular inference as vertex coloring. Theor. Comput. Sci. 558, 18–34 (2014). https://doi.org/10.1016/j.tcs.2014.09.023

  25. Frohme, M.T.: Active automata learning with adaptive distinguishing sequences. CoRR abs/1902.01139 (2019), http://arxiv.org/abs/1902.01139

  26. Geuvers, H., Jacobs, B.: Relating apartness and bisimulation. Logical Methods in Computer Science Volume 17, Issue 3 (Jul 2021). https://doi.org/10.46298/lmcs-17(3:15)2021

  27. Groz, R., Brémond, N., da Silva Simão, A., Oriat, C.: hW-inference: A heuristic approach to retrieve models through black box testing. J. Syst. Softw. 159 (2020). https://doi.org/10.1016/j.jss.2019.110426

  28. Hagerer, A., Margaria, T., Niese, O., Steffen, B., Brune, G., Ide, H.D.: Efficient regression testing of CTI-systems: Testing a complex call-center solution. Annual review of communication, Int.Engineering Consortium (IEC) 55, 1033–1040 (2001)

    Google Scholar 

  29. Heerdt, G.v.: CALF: Categorical Automata Learning Framework. Phd thesis, University College London (Oct 2020)

    Google Scholar 

  30. Heerdt, G.v., Kupke, C., Rot, J., Silva, A.: Learning weighted automata over principal ideal domains. In: Goubault-Larrecq, J., König, B. (eds.) Foundations of Software Science and Computation Structures - 23rd International Conference, FOSSACS 2020. vol. 12077, pp. 602–621. Springer (2020). https://doi.org/10.1007/978-3-030-45231-5_31

  31. Heyting, A.: Zur intuitionistischen Axiomatik der projektiven Geometrie. Mathematische Annalen 98, 491–538 (1927)

    Google Scholar 

  32. Howar, F.: Active learning of interface programs. Ph.D. thesis, University of Dortmund (Jun 2012)

    Google Scholar 

  33. Howar, F., Isberner, M., Steffen, B., Bauer, O., Jonsson, B.: Inferring semantic interfaces of data structures. In: ISoLA (1): Leveraging Applications of Formal Methods, Verification and Validation. Technologies for Mastering Change - 5th International Symposium, ISoLA 2012, 2012, Proceedings, Part I. Lecture Notes in Computer Science, vol. 7609, pp. 554–571. Springer (2012)

    Google Scholar 

  34. Howar, F., Steffen, B.: Active automata learning in practice. In: Bennaceur, A., Hähnle, R., Meinke, K. (eds.) Machine Learning for Dynamic Software Analysis: Potentials and Limits: International Dagstuhl Seminar 16172, Dagstuhl Castle, Germany, April 24-27, 2016, Revised Papers. pp. 123–148. Springer International Publishing (2018)

    Google Scholar 

  35. Irfan, M.N., Oriat, C., Groz, R.: Angluin style finite state machine inference with non-optimal counterexamples. In: Proceedings of the First International Workshop on Model Inference In Testing. p. 11–19. MIIT ’10, Association for Computing Machinery, New York, NY, USA (2010)

    Google Scholar 

  36. Isberner, M.: Foundations of active automata learning: an algorithmic perspective. Ph.D. thesis, Technical University Dortmund, Germany (2015), http://hdl.handle.net/2003/34282

  37. Isberner, M., Howar, F., Steffen, B.: The TTT algorithm: A redundancy-free approach to active automata learning. In: Bonakdarpour, B., Smolka, S.A. (eds.) Runtime Verification: 5th International Conference, RV 2014, Toronto, ON, Canada, September 22-25, 2014. Proceedings. pp. 307–322. Springer International Publishing, Cham (2014)

    Google Scholar 

  38. Kearns, M.J., Vazirani, U.V.: An introduction to computational learning theory. MIT Press (1994)

    Google Scholar 

  39. Lee, D., Yannakakis, M.: Testing finite-state machines: State identification and verification. IEEE Trans. Comput. 43(3), 306–320 (1994)

    Google Scholar 

  40. Maler, O., Mens, I.: 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 - Essays Dedicated to Kim Guldstrand Larsen on the Occasion of His 60th Birthday. Lecture Notes in Computer Science, vol. 10460, pp. 146–169. Springer (2017)

    Google Scholar 

  41. Maler, O., Pnueli, A.: On the learnability of infinitary regular sets. Inf. Comput. 118(2), 316–326 (1995). https://doi.org/10.1006/inco.1995.1070

  42. Margaria, T., Raffelt, H., Steffen, B.: Knowledge-based relevance filtering for efficient system-level test-based model generation. Innov. Syst. Softw. Eng. 1(2), 147–156 (2005). https://doi.org/10.1007/s11334-005-0016-y

  43. Meinke, K.: CGE: A sequential learning algorithm for Mealy automata. In: Sempere, J., García, P. (eds.) Grammatical Inference: Theoretical Results and Applications, 10th International Colloquium, ICGI 2010, Valencia, Spain, September 13-16, 2010. Proceedings. Lecture Notes in Computer Science, vol. 6339, pp. 148–162. Springer (2010)

    Google Scholar 

  44. Meinke, K., Niu, F., Sindhu, M.A.: Learning-based software testing: A tutorial. In: Hähnle, R., Knoop, J., Margaria, T., Schreiner, D., Steffen, B. (eds.) Leveraging Applications of Formal Methods, Verification, and Validation - International Workshops, SARS 2011 and MLSC 2011. Revised Selected Papers. Communications in Computer and Information Science, vol. 336, pp. 200–219. Springer (2011)

    Google Scholar 

  45. Merten, M., Howar, F., Steffen, B., Margaria, T.: Automata learning with on-the-fly direct hypothesis construction. In: Hähnle, R., Knoop, J., Margaria, T., Schreiner, D., Steffen, B. (eds.) Leveraging Applications of Formal Methods, Verification, and Validation - International Workshops, SARS 2011 and MLSC 2011. Revised Selected Papers. Communications in Computer and Information Science, vol. 336, pp. 248–260. Springer (2011)

    Google Scholar 

  46. Moerman, J., Sammartino, M., Silva, A., Klin, B., Szynwelski, M.: Learning nominal automata. In: Castagna, G., Gordon, A.D. (eds.) Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages, POPL 2017, Paris, France, January 18-20, 2017. pp. 613–625. ACM (2017). https://doi.org/10.1145/3009837.3009879

  47. Neider, D., Smetsers, R., Vaandrager, F.W., Kuppens, H.: Benchmarks for automata learning and conformance testing. In: Margaria, T., Graf, S., Larsen, K.G. (eds.) Models, Mindsets, Meta: The What, the How, and the Why Not? - Essays Dedicated to Bernhard Steffen on the Occasion of His 60th Birthday. Lecture Notes in Computer Science, vol. 11200, pp. 390–416. Springer (2018)

    Google Scholar 

  48. Niese, O.: An Integrated Approach to Testing Complex Systems. Ph.D. thesis, University of Dortmund (2003)

    Google Scholar 

  49. Petrenko, A., Avellaneda, F., Groz, R., Oriat, C.: From passive to active FSM inference via checking sequence construction. In: Yevtushenko, N., Cavalli, A.R., Yenigün, H. (eds.) Testing Software and Systems - 29th IFIP WG 6.1 International Conference, ICTSS 2017, St. Petersburg, Russia, October 9-11, 2017, Proceedings. Lecture Notes in Computer Science, vol. 10533, pp. 126–141. Springer (2017)

    Google Scholar 

  50. Petrenko, A., Li, K., Groz, R., Hossen, K., Oriat, C.: Inferring approximated models for systems engineering. In: 15th International IEEE Symposium on High-Assurance Systems Engineering, HASE 2014, Miami Beach, FL, USA, January 9-11, 2014. pp. 249–253. IEEE Computer Society (2014). https://doi.org/10.1109/HASE.2014.46

  51. Raffelt, H., Steffen, B., Berg, T., Margaria, T.: LearnLib: a framework for extrapolating behavioral models. STTT 11(5), 393–407 (2009)

    Google Scholar 

  52. Rivest, R., Schapire, R.: Inference of finite automata using homing sequences (extended abstract). In: Proceedings of the Twenty-First Annual ACM Symposium on Theory of Computing, 15-17 May 1989, Seattle, Washington, USA. pp. 411–420. ACM (1989)

    Google Scholar 

  53. Rivest, R., Schapire, R.: Inference of finite automata using homing sequences. Inf. Comput. 103(2), 299–347 (1993). https://doi.org/10.1006/inco.1993.1021

  54. Sakr, S., Bonifati, A., Voigt, H., Iosup, A., Ammar, K., Angles, R., Aref, W., Arenas, M., Besta, M., Boncz, P.A., Daudjee, K., Valle, E.D., Dumbrava, S., Hartig, O., Haslhofer, B., Hegeman, T., Hidders, J., Hose, K., Iamnitchi, A., Kalavri, V., Kapp, H., Martens, W., Özsu, M.T., Peukert, E., Plantikow, S., Ragab, M., Ripeanu, M.R., Salihoglu, S., Schulz, C., Selmer, P., Sequeda, J.F., Shinavier, J., Szárnyas, G., Tommasini, R., Tumeo, A., Uta, A., Varbanescu, A.L., Wu, H.Y., Yakovets, N., Yan, D., Yoneki, E.: The future is big graphs: A community view on graph processing systems. Commun. ACM 64(9), 62–71 (Aug 2021). https://doi.org/10.1145/3434642

  55. Schuts, M., Hooman, J., Vaandrager, F.: Refactoring of legacy software using model learning and equivalence checking: an industrial experience report. In: Ábrahám, E., Huisman, M. (eds.) Proceedings 12th International Conference on integrated Formal Methods (iFM). LNCS, vol. 9681, pp. 311–325 (2016)

    Google Scholar 

  56. Shahbaz, M., Groz, R.: Inferring Mealy machines. In: Cavalcanti, A., Dams, D. (eds.) FM 2009: Formal Methods, Second World Congress, Eindhoven, The Netherlands, November 2-6, 2009. Proceedings. Lecture Notes in Computer Science, vol. 5850, pp. 207–222. Springer (2009)

    Google Scholar 

  57. Smeenk, W., Moerman, J., Vaandrager, F.W., Jansen, D.N.: Applying automata learning to embedded control software. In: Butler, M.J., Conchon, S., Zaïdi, F. (eds.) Formal Methods and Software Engineering - 17th International Conference on Formal Engineering Methods, ICFEM 2015, France, 2015, Proceedings. Lecture Notes in Computer Science, vol. 9407, pp. 67–83. Springer (2015). https://doi.org/10.1007/978-3-319-25423-4_5

  58. Smetsers, R., Fiterau-Brostean, P., Vaandrager, F.W.: Model learning as a satisfiability modulo theories problem. In: Klein, S.T., Martín-Vide, C., Shapira, D. (eds.) Language and Automata Theory and Applications - 12th International Conference, LATA 2018, 2018, Proceedings. Lecture Notes in Computer Science, vol. 10792, pp. 182–194. Springer (2018)

    Google Scholar 

  59. Smetsers, R., Moerman, J., Jansen, D.N.: Minimal separating sequences for all pairs of states. In: Dediu, A., Janousek, J., Martín-Vide, C., Truthe, B. (eds.) Language and Automata Theory and Applications - 10th International Conference, LATA 2016, Proceedings. Lecture Notes in Computer Science, vol. 9618, pp. 181–193. Springer (2016). https://doi.org/10.1007/978-3-319-30000-9_14

  60. Soucha, M., Bogdanov, K.: Observation tree approach: Active learning relying on testing. Comput. J. 63(9), 1298–1310 (2020). https://doi.org/10.1093/comjnl/bxz056

  61. Troelstra, A.S., Schwichtenberg, H.: Basic Proof Theory. Cambridge Tracts in Theoretical Computer Science, Cambridge University Press, 2 edn. (2000). https://doi.org/10.1017/CBO9781139168717

  62. Urbat, H., Schröder, L.: Automata learning: An algebraic approach. In: LICS. pp. 900–914. ACM (2020)

    Google Scholar 

  63. Vaandrager, F.: Model learning. Communications of the ACM 60(2), 86–95 (2017). https://doi.org/10.1145/2967606.

  64. Vaandrager, F., Bloem, R., Ebrahimi, M.: Learning Mealy machines with one timer. In: Leporati, A., Martín-Vide, C., Shapira, D., Zandron, C. (eds.) Language and Automata Theory and Applications - 15th International Conference, LATA 2021, Proceedings. Lecture Notes in Computer Science, vol. 12638, pp. 157–170. Springer (2021)

    Google Scholar 

  65. Vaandrager, F., Garhewal, B., Rot, J., Wißmann, T.: A new approach for active automata learning based on apartness (2022), https://arxiv.org/abs/2107.05419

Download references

Author information

Authors and Affiliations

  1. Institute for Computing and Information Sciences, Radboud University, Nijmegen, the Netherlands

    Frits Vaandrager, Bharat Garhewal, Jurriaan Rot & Thorsten Wißmann

Authors
  1. Frits Vaandrager
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bharat Garhewal
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jurriaan Rot
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Thorsten Wißmann
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Frits Vaandrager .

Editor information

Editors and Affiliations

  1. Ben-Gurion University of the Negev, Be'er Sheva, Israel

    Dr. Dana Fisman

  2. University of Illinois Urbana-Champaign, Urbana, IL, USA

    Grigore Rosu

Rights and permissions

Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

Reprints and Permissions

Copyright information

© 2022 The Author(s)

About this paper

Verify currency and authenticity via CrossMark

Cite this paper

Vaandrager, F., Garhewal, B., Rot, J., Wißmann, T. (2022). A New Approach for Active Automata Learning Based on Apartness. In: Fisman, D., Rosu, G. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2022. Lecture Notes in Computer Science, vol 13243. Springer, Cham. https://doi.org/10.1007/978-3-030-99524-9_12

Download citation

  • .RIS
  • .ENW
  • .BIB

  • DOI: https://doi.org/10.1007/978-3-030-99524-9_12

  • Published: 30 March 2022

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-99523-2

  • Online ISBN: 978-3-030-99524-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Share this paper

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

  • The European Joint Conferences on Theory and Practice of Software.

    Published in cooperation with

    http://www.etaps.org/

Over 10 million scientific documents at your fingertips

Switch Edition
  • Academic Edition
  • Corporate Edition
  • Home
  • Impressum
  • Legal information
  • Privacy statement
  • California Privacy Statement
  • How we use cookies
  • Manage cookies/Do not sell my data
  • Accessibility
  • FAQ
  • Contact us
  • Affiliate program

Not affiliated

Springer Nature

© 2023 Springer Nature Switzerland AG. Part of Springer Nature.