State Identification for Labeled Transition Systems with Inputs and Outputs

  • Petra van den BosEmail author
  • Frits Vaandrager
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12018)


For Finite State Machines (FSMs) a rich testing theory has been developed to discover aspects of their behavior and ensure their correct functioning. Although this theory is widely used, e.g., to check conformance of protocol implementations, its applicability is limited by restrictions of the FSM framework: the fact that inputs and outputs alternate in an FSM, and outputs are fully determined by the previous input and state. Labeled Transition Systems with inputs and outputs (LTSs), as studied in ioco testing theory, provide a richer framework for testing component oriented systems, but lack the algorithms for test generation from FSM theory.

In this article, we propose an algorithm for the fundamental problem of state identification during testing of LTSs. Our algorithm is a direct generalization of the well-known algorithm for computing adaptive distinguishing sequences for FSMs proposed by Lee & Yannakakis. Our algorithm has to deal with so-called compatible states, states that cannot be distinguished in case of an adversarial system-under-test. Analogous to the result of Lee & Yannakakis, we prove that if an (adaptive) test exists that distinguishes all pairs of incompatible states of an LTS, our algorithm will find one. In practice, such adaptive tests typically do not exist. However, in experiments with an implementation of our algorithm on an industrial benchmark, we find that tests produced by our algorithm still distinguish more than 99% of the incompatible state pairs.


  1. 1.
    Alur, R., Courcoubetis, C., Yannakakis, M.: Distinguishing tests for nondeterministic and probabilistic machines. In: STOC, vol. 95, pp. 363–372. Citeseer (1995)Google Scholar
  2. 2.
    Baier, C., Katoen, J.P.: Principles of Model Checking. The MIT Press, Cambridge (2008)zbMATHGoogle Scholar
  3. 3.
    Beneš, N., Daca, P., Henzinger, T.A., Křetínskỳ, J., Ničković, D.: Complete composition operators for IOCO-testing theory. In: Proceedings of the 18th International ACM SIGSOFT Symposium on Component-Based Software Engineering. CBSE 2015, pp. 101–110. ACM, New York (2015).
  4. 4.
    van den Bos, P., Vaandrager, F.W.: State identification for labeled transition systems with inputs and outputs. CoRR abs/1907.11034 (2019).
  5. 5.
    van den Bos, P., Janssen, R., Moerman, J.: n-complete test suites for IOCO. Softw. Qual. J. 27(2), 563–588 (2019). Scholar
  6. 6.
    van den Bos, P., Stoelinga, M.: Tester versus bug: a generic framework for model-based testing via games. In: Orlandini, A., Zimmermann, M. (eds.) Proceedings Ninth International Symposium on Games, Automata, Logics, and Formal Verification. Electronic Proceedings in Theoretical Computer Science, Saarbrücken, Germany, 26–28th September 2018, vol. 277, pp. 118–132. Open Publishing Association (2018).
  7. 7.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 3rd edn. The MIT Press, Cambridge (2009)zbMATHGoogle Scholar
  8. 8.
    Dijkstra, E.W.: Guarded commands, nondeterminacy, and formal derivation of programs. In: Gries, D. (ed.) Programming Methodology: A Collection of Articles by Members of IFIP WG2.3. Texts and Monographs in Computer Science, pp. 166–175. Springer, New York (1978). Scholar
  9. 9.
    Dorofeeva, R., El-Fakih, K., Maag, S., Cavalli, A.R., Yevtushenko, N.: FSM-based conformance testing methods: a survey annotated with experimental evaluation. Inf. Softw. Technol. 52(12), 1286–1297 (2010)CrossRefGoogle Scholar
  10. 10.
    Gill, A.: Introduction to the Theory of Finite-State Machines. McGraw-Hill, New York (1962)zbMATHGoogle Scholar
  11. 11.
    Hierons, R.M.: Testing from a nondeterministic finite state machine using adaptive state counting. IEEE Trans. Comput. 53(10), 1330–1342 (2004). Scholar
  12. 12.
    Lee, D., Yannakakis, M.: Testing finite-state machines: state identification and verification. IEEE Trans. Comput. 43(3), 306–320 (1994). Scholar
  13. 13.
    Lee, D., Yannakakis, M.: Principles and methods of testing finite state machines – a survey. Proc. IEEE 84(8), 1090–1123 (1996)CrossRefGoogle Scholar
  14. 14.
    Mazala, R.: Infinite games. In: Grädel, E., Thomas, W., Wilke, T. (eds.) Automata Logics, and Infinite Games. LNCS, vol. 2500, pp. 23–38. Springer, Heidelberg (2002). Scholar
  15. 15.
    Milner, R.: Communication and Concurrency. Prentice-Hall Inc., Upper Saddle River (1989)zbMATHGoogle Scholar
  16. 16.
    Moerman, J.: Nominal techniques and black box testing for automata learning. Ph.D. thesis, Radboud University Nijmegen, July 2019Google Scholar
  17. 17.
    Moore, E.F.: Gedanken-experiments on sequential machines. In: Annals of Mathematics Studies, vol. 34, pp. 129–153. Princeton University Press, Princeton (1956)Google Scholar
  18. 18.
    Petrenko, A., Yevtushenko, N.: Conformance tests as checking experiments for partial nondeterministic FSM. In: Grieskamp, W., Weise, C. (eds.) FATES 2005. LNCS, vol. 3997, pp. 118–133. Springer, Heidelberg (2006). Scholar
  19. 19.
    Petrenko, A., Yevtushenko, N.: Adaptive testing of deterministic implementations specified by nondeterministic FSMs. In: Wolff, B., Zaïdi, F. (eds.) ICTSS 2011. LNCS, vol. 7019, pp. 162–178. Springer, Heidelberg (2011). Scholar
  20. 20.
    Bensalem, S., Krichen, M., Tripakis, S.: State identification problems for input/output transition systems. In: 2008 9th International Workshop on Discrete Event Systems, pp. 225–230, May 2008.
  21. 21.
    Simão, A., Petrenko, A.: Generating complete and finite test suite for ioco: is it possible? In: Proceedings Ninth Workshop on Model-Based Testing, MBT 2014, Grenoble, France, 6 April 2014, pp. 56–70 (2014).
  22. 22.
    Smeenk, W.: Applying automata learning to complex industrial software. Master’s thesis, Radboud University Nijmegen (2012)Google Scholar
  23. 23.
    Smeenk, W., Moerman, J., Vaandrager, 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, Cham (2015). Scholar
  24. 24.
    Sokolovskii, M.N.: Diagnostic experiments with automata. Cybernetics 7(6), 988–994 (1971). Scholar
  25. 25.
    Tretmans, J.: Model based testing with labelled transition systems. In: Hierons, R.M., Bowen, J.P., Harman, M. (eds.) Formal Methods and Testing. LNCS, vol. 4949, pp. 1–38. Springer, Heidelberg (2008). Scholar
  26. 26.
    Willemse, T.A.C.: Heuristics for ioco-based test-based modelling. In: Brim, L., Haverkort, B., Leucker, M., van de Pol, J. (eds.) FMICS 2006. LNCS, vol. 4346, pp. 132–147. Springer, Heidelberg (2007). Scholar
  27. 27.
    Yannakakis, M., Lee, D.: Testing finite state machines: fault detection. J. Comput. Syst. Sci. 50(2), 209–227 (1995). Scholar

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Institute for Computing and Information SciencesRadboud UniversityNijmegenThe Netherlands

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