Skip to main content
SpringerLink
Log in

Adaptive distinguishing test cases of nondeterministic finite state machines: test case derivation and length estimation

  • Original Article
  • Published:
Formal Aspects of Computing

Abstract

A top-down approach is presented for checking the existence and derivation of an adaptive distinguishing test case (called also an adaptive distinguishing sequence) for a nondeterministic finite state machine (NDFSM). When such a test case exists, the method returns a canonical test case that includes all other distinguishing tests of the given complete observable NDFSM. In the second part of the paper, a constructive approach is provided for deriving a class of complete observable NDFSMs with n states, n >  2, and 2n − n − 1 inputs such that a shortest adaptive distinguishing test case for each NDFSM in the intended class has the length (height) 2n − n − 1. In other words, we prove the reachability of the exponential upper bound on the length of a shortest adaptive distinguishing sequence for complete observable NDFSMs while for deterministic machines the upper bound is polynomial with respect to the number of states. For constructing the intended class of NDFSMs for a given n, we propose a special linear order over all the non-empty subsets without singletons of an n-element set. The obtained tight exponential upper bound initiates further research on identifying certain NDFSM classes where this upper bound is not reachable.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Alur R, Courcoubetis C, Yannakakis M (1995) Distinguishing tests for nondeterministic and probabilistic machines, In: Proceedings of the 27th ACM symposium on theory of computing, pp 363–372

  2. Bochmann GV, Petrenko A (1994) Protocol testing: review of methods and relevance for software testing, In: Proceedings of international symposium on software testing and analysis, Seattle, pp 109–123

  3. Gill A (1961) State-identification experiments in finite automata. Inf Control 4: 132–154

    Article  MathSciNet  MATH  Google Scholar 

  4. Dorofeeva R, El-Fakih K, Maag S, Cavalli AR, Yevtushenko N (2010) FSM-based conformance testing methods: a survey annotated with experimental evaluation. Inf Softw Technol 52: 1286–1297

    Article  Google Scholar 

  5. Günicen C, İnan K, Türker UC, Yenigün H (2014) The relation between preset distinguishing sequences and synchronizing sequences. Form Asp Comput 26(6): 1153–1167

    Article  MathSciNet  MATH  Google Scholar 

  6. Güniçen C, Jourdan G-V, Yenigün H (2015) Using multiple adaptive distinguishing sequences for checking sequence gen eration. In: Proceedings of the 27th international conference on testing software and systems ICTSS 2015, Lecture notes in computer science 9447, Springer, pp 19–34

  7. Hierons RM, Türker UC (2014) Distinguishing sequences for partially specified FSMs. In: Proceedings of NASA formal methods of the 6th international symposium (NFM 2014), Houston, TX, USA, April 29-May 1, 2014, pp 62–76

  8. Kohavi Z (1978) Switching and finite automata theory. McGraw- Hill, New York

    MATH  Google Scholar 

  9. Kushik N, El-Fakih K, Yevtushenko N (2011) Preset and adaptive homing experiments for nondeterministic finite state machines. In: Proceedings of the 16th international conference on implementation and application of automata (CIAA 2011), Blois, France, LNCS 6807, pp 215–224

  10. Kushik N, El-Fakih K, Yevtushenko N, Cavalli AR (2016) On adaptive experiments for nondeterministic finite statemachines. Softw Tools Technol Transf 18(3): 251–264

    Article  Google Scholar 

  11. Lee D, Yannakakis M (1994) finite-statemachines: state identification and verification. IEEETransComput 43(3): 306–320

    Google Scholar 

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

    Article  Google Scholar 

  13. Mathur A (2008) Foundations of software testing. Addison Wesley, Boston

    Google Scholar 

  14. Petrenko A, Yevtushenko N (2011) Adaptive testing of deterministic implementations specified by nondeterministic FSMs. Lecture notes in computer science, vol 7019, pp 162–178

  15. Spitsyna N, El-Fakih K, Yevtushenko N (2007) Studying the separability relation between finite state machines. Softw Test Verif Reliab 17(4): 227–241

    Article  Google Scholar 

  16. Türker UC, Yenigün H (2014) Hardness and inapproximability of minimizing adaptive distinguishing sequences. FormMeth ods Syst Des 44(3): 264–294

    MATH  Google Scholar 

  17. Türker UC, Ünlüyurt T, Yenigün H (2016) Effective algorithms for constructing minimum cost adaptive distinguishing se quences. Inf Softw Technol 74: 69–85

    Article  Google Scholar 

  18. El-Fakih K, Haddad A, Aleb N, Yevtushenko N (2016) for deriving distinguishing experiments of nondeterministic finite state machines. Appl Soft Comput 49: 1175–1184

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. American University of Sharjah, PO Box 26666, Sharjah, United Arab Emirates

    Khaled El-Fakih

  2. Tomsk State University, Tomsk, Russia

    Nina Yevtushenko

  3. Institute for System Programming RAS, Moscow, Russia

    Nina Yevtushenko

  4. SAMOVAR, CNRS, Télécom SudParis, Université Paris-Saclay, Évry, France

    Natalia Kushik

Authors
  1. Khaled El-Fakih
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nina Yevtushenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Natalia Kushik
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Khaled El-Fakih.

Additional information

Ana Cavalcanti

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

El-Fakih, K., Yevtushenko, N. & Kushik, N. Adaptive distinguishing test cases of nondeterministic finite state machines: test case derivation and length estimation. Form Asp Comp 30, 319–332 (2018). https://doi.org/10.1007/s00165-017-0450-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00165-017-0450-2

Keywords

Search

Navigation