Abstract
Homing and synchronizing sequences (HSs and SSs) are used in Finite State Machine (FSM)-based testing for state identification when deriving a test suite with guaranteed fault coverage or when performing a non-intrusive (passive) testing or monitoring. However, such preset sequences do not always exist for nondeterministic FSMs or can be rather long if existing. Adaptive HSs and SSs are known to exist more often and can be much shorter which makes them attractive for deriving test suites and adaptive checking sequences. As nowadays, a number of specifications are represented by nondeterministic FSMs, there is a need for the deeper study of such sequences, their derivation strategies, and related complexity estimation / reduction. In this paper, given an FSM and a subset \(S'\) of its states, we are concerned with the existence check and derivation of \(S'\)-homing and \(S'\)-synchronizing adaptive sequences (test cases) which allow to reduce the uncertainty about the current state of the FSM up to a state of the subset \(S'\). There are a number of research papers on evaluating the complexity of the existence check of adaptive HS / SS as well as on estimating the length of an HS / SS, and in the ICTSS’19 conference, we presented the complexity of their derivation for non-initialized complete nondeterministic FSMs. In this paper, we utilize the criteria of the ICTSS’19 paper to estimate the complexity of the existence check and derivation of \(S'\)-homing and \(S'\)-synchronizing test cases for non-initialized observable nondeterministic FSMs. Some sufficient conditions for weakly initialized FSMs to have adaptive \(S'\)-homing and \(S'\)-synchronizing test cases are also established.
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Notes
The FSM is represented by two arrays, the array of successors and the array of inputs that start a homing test case for each state pair; the complexity of the derivation of the latter is \(\mathrm {O}(|I|qn^4)\) for |I| inputs.
References
Alur, R., Courcoubetis, C., & Yannakakis, M. (1995). Distinguishing tests for nondeterministic and probabilistic machines. In Proceedings of the Twenty-Seventh Annual ACM Symposium on Theory of Computing, 29 May-1 June 1995, Las Vegas, Nevada, USA, pp. 363–372. https://doi.org/10.1145/225058.225161
Chow, T. S. (1978). Testing software design modeled by finite-state machines. IEEE Transactions on Software Engineering, 4(3), 178–187.
Gill, A. (1962). Introduction to the Theory of Finite-state Machines. New York: McGraw-Hill.
Hennie, F. C. (1964). Fault detecting experiments for sequential circuits. In 5th Annual Symposium on Switching Circuit Theory and Logical Design, Princeton, New Jersey, USA, November 11-13, 1964, pp. 95–110. https://doi.org/10.1109/SWCT.1964.8
Hierons, R. M., & Ural, H. (2002). Reduced length checking sequences. IEEE Trans. Computers, 51(9), 1111–1117. https://doi.org/10.1109/TC.2002.1032630
Ito, M. & Shikishima-Tsuji, K. (2004). Some results on directable automata. In Theory Is Forever, Essays Dedicated to Arto Salomaa on the Occasion of His 70th Birthday, pp. 125–133. https://doi.org/10.1007/978-3-540-27812-2n12
Kushik, N., El-Fakih, K., & Yevtushenko, N. (2013). Adaptive homing and distinguishing experiments for nondeterministic finite state machines. In Testing Software and Systems - 25th IFIP WG 6.1 International Conference, ICTSS 2013, Istanbul, Turkey, November 13-15, 2013, Proceedings, pp. 33–48. https://doi.org/10.1007/978-3-642-41707-8n3
Kushik, N., El-Fakih, K., Yevtushenko, N., & Cavalli, A. R. (2016a). On adaptive experiments for nondeterministic finite state machines. STTT, 18(3), 251–264. https://doi.org/10.1007/s10009-014-0357-7
Kushik, N., López, J., Cavalli, A. R., & Yevtushenko, N. (2016b). Improving protocol passive testing through gedanken experiments with finite state machines. In 2016 IEEE International Conference on Software Quality, Reliability and Security, QRS 2016, Vienna, Austria, August 1-3, 2016, pp. 315–322. https://doi.org/10.1109/QRS.2016.43
Kushik, N., & Yevtushenko, N. (2013). On the length of homing sequences for nondeterministic finite state machines. In Implementation and Application of Automata - 18th International Conference, CIAA 2013, Halifax, NS, Canada, July 16-19, 2013. Proceedings, pp. 220–231.
Kushik, N., & Yevtushenko, N. (2015). Adaptive homing is in P. In Proceedings Tenth Workshop on Model Based Testing, MBT 2015, London, UK, 18th April 2015., pp. 73–78.
Kushik, N., Yevtushenko, N., & Yenigün, H. (2016c). Reducing the complexity of checking the existence and derivation of adaptive synchronizing experiments for nondeterministic fsms. In Proceedings of the International Workshop on Domain Specific Model-based App Roaches to Verification and Validation, AMARETTO@MODELSWARD 2016, Rome, Italy, February 19-21, 2016., pp. 83–90. https://doi.org/10.5220/0005854500830090
Lee, D., & Yannakakis, M. (1994). Testing finite-state machines: State identification and verification. IEEE Transaction on Computers,43(3), 306–320. https://doi.org/10.1109/12.272431
Lee, D., & Yannakakis, M. (1996). Principles and methods of testing finite state machines-a survey. Proceedings of the IEEE,84, 1090–1123. https://doi.org/10.1109/5.533956
Petrenko, A., & Yevtushenko, H. (2005). Conformance tests as checking experiments for partial nondeterministic FSM. In Formal Approaches to Software Testing, 5th International Workshop, FATES 2005, Edinburgh, UK, July 11, 2005, Revised Selected Papers, pp. 118–133. https://doi.org/10.1007/11759744n9
Sandberg, S. (2004). Homing and synchronizing sequences. In Model-Based Testing of Reactive Systems, Advanced Lectures [The volume is the outcome of a research seminar that was held in Schloss Dagstuhl in January 2004], pp. 5–33. https://doi.org/101007/11498490n2
Türker, U. C., & Yenigün, H. (2014). Hardness and inapproximability of minimizing adaptive distinguishing sequences. Formal Methods in System Design,44(3), 264–294.
von Bochmann, G., & Petrenko, A. (1994). Protocol testing: Review of methods and relevance for software testing. In Proceedings of the 1994 International Symposium on Software Testing and Analysis, ISSTA 1994, Seattle, WA, USA, August 17-19, 1994, pp. 109–124. https://doi.org/10.1145/186258.187153
Yenigün, H., Yevtushenko, N., & Kushik, N. (2017). The complexity of checking the existence and derivation of adaptive synchronizing experiments for deterministic fsms. Inf. Process. Lett., 127, 49–53. https://doi.org/10.1016/j.ipl.2017.07.001
Yevtushenko, N., Kuliamin, V. V., & Kushik, N. (2019). Evaluating the complexity of deriving adaptive homing, synchronizing and distinguishing sequences for nondeterministic fsms. In Testing Software and Systems - 31st IFIP WG 6.1 International Conference, ICTSS 2019, Paris, France, October 15-17, 2019, Proceedings, pp. 86–103. https://doi.org/10.1007/978-3-030-31280-0n6
Acknowledgements
The authors would like to thank Dr. Hüsnü Yenigün for fruitful discussions on the complexity of FSM state identification sequences; those discussions together with the joint results on the existence check of the related sequences were very helpful for moving forward to the complexity of the HTC and STC derivation, i.e., the results presented in this paper. This work is partly supported by RFBR project N 19-0700327/19.
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Yevtushenko, N., Kuliamin, V. & Kushik, N. Evaluating the complexity of deriving adaptive \(S'\)-homing and \(S'\)-synchronizing sequences for nondeterministic FSMs. Software Qual J 30, 161–180 (2022). https://doi.org/10.1007/s11219-021-09548-z
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DOI: https://doi.org/10.1007/s11219-021-09548-z