State Identification for Labeled Transition Systems with Inputs and Outputs

P. van den Bos and F.W. Vaandrager. State Identification for Labeled Transition Systems with Inputs and Outputs. In Farhad Arbab and Sung-Shik Jongmans, editors. Proceedings Formal Aspects of Component Software - 16th International Conference, FACS 2019, Amsterdam, The Netherlands, October 23-25, 2019. Lecture Notes in Computer Science 12018, pages 191-212, Springer 2020, ISBN 978-3-030-40913-5. This paper received the FACS'19 best paper award. Full version available as CoRR arXiv:1907.11034, July 2019.


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 that tests produced by our algorithm still distinguish more than 99% of the incompatible state pairs.

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Journal version (pdf, December 2020)
CoRR arXiv:1907.11034
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