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Minimizing Characterizing Sets

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Formal Aspects of Component Software (FACS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12018))

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Abstract

A characterizing set (CS) for a given finite state machine (FSM) defines a set of input sequences such that for any pair of states of FSM, there exists an input sequence in a CS that can separate these states. There are techniques that generate test sequences with guaranteed fault detection power using CSs. The number of inputs and input sequences in a CS directly impacts the cost of the test: the higher the number of elements, the longer it takes to generate the test. Despite the direct benefits of using CSs with fewer sequences, there has been no work focused on generating minimum sized characterizing sets. In this paper, we show that constructing CS with fewer elements is a PSPACE-Hard problem and that the corresponding decision problem is PSPACE-Complete. We then introduce a heuristic to construct CSs with fewer input sequences. We evaluate the proposed algorithm using randomly generated FSMs as well as some benchmark FSMs. The results are promising, and the proposed method reduces the number of test sequences by \(37.3\%\) and decreases the total length of the tests by \(34.6\%\) on the average.

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Notes

  1. 1.

    Since the circuits receive inputs in bits, and since b bits correspond to \(2^b\) inputs, we do not consider FSMs with \(b \ge 10\) bits.

  2. 2.

    FSM specification Ex4 is partially specified. We complete the missing transitions by adding self looping transitions with a special output symbol, and do not use these inputs for W-set construction.

  3. 3.

    One way ANOVA test accepts null hypothesis [36].

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Acknowledgements

This work is supported by the scientific and technological council of Turkey (TUBITAK) under the grant 117E987.

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Authors and Affiliations

  1. Gebze Teknik Üniversitesi, 41400, Gebze, Kocaeli, Turkey

    Kadir Bulut & Uraz Cengiz Türker

  2. University of Ottowa, Ottawa, ON, Canada

    Guy Vincent Jourdan

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  1. Kadir Bulut
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Correspondence to Uraz Cengiz Türker .

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  1. CWI, University of Leiden, Leiden, The Netherlands

    Farhad Arbab

  2. Open University of the Netherlands, Heerlen, The Netherlands

    Sung-Shik Jongmans

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Bulut, K., Jourdan, G.V., Türker, U.C. (2020). Minimizing Characterizing Sets. In: Arbab, F., Jongmans, SS. (eds) Formal Aspects of Component Software. FACS 2019. Lecture Notes in Computer Science(), vol 12018. Springer, Cham. https://doi.org/10.1007/978-3-030-40914-2_4

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  • DOI: https://doi.org/10.1007/978-3-030-40914-2_4

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