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Playing with Abstraction and Representation

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Semantics, Logics, and Calculi

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9560))

Abstract

In this paper, we discuss partition refinement as an algorithmic pattern for explicating semantic properties of a system directly in the corresponding model structure in a co-inductive fashion. In particular, we review a landscape of analysis and verification approaches under this unifying perspective, which enables us to highlight their mutual profiles, while it at the same time establishes a basis for their combination: The common pattern establishes comparability, which reveals complementarity, and indicates where and under which circumstances the considered approaches may profit from one another. It can thus be regarded as a guideline for systematically exploring the benefits of the corresponding methods and their combinations.

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Notes

  1. 1.

    Note that in practice the correctness of the model cannot be guaranteed, as a perfect splitter oracle cannot be implemented but instead needs to be approximated through testing.

  2. 2.

    We assume that the non-determinism is due to presentation only: the conditions guarding the respective transitions are not displayed, since they do not matter for our example.

  3. 3.

    Here and in the following, \(\lambda _{\mathcal {L}}\) and \(\lambda _{\mathcal {H}}\) denote the labeling function of \(\mathcal {L}\) and \(\mathcal {L}(\mathcal {H})\), respectively: \(\lambda _{\mathcal {L}}(w) = 1\) if \(w\in \mathcal {L}\), and 0 otherwise.

  4. 4.

    It should be noted that this approach can only be applied to specifications that admit finite counterexample traces (e.g., safety LTL formulae), as an infinite-length counterexample cannot be tested on the system.

  5. 5.

    Even this is not really necessary. Our also partition refinement-based automated alphabet abstraction technology [24, 25] may be used to automatically derive an adequate level of observation. Of course, for learning realistic system it is important to provide a functioning test harness for triggering the system behavior [35, 52].

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Authors and Affiliations

  1. TU Dortmund University, 44221, Dortmund, Germany

    Bernhard Steffen, Malte Isberner & Marc Jasper

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  1. Bernhard Steffen
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  2. Malte Isberner
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Correspondence to Malte Isberner .

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  1. Technical University of Denmark, Kongens Lyngby, Denmark

    Christian W. Probst

  2. Imperial College London, London, United Kingdom

    Chris Hankin

  3. Aalborg University, Aalborg, Denmark

    René Rydhof Hansen

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Steffen, B., Isberner, M., Jasper, M. (2016). Playing with Abstraction and Representation. In: Probst, C., Hankin, C., Hansen, R. (eds) Semantics, Logics, and Calculi. Lecture Notes in Computer Science(), vol 9560. Springer, Cham. https://doi.org/10.1007/978-3-319-27810-0_10

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