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Explaining counterexamples using causality

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Abstract

When a model does not satisfy a given specification, a counterexample is produced by the model checker to demonstrate the failure. A user must then examine the counterexample trace, in order to visually identify the failure that it demonstrates. If the trace is long, or the specification is complex, finding the failure in the trace becomes a non-trivial task. In this paper, we address the problem of analyzing a counterexample trace and highlighting the failure that it demonstrates. Using the notion of causality introduced by Halpern and Pearl, we formally define a set of causes for the failure of the specification on the given counterexample trace. These causes are marked as red dots and presented to the user as a visual explanation of the failure. We study the complexity of computing the exact set of causes, and provide a polynomial-time algorithm that approximates it. We then analyze the output of the algorithm and compare it to the one expected by the definition. The algorithm is implemented as a feature in the IBM formal verification platform RuleBase PE, where the visual explanations are an integral part of every counterexample trace. Our approach is independent of the tool that produced the counterexample, and can be applied as a light-weight external layer to any model checking tool, or used to explain simulation traces.

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Notes

  1. Red dots are used in IBM’S RuleBase PE for displaying counterexample explanations.

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Acknowledgements

We thank Cindy Eisner for helpful discussions on the truncated semantics. Shoham Ben-David is grateful to the Azrieli Foundation for the award of an Azrieli Fellowship.

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Authors and Affiliations

  1. IBM Research, Mount Carmel, Haifa, 31905, Israel

    Ilan Beer, Hana Chockler & Avigail Orni

  2. The Hebrew University, Jerusalem, 91904, Israel

    Shoham Ben-David

  3. David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada

    Richard Trefler

Authors
  1. Ilan Beer
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  2. Shoham Ben-David
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  3. Hana Chockler
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  4. Avigail Orni
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  5. Richard Trefler
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Corresponding author

Correspondence to Hana Chockler.

Additional information

A preliminary version of the paper appeared in the proceedings of CAV 2009.

The research of S. Ben-David was supported in part by the Ontario Ministry of Research and Innovation and by the Azrieli Foundation.

The research of R. Trefler was supported in part by the Natural Sciences and Engineering Research Council of Canada.

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Beer, I., Ben-David, S., Chockler, H. et al. Explaining counterexamples using causality. Form Methods Syst Des 40, 20–40 (2012). https://doi.org/10.1007/s10703-011-0132-2

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