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Symbolic Model Checking with Sentential Decision Diagrams

Part of the Lecture Notes in Computer Science book series (LNPSE,volume 12153)

Abstract

We demonstrate the viability of symbolic model checking using Sentential Decision Diagrams (SDD), in lieu of the more common Binary Decision Diagram (BDD). The SDD data structure can be up to exponentially more succinct than BDDs, using a generalized notion of variable order called a variable tree (“vtree”). We also contribute to the practice of SDDs, giving a novel heuristic for constructing a vtree that minimizes SDD size in the context of model checking, and identifying which SDD operations form a performance bottleneck.

Experiments on 707 benchmarks, written in various specification languages, show that SDD often use an order of magnitude less memory than BDDs, at the expense of a smaller slowdown in runtime performance.

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Notes

  1. 1.

    Our implementation’s source code is available at https://doi.org/10.5281/zenodo.3940936.

  2. 2.

    More precisely, they show that exponential blowups may occur when disjoining two SDDs if the output SDD must obey the same vtree, but it remains an open question whether the blowup is unavoidable when the vtree is allowed to change.

  3. 3.

    While for some specification languages this information has to be estimated using static analysis, there are ways to support dynamic read/write dependencies  [30], but for the sake of simplicity, we do not consider them here.

  4. 4.

    The benchmarks are available at https://github.com/utwente-fmt/BW-NFM2016.

  5. 5.

    Again, the implementation is available at https://doi.org/10.5281/zenodo.3940936.

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Acknowledgements

This work is part of the research programme VENI with project number 639.021.649, which is financed by the Netherlands Organisation for Scientific Research (NWO).

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Vinkhuijzen, L., Laarman, A. (2020). Symbolic Model Checking with Sentential Decision Diagrams. In: Pang, J., Zhang, L. (eds) Dependable Software Engineering. Theories, Tools, and Applications. SETTA 2020. Lecture Notes in Computer Science(), vol 12153. Springer, Cham. https://doi.org/10.1007/978-3-030-62822-2_8

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