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Revisiting Polyhedral Analysis for Hybrid Systems

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Static Analysis (SAS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11822))

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Abstract

Thanks to significant progress in the adopted implementation techniques, the recent years have witnessed a renewed interest in the development of analysis tools based on the domain of convex polyhedra. In this paper we revisit the application of this abstract domain to the case of reachability analysis for hybrid systems, focusing on the lesson learned during the development of the tool PHAVerLite. In particular, we motivate the implementation of specialized versions of several well known abstract operators, as well as the adoption of a heuristic technique (boxed polyhedra) for the handling of finite collections of polyhedra, showing their impact on the efficiency of the analysis tool.

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Notes

  1. 1.

    The tests on PHAVer-lite/SX and PHAVerLite have been executed on an Intel Core i7-3632QM CPU; the tests on PHAVer/SX were executed on a faster CPU (\({\sim }25\%\)).

  2. 2.

    The synchronization label \(a \in Lab \) only plays a role when a hybrid automaton is defined as the parallel composition of several smaller automata.

  3. 3.

    This is the case for the Apron library [24] and for PPLite up to version 0.3.

  4. 4.

    This was done for exposition purposes, since this specific benchmark can be successfully verified, more efficiently, by using a single polyhedron for each location.

  5. 5.

    Note that this implies that neither Lemma 2 applies.

  6. 6.

    To some extent, the reasoning should also apply to constraint-only representations, if the implementation attempts to identify and remove redundant constraints.

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Acknowledgment

The work of Enea Zaffanella has been partially supported by Gruppo Nazionale per il Calcolo Scientifico of Istituto Nazionale di Alta Matematica.

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Authors and Affiliations

  1. University of Udine, Udine, Italy

    Anna Becchi

  2. University of Parma, Parma, Italy

    Enea Zaffanella

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  1. Anna Becchi
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Correspondence to Anna Becchi or Enea Zaffanella .

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  1. University of Colorado, Boulder, CO, USA

    Bor-Yuh Evan Chang

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Becchi, A., Zaffanella, E. (2019). Revisiting Polyhedral Analysis for Hybrid Systems. In: Chang, BY. (eds) Static Analysis. SAS 2019. Lecture Notes in Computer Science(), vol 11822. Springer, Cham. https://doi.org/10.1007/978-3-030-32304-2_10

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  • DOI: https://doi.org/10.1007/978-3-030-32304-2_10

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