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International Symposium on Formal Methods

FM 2018: Formal Methods pp 588–607Cite as

Approximate Partial Order Reduction

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10951))

Abstract

We present a new partial order reduction method for reachability analysis of nondeterministic labeled transition systems over metric spaces. Nondeterminism arises from both the choice of the initial state and the choice of actions, and the number of executions to be explored grows exponentially with their length. We introduce a notion of \(\varepsilon \)-independence relation over actions that relates approximately commutative actions; \(\varepsilon \)-equivalent action sequences are obtained by swapping \(\varepsilon \)-independent consecutive action pairs. Our reachability algorithm generalizes individual executions to cover sets of executions that start from different, but \(\delta \)-close initial states, and follow different, but \(\varepsilon \)-independent, action sequences. The constructed over-approximations can be made arbitrarily precise by reducing the \(\delta ,\varepsilon \) parameters. Exploiting both the continuity of actions and their approximate independence, the algorithm can yield an exponential reduction in the number of executions explored. We illustrate this with experiments on consensus, platooning, and distributed control examples.

This work is supported by the grants CAREER 1054247 and CCF 1422798 from the National Science Foundation.

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Authors and Affiliations

  1. ECE Department, University of Illinois at Urbana-Champaign, Champaign, USA

    Chuchu Fan, Zhenqi Huang & Sayan Mitra

Authors
  1. Chuchu Fan
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  2. Zhenqi Huang
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  3. Sayan Mitra
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Correspondence to Chuchu Fan .

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Editors and Affiliations

  1. NASA Jet Propulsion Laboratory, Pasadena, California, USA

    Klaus Havelund

  2. University of Bremen, Bremen, Germany

    Jan Peleska

  3. University of Oxford, Oxford, United Kingdom

    Bill Roscoe

  4. Eindhoven University of Technology, Eindhoven, The Netherlands

    Erik de Vink

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Fan, C., Huang, Z., Mitra, S. (2018). Approximate Partial Order Reduction. In: Havelund, K., Peleska, J., Roscoe, B., de Vink, E. (eds) Formal Methods. FM 2018. Lecture Notes in Computer Science(), vol 10951. Springer, Cham. https://doi.org/10.1007/978-3-319-95582-7_35

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  • DOI: https://doi.org/10.1007/978-3-319-95582-7_35

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  • Online ISBN: 978-3-319-95582-7

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