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Weak Bisimulation Metrics in Models with Nondeterminism and Continuous State Spaces

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Theoretical Aspects of Computing – ICTAC 2018 (ICTAC 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11187))

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Abstract

Bisimulation metrics are used to estimate the behavioural distance between probabilistic systems. They have been defined in discrete and continuous state space models. However, the weak semantics approach, where non-observable actions are abstracted away, has been adopted only in the discrete case. We fill this gap and provide a weak bisimulation metric for models with continuous state spaces. A difficulty is to provide a notion of weak transition leaving from a continuous distribution over states. Our weak bisimulation metric allows for compositional reasoning. Systems at distance zero are equated by a notion of weak bisimulation. We apply our theory in a case study where continuous distributions derive by the evolution of the physical environment.

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Authors and Affiliations

  1. Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell’Insubria, via Valleggio, 11, 22100, Como, Italy

    Ruggero Lanotte & Simone Tini

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  1. Ruggero Lanotte
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  2. Simone Tini
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Correspondence to Simone Tini .

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Editors and Affiliations

  1. Stellenbosch University, Stellenbosch, South Africa

    Bernd Fischer

  2. Reykjavík University, Reykjavik, Iceland

    Tarmo Uustalu

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Lanotte, R., Tini, S. (2018). Weak Bisimulation Metrics in Models with Nondeterminism and Continuous State Spaces. In: Fischer, B., Uustalu, T. (eds) Theoretical Aspects of Computing – ICTAC 2018. ICTAC 2018. Lecture Notes in Computer Science(), vol 11187. Springer, Cham. https://doi.org/10.1007/978-3-030-02508-3_16

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  • DOI: https://doi.org/10.1007/978-3-030-02508-3_16

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  • Online ISBN: 978-3-030-02508-3

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