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Minimisation of Spatial Models Using Branching Bisimilarity

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Book cover Formal Methods (FM 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14000))

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Abstract

Spatial logic and spatial model checking have great potential for traditional computer science domains and beyond. Reasoning about space involves two different conditional reachability modalities: a forward reachability, similar to that used in temporal logic, and a backward modality representing that a point can be reached from another point, under certain conditions. Since spatial models can be huge, suitable model minimisation techniques are crucial for efficient model checking. An effective minimisation method for the recent notion of spatial Compatible Path (CoPa)-bisimilarity is proposed, and shown to be correct. The core of our method is the encoding of Closure Models as Labelled Transition Systems, enabling minimisation algorithms for branching bisimulation to compute CoPa equivalence classes. Initial validation via benchmark examples demonstrates a promising speed-up in model checking of spatial properties for models of realistic size.

Research partially funded by the Italian MUR Projects PRIN 2017FTXR7S, “IT- MaTTerS”, PRIN 2020TL3X8X “T-LADIES”, and Next Generation EU - MUR Project PNRR PRI ECS00000017 “THE - Tuscany Health Ecosystem”. The authors are listed in alphabetical order; they contributed to this work equally.

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Notes

  1. 1.

    Intel Core I9 9900K processor (with 8 cores) and 32 GB of RAM.

  2. 2.

    Note that, different from the context of classical temporal logics, in the context of space, and in particular when dealing with notions of directionality (e.g. one way roads, public area gates), it is important to be able to distinguish between the concept of “reaching” and that of “being reached”. The interested reader is referred to [13] for a discussion on the issue.

  3. 3.

    Or its dual operator called ‘interior’.

  4. 4.

    Note that VoxLogicA is inherently much faster than GraphLogicA as it is specialised for images, exploiting state-of-the-art imaging libraries and automatic parallelisation. This poses a further challenge to the speed-up via minimisation and is the reason why we use VoxLogicA instead of GraphLogicA for the full model.

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Acknowledgements

We thank the anonymous reviewers for their valuable suggestions for improvement of this work.

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Authors and Affiliations

  1. CNR-ISTI, Pisa, Italy

    Vincenzo Ciancia, Diego Latella & Mieke Massink

  2. Eindhoven University of Technology, Eindhoven, The Netherlands

    Jan Friso Groote & Erik P. de Vink

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  1. Vincenzo Ciancia
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Correspondence to Mieke Massink .

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Editors and Affiliations

  1. University of Toronto, Toronto, ON, Canada

    Marsha Chechik

  2. RWTH Aachen University, Aachen, Germany

    Joost-Pieter Katoen

  3. University of Lübeck, Lübeck, Germany

    Martin Leucker

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Ciancia, V., Groote, J.F., Latella, D., Massink, M., de Vink, E.P. (2023). Minimisation of Spatial Models Using Branching Bisimilarity. In: Chechik, M., Katoen, JP., Leucker, M. (eds) Formal Methods. FM 2023. Lecture Notes in Computer Science, vol 14000. Springer, Cham. https://doi.org/10.1007/978-3-031-27481-7_16

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