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Towards a Spatial Model Checker on GPU

Part of the Lecture Notes in Computer Science book series (LNPSE,volume 12719)


The tool VoxLogicA merges the state-of-the-art library of computational imaging algorithms ITK with the combination of declarative specification and optimised execution provided by spatial logic model checking. The analysis of an existing benchmark for segmentation of brain tumours via a simple logical specification reached very high accuracy. We introduce a new, GPU-based version of VoxLogicA and present preliminary results on its implementation, scalability, and applications.


  • Spatial logics
  • Model checking
  • GPU computation

Research partially supported by the MIUR Project PRIN 2017FTXR7S “IT- MaTTerS” and by POR FESR Toscana 2014–2020 As. 1 - Az. 1.1.5 – S.A. A1 N. 7165 project STINGRAY. The authors are thankful to: Raffaele Perego, Franco Maria Nardini and the HPC-Lab at ISTI-CNR for a powerful GPU used in early development; Gina Belmonte, Diego Latella, and Mieke Massink, for fruitful discussions. The authors are listed in alphabetical order, having equally contributed to this work.

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  1. 1.

    VoxLogicA: see

  2. 2.

    VoxLogicA-GPU is Free and Open Source software. Its source code is currently available at

  3. 3.

    FSharp: see NET Core: see OpenCL: see ITK: see

  4. 4.

    Pointer jumping or path doubling is a design technique for parallel algorithms that operate on pointer structures, such as linked lists and directed graphs. It allows an algorithm to follow paths with a time complexity that is logarithmic with respect to the length of the longest path. It does this by “jumping” to the end of the path computed by neighbors. See

  5. 5.

    See e.g.

  6. 6.

    Since checking termination takes log(N) iterations, instead of waiting for mainIteration to converge, reconnect is called each k iterations (\(k = 8\) in the current implementation, which experimentally proved to be a reasonable compromise).

  7. 7.

    All the tests we present, and the script to run them, are available in the source code repository


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Bussi, L., Ciancia, V., Gadducci, F. (2021). Towards a Spatial Model Checker on GPU. In: Peters, K., Willemse, T.A.C. (eds) Formal Techniques for Distributed Objects, Components, and Systems. FORTE 2021. Lecture Notes in Computer Science(), vol 12719. Springer, Cham.

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