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Diddy: A Python Toolbox for Infinite Discrete Dynamical Systems

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Cellular Automata and Discrete Complex Systems (AUTOMATA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14152))

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Abstract

We introduce Diddy, a collection of Python scripts for analyzing infinite discrete dynamical systems. The main focus is on generalized multidimensional shifts of finite type (SFTs). We show how Diddy can be used to easily define SFTs and cellular automata, and analyze their basic properties. We also showcase how to verify or rediscover some results from coding theory and cellular automata theory.

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Notes

  1. 1.

    This representation allows nondeterministic cellular automata, but Diddy always uses the first formula that applies, in the given order.

  2. 2.

    Note that our graph is not right resolving in the sense of [9, Definition 3.3.1], which corresponds to being a DFA instead of an NFA. Thus the result may not be minimal in the sense of having the absolute smallest number of vertices of any graph with the same set of labels of walks. Nevertheless, the algorithm never increases the number of vertices, and in practice can substantially decrease it.

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Acknowledgments

Ilkka Törmä was supported by the Academy of Finland under grant 346566.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Turku, Turku, Finland

    Ville Salo & Ilkka Törmä

Authors
  1. Ville Salo
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  2. Ilkka Törmä
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Corresponding author

Correspondence to Ville Salo .

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Editors and Affiliations

  1. University of Trieste, Trieste, Italy

    Luca Manzoni

  2. University of Twente, Enschede, The Netherlands

    Luca Mariot

  3. Indian Institute of Technology Kharagpur, Kharagpur, India

    Dipanwita Roy Chowdhury

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Salo, V., Törmä, I. (2023). Diddy: A Python Toolbox for Infinite Discrete Dynamical Systems. In: Manzoni, L., Mariot, L., Roy Chowdhury, D. (eds) Cellular Automata and Discrete Complex Systems. AUTOMATA 2023. Lecture Notes in Computer Science, vol 14152. Springer, Cham. https://doi.org/10.1007/978-3-031-42250-8_3

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  • DOI: https://doi.org/10.1007/978-3-031-42250-8_3

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-031-42250-8

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