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System Reduction: An Approach Based on Probabilistic Cellular Automata

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Cellular Automata (ACRI 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13402))

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Abstract

The problem of cellular automata coarse-graining is considered. The case of 1D boolean cellular automata (CA) is investigated. Probabilistic rules for 1D CA are parameterized. Then the coarse-graining procedure and the reduced probabilistic CA are defined in the general case. The reduction procedure is illustrated on the example of the Wolfram CA deterministic rule 30. It is then analyzed on the example of a 1D ring probabilistic voter model. The coarse-grained transition rule is improved by making use of the network adjacency matrix. Results obtained for the original and the coarse-grained models are compared, both in the uncontrolled and controlled cases.

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Authors and Affiliations

  1. University of Geneva, Geneva, Switzerland

    Pierre-Alain Toupance & Bastien Chopard

  2. Univ. Grenoble Alpes, Grenoble INP, LCIS, Valence, France

    Pierre-Alain Toupance & Laurent Lefèvre

Authors
  1. Pierre-Alain Toupance
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  2. Bastien Chopard
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  3. Laurent Lefèvre
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Corresponding author

Correspondence to Pierre-Alain Toupance .

Editor information

Editors and Affiliations

  1. University of Geneva, Geneva, Switzerland

    Bastien Chopard

  2. University of Milano-Bicocca, Milan, Italy

    Stefania Bandini

  3. University of Milano-Bicocca, Milan, Italy

    Alberto Dennunzio

  4. University of Geneva, Geneva, Switzerland

    Mira Arabi Haddad

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Toupance, PA., Chopard, B., Lefèvre, L. (2022). System Reduction: An Approach Based on Probabilistic Cellular Automata. In: Chopard, B., Bandini, S., Dennunzio, A., Arabi Haddad, M. (eds) Cellular Automata. ACRI 2022. Lecture Notes in Computer Science, vol 13402. Springer, Cham. https://doi.org/10.1007/978-3-031-14926-9_9

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  • DOI: https://doi.org/10.1007/978-3-031-14926-9_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-14925-2

  • Online ISBN: 978-3-031-14926-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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