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Commutators of Bipermutive and Affine Cellular Automata

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Cellular Automata and Discrete Complex Systems (AUTOMATA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8155))

Abstract

We discuss bipermutive cellular automata from a combinatorial and topological perspective. We prove a type of topological randomizing property for bipermutive CA, show that the commutator of a bipermutive CA is always small and that bipermutive affine CA have only affine CA in their commutator. We show the last result also in the multidimensional case, proving a conjecture of [Moore-Boykett, 97].

Research supported by the Academy of Finland Grant 131558.

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References

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Author information

Authors and Affiliations

  1. TUCS – Turku Centre for Computer Science, University of Turku, Finland

    Ville Salo & Ilkka Törmä

Authors
  1. Ville Salo
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  2. Ilkka Törmä
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Editor information

Editors and Affiliations

  1. University of Turku, Department of Mathematics, 20014, Turku, Finland

    Jarkko Kari

  2. Institut für Informatik, Universität Giessen, Arndtstr. 2, 35392, Giessen, Germany

    Martin Kutrib  & Andreas Malcher  & 

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Salo, V., Törmä, I. (2013). Commutators of Bipermutive and Affine Cellular Automata. In: Kari, J., Kutrib, M., Malcher, A. (eds) Cellular Automata and Discrete Complex Systems. AUTOMATA 2013. Lecture Notes in Computer Science, vol 8155. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40867-0_11

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  • DOI: https://doi.org/10.1007/978-3-642-40867-0_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40866-3

  • Online ISBN: 978-3-642-40867-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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