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The Garden of Eden Theorem for Cellular Automata on Group Sets

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Cellular Automata (ACRI 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9863))

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Abstract

We prove the Garden of Eden theorem for cellular automata with finite set of states and finite neighbourhood on right amenable left homogeneous spaces with finite stabilisers. It states that the global transition function of such an automaton is surjective if and only if it is pre-injective. Pre-Injectivity means that two global configurations that differ at most on a finite subset and have the same image under the global transition function must be identical.

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References

  1. Ceccherini-Silberstein, T., Coornaert, M.: Cellular Automata and Groups. Springer Monographs in Mathematics. Springer, Heidelberg (2010)

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  4. Moriceau, S.: Cellular automata on a \(G\)-Set. Journal Cellular Automata 6(6), 461–486 (2011)

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  5. Wacker, S.: Cellular automata on group sets and the uniform Curtis-Hedlund-Lyndon theorem. In: Cook, M., Neary, T. (eds.) AUTOMATA 2016. LNCS, vol. 9664, pp. 185–198. Springer, Heidelberg (2016). doi:10.1007/978-3-319-39300-1_15

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  6. Wacker, S.: Right Amenable Left Group Sets and the Tarski-Følner Theorem [math.GR]. arXiv:1603.06460

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Author information

Authors and Affiliations

  1. Karlsruhe Institute of Technology, Karlsruhe, Germany

    Simon Wacker

Authors
  1. Simon Wacker
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Correspondence to Simon Wacker .

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Editors and Affiliations

  1. University of Perpignan, Perpignan, France

    Samira El Yacoubi

  2. AGH University of Science and Techn, Kraków, Poland

    Jaroslaw Wąs

  3. Department of Computer Science, University of Milano-Bicocca, Milan, Italy

    Stefania Bandini

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© 2016 Springer International Publishing Switzerland

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Wacker, S. (2016). The Garden of Eden Theorem for Cellular Automata on Group Sets. In: El Yacoubi, S., Wąs, J., Bandini, S. (eds) Cellular Automata. ACRI 2016. Lecture Notes in Computer Science(), vol 9863. Springer, Cham. https://doi.org/10.1007/978-3-319-44365-2_7

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  • DOI: https://doi.org/10.1007/978-3-319-44365-2_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-44364-5

  • Online ISBN: 978-3-319-44365-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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