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On the Garden of Eden theorem for ℬ-free subshifts

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Abstract

We prove that on ℬ-free subshifts, with ℬ satisfying the Erdős condition, all cellular automata are determined by monotone sliding block codes. In particular, this implies the validity of the Garden of Eden theorem for such systems.

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Acknowledgments

CR would like to thank ML for an invitation to Toruń in September 2018, where this project had been initially discussed. Research of ML is supported by Narodowe Centrum Nauki grant UMO-2019/33/B/ST1/00364.

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Authors and Affiliations

  1. Department of Mathematics, University of Erlangen-Nürnberg, Cauerstraße 11, 91058, Erlangen, Germany

    Gerhard Keller & Christoph Richard

  2. Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopin street 12/18, 87-100, Toruń, Poland

    Mariusz Lemańczyk & Daniel Sell

Authors
  1. Gerhard Keller
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  2. Mariusz Lemańczyk
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  3. Christoph Richard
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  4. Daniel Sell
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Corresponding author

Correspondence to Mariusz Lemańczyk.

Additional information

Dedicated to Benji Weiss with congratulations for his deep contribution to mathematics and with thanks for all the years of help, inspiration, collaboration, kindness, and sharing the joy of the results achieved.

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Keller, G., Lemańczyk, M., Richard, C. et al. On the Garden of Eden theorem for ℬ-free subshifts. Isr. J. Math. 251, 567–594 (2022). https://doi.org/10.1007/s11856-022-2437-9

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  • DOI: https://doi.org/10.1007/s11856-022-2437-9

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