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The Weak Universality of Two-Dimensional Five-State von Neumann Neighborhood Number-Conserving Cellular Automaton

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Abstract

We study the computing abilities of small-state rotation symmetric von Neumann neighborhood NCCAs (RNCAs). It is known that such RNCAs with four states or less are trivial and any 5-state RNCAs cannot be strongly universal. In this paper, we show there is a weakly-universal 5-state RNCA, i.e., it is possible to simulate any combinational logic circuit. We also show a configuration which simulates the rule 110 cellular automaton.

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Notes

  1. This is the von Neumann neighborhood.

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Acknowledgements

We thank Victor Poupet from Université Montpellier 2 for the helpful discussions and comments. This research was partly supported by JSPS KAKENHI Grant Number 17K00015.

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  1. Hiroshima University, Hiroshima, Japan

    Hisamichi Ishizaka, Gil-Tak Kong & Katsunobu Imai

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  1. Hisamichi Ishizaka
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  2. Gil-Tak Kong
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  3. Katsunobu Imai
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Correspondence to Gil-Tak Kong.

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Ishizaka, H., Kong, GT. & Imai, K. The Weak Universality of Two-Dimensional Five-State von Neumann Neighborhood Number-Conserving Cellular Automaton. New Gener. Comput. 40, 541–551 (2022). https://doi.org/10.1007/s00354-021-00150-2

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