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A mathematical classification of the one-dimensional deterministic cellular automata

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Abstract

We propose a theoretical classification of one-dimensional deterministic cellular automata in two types, typeS and typeO. This classification is connected with the phenomenological classification of S. Wolfram.

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References

  1. Farmer, D., Toffoli, T., Wolfram, S. (eds.): Cellular automata, Physica10D (1984)

  2. Wolfram, S.: Rev. Mod. Phys.55, 3 (1983)

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  3. Wolfram, S.: Universality and complexity in cellular automata. Physica10D (1984)

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Authors and Affiliations

  1. Laboratoire de Physique Théorique et Hautes Energies, L.A. 063, Université Paris Sud, Bâtiment 211, F-91405, Orsay, France

    Michel Dubois-Violette

  2. Laboratoire de Physique Théorique et Hautes Energies, L.A. 280, Université Paris VII-Tour 24/14-2, place Jussieu, F-75231, Paris Cedex 05, France

    Alain Rouet

Authors
  1. Michel Dubois-Violette
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  2. Alain Rouet
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Communicated by J.-P. Eckmann

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Dubois-Violette, M., Rouet, A. A mathematical classification of the one-dimensional deterministic cellular automata. Commun.Math. Phys. 112, 627–631 (1987). https://doi.org/10.1007/BF01225376

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  • DOI: https://doi.org/10.1007/BF01225376

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