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Computations on one-dimensional cellular automata

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Abstract

Cellular automata may be viewed as a modelization of synchronous parallel computation. Even in the one-dimensional case, they are known as capable of universal computations. The usual proof uses a simulation of a universal Turing machine. In this paper, we present how a one-dimensional cellular automata can simulate any recursive function in such a way that composition of computations occurs as soon as possible. In addition, this allows us to show that one-dimensional cellular automata may simulate asynchronous computations.

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Authors and Affiliations

  1. Laboratoire de l'Informatique du Parallélisme, Ecole Normale Supérieure de Lyon, 46 Allée d'Italie, 69364, Lyon Cedex 07, France

    Jacques Mazoyer

  2. Institut Universitaire de Formation des Maitres de Lyon, 5 rue Anselme, 69317, Lyon Cedex 04, France

    Jacques Mazoyer

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  1. Jacques Mazoyer
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Additional information

This work was supported by the Programme de Recherches Coordonnées Mathématiques et Informatique and the Esprit Basic Research Action “Algebraic and Syntactical Methods in Computer Science”.

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Mazoyer, J. Computations on one-dimensional cellular automata. Ann Math Artif Intell 16, 285–309 (1996). https://doi.org/10.1007/BF02127801

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