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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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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DOI: https://doi.org/10.1007/BF02127801