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Cellular Automata: Real-Time Equivalence between One-Dimensional Neighborhoods

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Abstract

It is well known that one-dimensional cellular automata working on the usual neighborhood are Turing complete, and many acceleration theorems are known. However, very little is known about the other neighborhoods. In this article we prove that every one-dimensional neighborhood that is big enough so that every letter of the entry word can affect the computation is equivalent (in terms of real-time recognition) either to the usual neighborhood {-1,0,1} or to the one-way neighborhood {0,1}.

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  1. LIP, Ecole Normale Superieure de Lyon, 46 allee d'Italie, F-69364 Lyon Cedex 07, France

    Victor Poupet

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  1. Victor Poupet
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Poupet, V. Cellular Automata: Real-Time Equivalence between One-Dimensional Neighborhoods. Theory Comput Syst 40, 409–421 (2007). https://doi.org/10.1007/s00224-006-1315-x

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  • DOI: https://doi.org/10.1007/s00224-006-1315-x

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