Cellular automata: real-time equivalence between one-dimensional neighborhoods

Authors:
Victor Poupet
Affiliations:
LIP (UMR CNRS, ENS Lyon, INRIA, Univ. Claude Bernard Lyon 1), École Normale Supérieure de Lyon, LYON, France
Venue:
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Year:
2005

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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 sufficient to recognize every Turing language is equivalent (in terms of real-time recognition) either to the usual neighborhood {–1,0,1} or to the one-way neighborhood {0,1}.