Abstract
In this article we deal with two of the numerous instances in which automata play a part in Topological or Measurable Dynamics. The first is preservation of normality by transducers; here we give a detailed account of the main proof in [2], that of normality preservation under multiplication by rationals. The second instance is an introduction to the dynamical properties of onto cellular automata—since there are but a few known results about them, we mainly give definitions, point out some elementary properties and ask questions. These two applications of automata in the field of Dynamics, though very different in spirit, are strongly linked, because cellular automata are a particular class of transducers, because entropy and other, mainly topological, notions from Dynamical Systems play an important part in both, and finally because one of the underlying aims is to study the transformations of the interval associated to some of these automata.
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© 1994 Springer Science+Business Media Dordrecht
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Blanchard, F. (1994). Cellular Automata and Transducers. A Topological View. In: Goles, E., Martínez, S. (eds) Cellular Automata, Dynamical Systems and Neural Networks. Mathematics and Its Applications, vol 282. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1005-3_1
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DOI: https://doi.org/10.1007/978-94-017-1005-3_1
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