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arXiv · 0711.3841

On the Induction Operation for Shift Subspaces and Cellular Automata as Presentations of Dynamical Systems

Silvio Capobianco
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Abstract

We consider continuous, translation-commuting transformations of compact, translation-invariant families of mappingsfrom finitely generated groups into finite alphabets. It is well-known that such transformations and spaces can be described "locally" via families of patterns and finitary functions; such descriptions can be re-used on groups larger than the original, usually defining non-isomorphic structures. We show how some of the properties of the "induced" entities can be deduced from those of the original ones, and vice versa; then, we show how to "simulate" the smaller structure into the larger one, and obtain a characterization in terms of group actions for the dynamical systems admitting of presentations via structures as such. Special attention is given to the class of sofic shifts.

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Silvio Capobianco. 2008-06-16. On the Induction Operation for Shift Subspaces and Cellular Automata as Presentations of Dynamical Systems. https://arxiv.org/abs/0711.3841

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