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Cellular Automata on Group Sets and the Uniform Curtis-Hedlund-Lyndon Theorem

Abstract : We introduce cellular automata whose cell spaces are left homogeneous spaces and prove a uniform as well as a topological variant of the Curtis-Hedlund-Lyndon theorem. Examples of left homogeneous spaces are spheres, Euclidean spaces, as well as hyperbolic spaces acted on by isometries; vertex-transitive graphs, in particular, Cayley graphs, acted on by automorphisms; groups acting on themselves by multiplication; and integer lattices acted on by translations.
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Simon Wacker. Cellular Automata on Group Sets and the Uniform Curtis-Hedlund-Lyndon Theorem. 22th International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA), Jun 2016, Zurich, Switzerland. pp.185-198, ⟨10.1007/978-3-319-39300-1_15⟩. ⟨hal-01435028⟩

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