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Cellular Automata on Group Sets and the Uniform Curtis-Hedlund-Lyndon Theorem (1603.07271v2)
Published 21 Mar 2016 in math.GR and cs.FL
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.