Cellular Automata on Group Sets and the Uniform Curtis-Hedlund-Lyndon Theorem
Group Theory
2016-07-15 v2 Formal Languages and Automata Theory
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.
Keywords
Cite
@article{arxiv.1603.07271,
title = {Cellular Automata on Group Sets and the Uniform Curtis-Hedlund-Lyndon Theorem},
author = {Simon Wacker},
journal= {arXiv preprint arXiv:1603.07271},
year = {2016}
}