On algebraic cellular automata
Algebraic Geometry
2014-02-26 v2 Dynamical Systems
Group Theory
Abstract
We investigate some general properties of algebraic cellular automata, i.e., cellular automata over groups whose alphabets are affine algebraic sets and which are locally defined by regular maps. When the ground field is assumed to be uncountable and algebraically closed, we prove that such cellular automata always have a closed image with respect to the prodiscrete topology on the space of configurations and that they are reversible as soon as they are bijective.
Cite
@article{arxiv.1011.4759,
title = {On algebraic cellular automata},
author = {Tullio Ceccherini-Silberstein and Michel Coornaert},
journal= {arXiv preprint arXiv:1011.4759},
year = {2014}
}