A converse to Moore's theorem on cellular automata
Combinatorics
2009-12-17 v1 Information Theory
Dynamical Systems
Group Theory
math.IT
Abstract
We prove a converse to Moore's ``Garden-of-Eden'' theorem: a group G is amenable if and only if all cellular automata living on G that admit mutually erasable patterns also admit gardens of Eden. It had already been conjectured in that amenability could be characterized by cellular automata. We prove the first part of that conjecture.
Keywords
Cite
@article{arxiv.0709.4280,
title = {A converse to Moore's theorem on cellular automata},
author = {Laurent Bartholdi},
journal= {arXiv preprint arXiv:0709.4280},
year = {2009}
}