%0 Journal Article
%T Surjective cellular automata far from the Garden of Eden
%+ Institute of Cybernetics [Tallinn]
%+ Department of Mathematics
%+ Institut de mathématiques de Luminy (IML)
%A Capobianco, Silvio
%A Guillon, Pierre
%A Kari, Jarkko
%Z Automata, Logic and Semantics
%< avec comité de lecture
%@ 1462-7264
%J Discrete Mathematics and Theoretical Computer Science
%I DMTCS
%V Vol. 15 no. 3
%N 3
%P 41--60
%8 2013-10-18
%D 2013
%R 10.46298/dmtcs.618
%Z Computer Science [cs]/Discrete Mathematics [cs.DM]Journal articles
%X One of the first and most famous results of cellular automata theory, Moore's Garden-of-Eden theorem has been proven to hold if and only if the underlying group possesses the measure-theoretic properties suggested by von Neumann to be the obstacle to the Banach-Tarski paradox. We show that several other results from the literature, already known to characterize surjective cellular automata in dimension d, hold precisely when the Garden-of-Eden theorem does. We focus in particular on the balancedness theorem, which has been proven by Bartholdi to fail on amenable groups, and we measure the amount of such failure.
%G English
%2 https://inria.hal.science/hal-00966380/document
%2 https://inria.hal.science/hal-00966380/file/2336-8374-1-PB.pdf
%L hal-00966380
%U https://inria.hal.science/hal-00966380
%~ CNRS
%~ UNIV-AMU
%~ IML
%~ I2M
%~ DMTCS
%~ TDS-MACS