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Surjective cellular automata far from the Garden of Eden
Tekijät: Silvio Capobianco, Pierre Guillon, Jarkko Kari
Kustantaja: Discrete Mathematics & Theoretical Computer Science
Julkaisuvuosi: 2013
Journal: Discrete Mathematics and Theoretical Computer Science
Lehden akronyymi: DMTCS
Numero sarjassa: 3
Vuosikerta: 15
Numero: 3
Aloitussivu: 41
Lopetussivu: 60
Sivujen määrä: 20
ISSN: 1462-7264
DOI: https://doi.org/10.46298/dmtcs.618
Verkko-osoite: https://dx.doi.org/10.46298/dmtcs.618
Rinnakkaistallenteen osoite: https://research.utu.fi/converis/portal/detail/Publication/2052752
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.
Ladattava julkaisu This is an electronic reprint of the original article. |  |
