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Article Dans Une Revue Discrete Mathematics and Theoretical Computer Science Année : 2013

Surjective cellular automata far from the Garden of Eden

Silvio Capobianco
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Jarkko Kari

Résumé

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.
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Dates et versions

hal-00966380 , version 1 (26-03-2014)

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Silvio Capobianco, Pierre Guillon, Jarkko Kari. Surjective cellular automata far from the Garden of Eden. Discrete Mathematics and Theoretical Computer Science, 2013, Vol. 15 no. 3 (3), pp.41--60. ⟨10.46298/dmtcs.618⟩. ⟨hal-00966380⟩
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