A converse to Moore's theorem on cellular automata

Details A converse to Moore's theorem on cellular automata A converse to Moore's theorem on cellular automata

2007-09-26

arxiv.org/abs/0709.4280v1

J. Eur. Math. Soc. 12 (2010), 241-248

Mathematics

Combinatorics

Scientific paper

10.471/JEMS/196

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.

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