A converse to Moore's theorem on cellular automata

نویسنده

  • Laurent Bartholdi
چکیده

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 [11; 1, Conjecture 6.2] that amenability could be characterized by cellular automata. We prove the first part of that conjecture.

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عنوان ژورنال:
  • CoRR

دوره abs/0709.4280  شماره 

صفحات  -

تاریخ انتشار 2007