Amenability of groups is characterized by Myhill's Theorem
نویسنده
چکیده
We prove a converse to Myhill’s “Garden-of-Eden” theorem and obtain in this manner a characterization of amenability in terms of cellular automata: A group G is amenable if and only if every cellular automaton with carrier G that has gardens of Eden also has mutually erasable patterns. This answers a question by Schupp, and solves a conjecture by CeccheriniSilberstein, Mach̀ı and Scarabotti.
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ورودعنوان ژورنال:
- CoRR
دوره abs/1605.09133 شماره
صفحات -
تاریخ انتشار 2016