Abstract:We consider linear cellular automata on groups, introduce a notion of adjoint cellular automaton, and prove that a linear cellular automaton is pre-injective if and only if its adjoint is surjective. ...We consider linear cellular automata on groups, introduce a notion of adjoint cellular automaton, and prove that a linear cellular automaton is pre-injective if and only if its adjoint is surjective.
In this manner, and relying on a previous construction (for arbitrary non-amenable group $G$ and field $k$) of a pre-injective, non-surjective linear cellular automaton, we produce for arbitrary non-amenable group $G$ and field $k$ a non-pre-injective, surjective linear cellular automaton. This answers positively Open Problem (OP-14) in Ceccherini-Silberstein and Coornaert's monograph Cellular Automata and Groups.Read More
Publication Year: 2016
Publication Date: 2016-12-19
Language: en
Type: preprint
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Cited By Count: 2
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