The Myhill property for cellular automata on amenable semigroups
classification
🧮 math.DS
math.FAmath.GR
keywords
cellularamenableautomataautomatoncancellativecoloneveryfinite
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Let $S$ be a cancellative left-amenable semigroup and let $A$ be a finite set. We prove that every pre-injective cellular automaton $\tau \colon A^S \to A^S$ is surjective.
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