Sofic Trace of a Cellular Automaton

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The trace subshift of a cellular automaton is the subshift of all possible columns that may appear in a space-time diagram, ie the infinite sequence of states of a particular cell of a configuration; in the language of symbolic dynamics one says that it is a factor system. In this paper we study conditions for a sofic subshift to be the trace of a cellular automaton.
10 pages + 6 for included proofs

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