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Linear Cellular Automata and Finite Automata

Linear cellular automata have a canonical representation in terms of labeled de Bruijn graphs. We will show that these graphs, construed as semiautomata, provide a natural setting for the study of cellular automata. For example, we give a simple algorithm to determine reversibility and surjectivity of the global maps. We also comment on Wolfram’s question about the growth rates of the minimal finite state machines associated with iterates of a cellular automaton.