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Classes of linear automata. (English) Zbl 0588.68029
Let S be a finite set and X the set of all maps from the integers to S. The discrete topology on S determines a product topology on X. The successor map on the integers induces a shift homeomorphism of X to itself. A linear automaton (or one-dimensional cellular automaton) is a continuous self-map of X which commutes with the shift. Computer simulations suggest that linear automata may be divided into classes based on their dynamical behavior. This paper makes a division (based on the topological notions of equicontinuity and expansiveness) into three classes and shows the classes have distinct dynamical behavior. Also passing from an automaton to a certain kind of factor preserves the class of the automaton.

68Q45 Formal languages and automata
68Q80 Cellular automata (computational aspects)
54H20 Topological dynamics (MSC2010)
Full Text: DOI
[1] Feller, An Introduction to Probability Theory and its Applications 1 (1950) · Zbl 0039.13201
[2] Farmer, Cellular Automata (1984)
[3] DOI: 10.1007/BF01705882 · Zbl 0191.21402 · doi:10.1007/BF01705882
[4] Adler, Mem. Amer. Math. Soc. 20 pp none– (1979)
[5] Furstenberg, Recurrence in Ergodic Theory and Combinatorial Number Theory (1981) · Zbl 0459.28023 · doi:10.1515/9781400855162
[6] DOI: 10.1007/BF01217347 · Zbl 0587.68050 · doi:10.1007/BF01217347
[7] Walters, An Introduction to Ergodic Theory (1982) · Zbl 0475.28009 · doi:10.1007/978-1-4612-5775-2
[8] DOI: 10.1007/BF01691062 · Zbl 0182.56901 · doi:10.1007/BF01691062
[9] Grassberger, Physica 10D pp 52– (1984)
[10] Wolfram, Physica 10D pp 1– (1984)
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