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Applications of ergodic theory and sofic systems to cellular automata. (English) Zbl 0562.68038
Cellular automata, Proc. Interdisc. Workshop, Los Alamos/N.M. 1983, Physica D 10, No. 1-2, 36-44 (1984).
Summary: We indicate a mathematical framework for analysing the evolution of cellular automata. Those automata obeying an additive rule are shown to be the same as endomorphisms of a compact abelian group, and therefore their statistical and dynamical behavior can be told exactly by using Fourier analysis and ergodic theory. Those obeying certain nonlinear rules are closely tied to a finitely-described object called a sofic system, but the underlying statistics appear to be more complicated and interesting. We conclude by formulating several conjectures about one such system.
[For the entire collection see Zbl 0556.00013.]

68Q80 Cellular automata (computational aspects)
37B15 Dynamical aspects of cellular automata
37A25 Ergodicity, mixing, rates of mixing
22D40 Ergodic theory on groups
22C05 Compact groups
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