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Complexity of Generic Limit Sets of Cellular Automata
The generic limit set of a topological dynamical system of the smallest
closed subset of the phase space that has a comeager realm of attraction. It
intuitively captures the asymptotic dynamics of almost all initial conditions.
It was defined by Milnor and studied in the context of cellular automata, whose
generic limit sets are subshifts, by Djenaoui and Guillon. In this article we
study the structural and computational restrictions that apply to generic limit
sets of cellular automata. As our main result, we show that the language of a
generic limit set can be at most -hard, and lower in various
special cases. We also prove a structural restriction on generic limit sets
with a global period.Comment: 13 pages, 2 figure