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arXiv · 2108.12925

Generically Nilpotent Cellular Automata

Ilkka Törmä
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Abstract

We study the generic limit sets of one-dimensional cellular automata, which intuitively capture their asymptotic dynamics while discarding transient phenomena. As our main results, we characterize the automata whose generic limit set is a singleton, and show that this class is $\Sigma^0_2$-complete. We also prove that given a CA whose generic limit set is guaranteed to be a singleton, the sole configuration it contains cannot be algorithmically determined.

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Ilkka Törmä. 2021-08-29. Generically Nilpotent Cellular Automata. https://arxiv.org/abs/2108.12925

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