Abstract
The decidability of the finiteness problem for automaton groups is a well-studied open question on Mealy automata. We connect this question of algebraic nature to the periodicity problem of one-way cellular automata, a dynamical question known to be undecidable in the general case. We provide a first undecidability result on the dynamics of one-way permutive cellular automata, arguing in favor of the undecidability of the finiteness problem for reset Mealy automata.
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Delacourt, M., & Ollinger, N. (2017). Permutive one-way cellular automata and the finiteness problem for automaton groups. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10307 LNCS, pp. 234–245). Springer Verlag. https://doi.org/10.1007/978-3-319-58741-7_23
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