# On von Neumann regularity of cellular automata

@article{Salo2022OnVN, title={On von Neumann regularity of cellular automata}, author={Ville Salo}, journal={ArXiv}, year={2022}, volume={abs/2209.13373} }

We show that a cellular automaton on a one-dimensional two-sided mixing subshift of finite type is a von Neumann regular element in the semigroup of cellular automata if and only if it is split epic onto its image in the category of sofic shifts and block maps. It follows from previous joint work of the author and Törmä that von Neumann regularity is a decidable condition, and we decide it for all elementary CA, obtaining the optimal radii for weak generalized inverses. Two sufficient…

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