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Von Neumann Regularity, Split Epicness and Elementary Cellular Automata Salo, Ville cellular automata elementary cellular automata von Neumann regularity split epicness We show that a cellular automaton on a 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 [S.-Törmä, 2015] that von Neumann regularity is decidable condition, and we decide it for all elementary CA. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Ville Salo 2021 Is Part Of OASIcs, Volume 90, 27th IFIP WG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/OASIcs.AUTOMATA.2021.11 urn:nbn:de:0030-drops-140209 https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.AUTOMATA.2021.11 eng https://creativecommons.org/licenses/by/4.0/legalcode