Von Neumann Regularity, Split Epicness and Elementary Cellular Automata

Author Ville Salo

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Ville Salo
  • University of Turku, Finland


We thank Jarkko Kari for observing that Proposition 12 works in all dimensions. We thank Johan Kopra for pointing out that Lemma 11 is easier to prove than to find in [Lind and Marcus, 1995].

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Ville Salo. Von Neumann Regularity, Split Epicness and Elementary Cellular Automata. In 27th IFIP WG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA 2021). Open Access Series in Informatics (OASIcs), Volume 90, pp. 11:1-11:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Automata over infinite objects
  • cellular automata
  • elementary cellular automata
  • von Neumann regularity
  • split epicness


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