Von neumann regularity, split epicness and elementary cellular automata
: Salo Ville
: Castillo-Ramirez Alonso, Guillon Pierre, Perrot Kévin
: International Workshop on Cellular Automata and Discrete Complex Systems
Publisher: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
: 2021
: Open Access Series in Informatics
: 27th IFIP WG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA 2021)
: OpenAccess Series in Informatics
: Open access series in informatics
: 90
: 11:1
: 11:10
: 978-3-95977-189-4
: 2190-6807
DOI: https://doi.org/10.4230/OASIcs.AUTOMATA.2021.11
: https://drops.dagstuhl.de/opus/volltexte/2021/14020/
: https://research.utu.fi/converis/portal/detail/Publication/67640097
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.
