License: 
Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/OASIcs.AUTOMATA.2021.11
URN: urn:nbn:de:0030-drops-140209
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14020/
Salo, Ville
Von Neumann Regularity, Split Epicness and Elementary Cellular Automata
Abstract
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.
BibTeX - Entry
@InProceedings{salo:OASIcs.AUTOMATA.2021.11,
author = {Salo, Ville},
title = {{Von Neumann Regularity, Split Epicness and Elementary Cellular Automata}},
booktitle = {27th IFIP WG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA 2021)},
pages = {11:1--11:10},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-189-4},
ISSN = {2190-6807},
year = {2021},
volume = {90},
editor = {Castillo-Ramirez, Alonso and Guillon, Pierre and Perrot, K\'{e}vin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/14020},
URN = {urn:nbn:de:0030-drops-140209},
doi = {10.4230/OASIcs.AUTOMATA.2021.11},
annote = {Keywords: cellular automata, elementary cellular automata, von Neumann regularity, split epicness}
}
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Keywords: |
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cellular automata, elementary cellular automata, von Neumann regularity, split epicness |
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Collection: |
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27th IFIP WG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA 2021) |
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Issue Date: |
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2021 |
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Date of publication: |
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28.06.2021 |
