License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2021.9
URN: urn:nbn:de:0030-drops-144490
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14449/
Arrighi, Pablo ;
Costes, Marin ;
Eon, Nathanaƫl
Universal Gauge-Invariant Cellular Automata
Abstract
Gauge symmetries play a fundamental role in Physics, as they provide a mathematical justification for the fundamental forces. Usually, one starts from a non-interactive theory which governs "matter", and features a global symmetry. One then extends the theory so as make the global symmetry into a local one (a.k.a gauge-invariance). We formalise a discrete counterpart of this process, known as gauge extension, within the Computer Science framework of Cellular Automata (CA). We prove that the CA which admit a relative gauge extension are exactly the globally symmetric ones (a.k.a the colour-blind). We prove that any CA admits a non-relative gauge extension. Both constructions yield universal gauge-invariant CA, but the latter allows for a first example where the gauge extension mediates interactions within the initial CA.
BibTeX - Entry
@InProceedings{arrighi_et_al:LIPIcs.MFCS.2021.9,
author = {Arrighi, Pablo and Costes, Marin and Eon, Nathana\"{e}l},
title = {{Universal Gauge-Invariant Cellular Automata}},
booktitle = {46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
pages = {9:1--9:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-201-3},
ISSN = {1868-8969},
year = {2021},
volume = {202},
editor = {Bonchi, Filippo and Puglisi, Simon J.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/14449},
URN = {urn:nbn:de:0030-drops-144490},
doi = {10.4230/LIPIcs.MFCS.2021.9},
annote = {Keywords: Cellular automata, Gauge-invariance, Universality}
}
Keywords: |
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Cellular automata, Gauge-invariance, Universality |
Collection: |
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46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021) |
Issue Date: |
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2021 |
Date of publication: |
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18.08.2021 |