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: https://drops.dagstuhl.de/opus/volltexte/2021/14449/
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Arrighi, Pablo ; Costes, Marin ; Eon, Nathanaƫl

Universal Gauge-Invariant Cellular Automata

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LIPIcs-MFCS-2021-9.pdf (0.7 MB)


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: Cellular automata, Gauge-invariance, Universality
Collection: 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)
Issue Date: 2021
Date of publication: 18.08.2021


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