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Universal Gauge-Invariant Cellular Automata

Authors: Pablo Arrighi, Marin Costes, and Nathanaël Eon

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

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.

Cite as

Pablo Arrighi, Marin Costes, and Nathanaël Eon. Universal Gauge-Invariant Cellular Automata. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 9:1-9:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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  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/entities/document/10.4230/LIPIcs.MFCS.2021.9},
  URN =		{urn:nbn:de:0030-drops-144490},
  doi =		{10.4230/LIPIcs.MFCS.2021.9},
  annote =	{Keywords: Cellular automata, Gauge-invariance, Universality}
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