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Universal Gauge-Invariant Cellular Automata

Authors Pablo Arrighi , Marin Costes , Nathanaël Eon

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Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
Keywords
  • Cellular automata
  • Gauge-invariance
  • Universality

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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.

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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) https://doi.org/10.4230/LIPIcs.MFCS.2021.9

Author Details

Pablo Arrighi
  • Université Paris-Saclay, CNRS, LMF, 91190 Gif-sur-Yvette, France
  • IXXI, Lyon, France
Marin Costes
  • ENS Paris-Saclay, CNRS, LMF, 91190 Gif-sur-Yvette, France
Nathanaël Eon
  • Aix-Marseille Université, Université de Toulon, CNRS, LIS, Marseille, France

Funding

This publication was made possible through the support of the ID# 61466 grant from the John Templeton Foundation, as part of the “The Quantum Information Structure of Spacetime (QISS)” Project (qiss.fr). The opinions expressed in this publication are those of the author(s) and do not necessarily reflect the views of the John Templeton Foundation.

Acknowledgements

The authors would like to thank Guillaume Theyssier for asking us the question whether any CA admits a gauge extension.

References

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