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The Domino Problem is Undecidable on Surface Groups

Authors: Nathalie Aubrun, Sebastián Barbieri, and Etienne Moutot

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)


Abstract
We show that the domino problem is undecidable on orbit graphs of non-deterministic substitutions which satisfy a technical property. As an application, we prove that the domino problem is undecidable for the fundamental group of any closed orientable surface of genus at least 2.

Cite as

Nathalie Aubrun, Sebastián Barbieri, and Etienne Moutot. The Domino Problem is Undecidable on Surface Groups. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 46:1-46:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{aubrun_et_al:LIPIcs.MFCS.2019.46,
  author =	{Aubrun, Nathalie and Barbieri, Sebasti\'{a}n and Moutot, Etienne},
  title =	{{The Domino Problem is Undecidable on Surface Groups}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{46:1--46:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.46},
  URN =		{urn:nbn:de:0030-drops-109900},
  doi =		{10.4230/LIPIcs.MFCS.2019.46},
  annote =	{Keywords: tilings, substitutions, SFTs, decidability, domino problem}
}
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