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The Domino Problem is Undecidable on Surface Groups

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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.

BibTeX - Entry

@InProceedings{aubrun_et_al:LIPIcs:2019:10990,
  author =	{Nathalie Aubrun and Sebasti{\'a}n Barbieri and Etienne Moutot},
  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 =	{Peter Rossmanith and Pinar Heggernes and Joost-Pieter Katoen},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10990},
  URN =		{urn:nbn:de:0030-drops-109900},
  doi =		{10.4230/LIPIcs.MFCS.2019.46},
  annote =	{Keywords: tilings, substitutions, SFTs, decidability, domino problem}
}

Keywords: tilings, substitutions, SFTs, decidability, domino problem
Seminar: 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)
Issue date: 2019
Date of publication: 20.08.2019


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