License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2019.44
URN: urn:nbn:de:0030-drops-106209
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10620/
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Colcombet, Thomas ; Ouaknine, Joël ; Semukhin, Pavel ; Worrell, James

On Reachability Problems for Low-Dimensional Matrix Semigroups

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Abstract

We consider the Membership and the Half-Space Reachability problems for matrices in dimensions two and three. Our first main result is that the Membership Problem is decidable for finitely generated sub-semigroups of the Heisenberg group over rational numbers. Furthermore, we prove two decidability results for the Half-Space Reachability Problem. Namely, we show that this problem is decidable for sub-semigroups of GL(2,Z) and of the Heisenberg group over rational numbers.

BibTeX - Entry

@InProceedings{colcombet_et_al:LIPIcs:2019:10620,
  author =	{Thomas Colcombet and Jo{\"e}l Ouaknine and Pavel Semukhin and James Worrell},
  title =	{{On Reachability Problems for Low-Dimensional Matrix Semigroups}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{44:1--44:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Christel Baier and Ioannis Chatzigiannakis and Paola Flocchini and Stefano Leonardi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10620},
  URN =		{urn:nbn:de:0030-drops-106209},
  doi =		{10.4230/LIPIcs.ICALP.2019.44},
  annote =	{Keywords: membership problem, half-space reachability problem, matrix semigroups, Heisenberg group, general linear group}
}

Keywords: membership problem, half-space reachability problem, matrix semigroups, Heisenberg group, general linear group
Collection: 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)
Issue Date: 2019
Date of publication: 04.07.2019

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