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DOI: 10.4230/LIPIcs.ICALP.2019.44
URN: urn:nbn:de:0030-drops-106209
URL: https://drops.dagstuhl.de/opus/volltexte/2019/10620/
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 | |
| Seminar: | 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019) | |
| Issue date: | 2019 | |
| Date of publication: | 04.07.2019 |
