License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2022.43
URN: urn:nbn:de:0030-drops-168415
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16841/
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Dong, Ruiwen

On the Identity Problem for Unitriangular Matrices of Dimension Four

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LIPIcs-MFCS-2022-43.pdf (0.7 MB)

Abstract

We show that the Identity Problem is decidable in polynomial time for finitely generated sub-semigroups of the group UT(4, ℤ) of 4 × 4 unitriangular integer matrices. As a byproduct of our proof, we also show the polynomial-time decidability of several subset reachability problems in UT(4, ℤ).

BibTeX - Entry

@InProceedings{dong:LIPIcs.MFCS.2022.43,
  author =	{Dong, Ruiwen},
  title =	{{On the Identity Problem for Unitriangular Matrices of Dimension Four}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{43:1--43:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16841},
  URN =		{urn:nbn:de:0030-drops-168415},
  doi =		{10.4230/LIPIcs.MFCS.2022.43},
  annote =	{Keywords: identity problem, matrix semigroups, unitriangular matrices}
}

Keywords: identity problem, matrix semigroups, unitriangular matrices
Collection: 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)
Issue Date: 2022
Date of publication: 22.08.2022

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