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.STACS.2015.329
URN: urn:nbn:de:0030-drops-49240
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/4924/
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Galby, Esther ; Ouaknine, Joël ; Worrell, James

On Matrix Powering in Low Dimensions

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Abstract

We investigate the Matrix Powering Positivity Problem, PosMatPow: given an m X m square integer matrix M, a linear function f: Z^{m X m} -> Z with integer coefficients, and a positive integer n (encoded in binary), determine whether f(M^n) \geq 0. We show that for fixed dimensions m of 2 and 3, this problem is decidable in polynomial time.

BibTeX - Entry

@InProceedings{galby_et_al:LIPIcs:2015:4924,
  author =	{Esther Galby and Jo{\"e}l Ouaknine and James Worrell},
  title =	{{On Matrix Powering in Low Dimensions}},
  booktitle =	{32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
  pages =	{329--340},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-78-1},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{30},
  editor =	{Ernst W. Mayr and Nicolas Ollinger},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/4924},
  URN =		{urn:nbn:de:0030-drops-49240},
  doi =		{10.4230/LIPIcs.STACS.2015.329},
  annote =	{Keywords: matrix powering, complexity, Baker's theorem}
}

Keywords: matrix powering, complexity, Baker's theorem
Collection: 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)
Issue Date: 2015
Date of publication: 26.02.2015

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