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DOI: 10.4230/LIPIcs.STACS.2015.329
URN: urn:nbn:de:0030-drops-49240
URL: https://drops.dagstuhl.de/opus/volltexte/2015/4924/
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 | |
| Seminar: | 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015) | |
| Issue date: | 2015 | |
| Date of publication: | 26.02.2015 |
