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DOI: 10.4230/LIPIcs.STACS.2008.1362
URN: urn:nbn:de:0030-drops-13620
URL: https://drops.dagstuhl.de/opus/volltexte/2008/1362/
Kao, Jui-Yi ; Shallit, Jeffrey ; Xu, Zhi
The Frobenius Problem in a Free Monoid
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Abstract
The classical Frobenius problem over ${mathbb N}$ is to computethe largest integer $g$ not representable as a non-negative integer
linear combination of non-negative integers $x_1, x_2, ldots,
x_k$, where $gcd(x_1, x_2, ldots, x_k) = 1$. In this paper we
consider novel generalizations of the Frobenius problem to the
noncommutative setting of a free monoid. Unlike the commutative
case, where the bound on $g$ is quadratic, we are able to show
exponential or subexponential behavior for several analogues of
$g$, with the precise bound depending on the particular measure
chosen.
BibTeX - Entry
@InProceedings{kao_et_al:LIPIcs:2008:1362,
author = {Jui-Yi Kao and Jeffrey Shallit and Zhi Xu},
title = {{The Frobenius Problem in a Free Monoid}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {421--432},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Susanne Albers and Pascal Weil},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2008/1362},
URN = {urn:nbn:de:0030-drops-13620},
doi = {10.4230/LIPIcs.STACS.2008.1362},
annote = {Keywords: Combinatorics on words, Frobenius problem, free monoid}
}
| Keywords: | Combinatorics on words, Frobenius problem, free monoid | |
| Seminar: | 25th International Symposium on Theoretical Aspects of Computer Science | |
| Issue date: | 2008 | |
| Date of publication: | 06.02.2008 |
