The Frobenius Problem in a Free Monoid

Authors Jui-Yi Kao, Jeffrey Shallit, Zhi Xu



PDF
Thumbnail PDF

File

LIPIcs.STACS.2008.1362.pdf
  • Filesize: 188 kB
  • 12 pages

Document Identifiers

Author Details

Jui-Yi Kao
Jeffrey Shallit
Zhi Xu

Cite As Get BibTex

Jui-Yi Kao, Jeffrey Shallit, and Zhi Xu. The Frobenius Problem in a Free Monoid. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 421-432, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008) https://doi.org/10.4230/LIPIcs.STACS.2008.1362

Abstract

The classical Frobenius problem over ${mathbb N}$ is to compute
   the 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.

Subject Classification

Keywords
  • Combinatorics on words
  • Frobenius problem
  • free monoid

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail