State Complexity and the Monoid of Transformations of a Finite Set
Group Theory
2007-05-23 v2 Combinatorics
Abstract
In this paper we consider the state complexity of an operation on formal languages, root(L). This naturally entails the discussion of the monoid of transformations of a finite set. We obtain good upper and lower bounds on the state complexity of root(L) over alphabets of all sizes.
Cite
@article{arxiv.math/0306416,
title = {State Complexity and the Monoid of Transformations of a Finite Set},
author = {Bryan Krawetz and John Lawrence and Jeffery Shallit},
journal= {arXiv preprint arXiv:math/0306416},
year = {2007}
}
Comments
Added discussion of prior work. Generalized results to both even and odd cases. Corrected mistakes