English

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