An Effective Lower Bound for Group Complexity of Finite Semigroups and Automata
Group Theory
2008-12-19 v1 Combinatorics
Abstract
The question of computing the group complexity of finite semigroups and automata was first posed in K. Krohn and J. Rhodes, \textit{Complexity of finite semigroups}, Annals of Mathematics (2) \textbf{88} (1968), 128--160, motivated by the Prime Decomposition Theorem of K. Krohn and J. Rhodes, \textit{Algebraic theory of machines, {I}: {P}rime decomposition theorem for finite semigroups and machines}, Transactions of the American Mathematical Society \textbf{116} (1965), 450--464. Here we provide an effective lower bound for group complexity.
Cite
@article{arxiv.0812.3499,
title = {An Effective Lower Bound for Group Complexity of Finite Semigroups and Automata},
author = {Karsten Henckell and John Rhodes and Benjamin Steinberg},
journal= {arXiv preprint arXiv:0812.3499},
year = {2008}
}