Asymptotic enumeration of Minimal Automata
Formal Languages and Automata Theory
2011-09-27 v1 Combinatorics
Abstract
We determine the asymptotic proportion of minimal automata, within n-state accessible deterministic complete automata over a k-letter alphabet, with the uniform distribution over the possible transition structures, and a binomial distribution over terminal states, with arbitrary parameter b. It turns out that a fraction ~ 1-C(k,b) n^{-k+2} of automata is minimal, with C(k,b) a function, explicitly determined, involving the solution of a transcendental equation.
Keywords
Cite
@article{arxiv.1109.5683,
title = {Asymptotic enumeration of Minimal Automata},
author = {Frederique Bassino and Julien David and Andrea Sportiello},
journal= {arXiv preprint arXiv:1109.5683},
year = {2011}
}
Comments
12+5 pages, 2 figures, submitted to STACS 2012