The average state complexity of the star of a finite set of words is linear
by
Frédérique Bassino
,
Laura Giambruno
,
Cyril Nicaud
BibTeX
@MISC{Bassino_theaverage,
author = {Frédérique Bassino and Laura Giambruno and Cyril Nicaud},
title = {The average state complexity of the star of a finite set of words is linear},
year = {}
}
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Abstract
We prove that, for the uniform distribution over all sets X of m (that is a fixed integer) non-empty words whose sum of lengths is n, D_X , one of the usual deterministic automata recognizing X^∗ , has on average O(n) states and that the average state complexity of X^∗ is Θ(n). We also show that the average time complexity of the computation of the automaton D_X is O(n log n), when the alphabet is of size at least three.
