The average state complexity of the star of a finite set of words is linear.
Résumé
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, DX, one of the usual deterministic automata recognizing X*, has on average O(n) states and that the average state complexity of X* is O(n). We also show that the average time complexity of the computation of the automaton DX is O(n log n), when the alphabet is of size at least three.
Domaines
Mathématique discrète [cs.DM]Origine | Fichiers produits par l'(les) auteur(s) |
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