The state complexities of some basic operations on regular languages
Theoretical Computer Science
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LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
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We prove that, for the uniform distribution over all sets Xof m(that is a fixed integer) non-empty words whose sum of lengths is n, $\mathcal{D}_X$, one of the usual deterministic automata recognizing X*, has on average $\mathcal{O}(n)$ states and that the average state complexity of X*is 茂戮驴(n). We also show that the average time complexity of the computation of the automaton $\mathcal{D}_X$ is $\mathcal{O}(n\log n)$, when the alphabet is of size at least three.