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Communication Dans Un Congrès Année : 2008

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.
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Dates et versions

hal-00452752 , version 1 (03-02-2010)

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  • HAL Id : hal-00452752 , version 1

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Frédérique Bassino, Laura Giambruno, Cyril Nicaud. The average state complexity of the star of a finite set of words is linear.. International Conference on Developments in Language Theory, 2008, Japan. pp.134-145. ⟨hal-00452752⟩
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