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In this paper we describe a "light" algorithm for the on-line construction of a small automaton recognising a finite set of words. The algorithm runs in linear time. We carried out good experimental results on real dictionaries, on biological sequences and on the sets of suffixes (resp. factors) of a set of words that shows how our automaton is near to the minimal one. For the suffixes of a text, we propose a modified construction that leads to an even smaller automaton. We moreover construct linear algorithms for the insertion and deletion of a word in a finite set, directly from the constructed automaton. [ABSTRACT FROM AUTHOR]

Considering the uniform distribution on sets of m non-empty words whose sum of lengths is n, we establish that the average state complexities of the rational operations are asymptotically linear. [ABSTRACT FROM AUTHOR]