Abstract

We solve the following problem proposed by Straubing. Given a two-letter alphabet A, what is the maximal number of states f( n) of the minimal automaton of a subset of A n , the set of all words of length n. We give an explicit formula to compute f( n) and we show that 1= lim inf n→∞nƒ(n)/2 n≤lim sup n→∞nƒ(n)/2 n=2 .

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