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Maximal State Complexity and Generalized de Bruijn Words (1903.05442v2)
Published 13 Mar 2019 in cs.FL, cs.DM, and math.CO
Abstract: We compute the exact maximum state complexity for the language consisting of $m$ words of length $N$, and characterize languages achieving the maximum. We also consider a special case, namely languages $C(w)$ consisting of the conjugates of a single word $w$. The words for which the maximum state complexity of $C(w)$ is achieved turn out to be a natural generalization of de Bruijn words. We show that generalized de Bruijn words exist for each length and consider the number of them.