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.

中文翻译：

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最大状态复杂度和广义 de Bruijn 词

我们计算由长度为N的m个单词组成的语言的确切最大状态复杂度，并表征达到最大值的语言。我们还考虑一种特殊情况，即语言$C(w)$由单个单词w的变位词组成。最大状态复杂度的词$C(w)$被证明是对 de Bruijn 词的自然概括。我们证明每个长度都存在广义的 de Bruijn 词，并考虑它们的数量。