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Maximal state complexity and generalized de Bruijn words
Information and Computation ( IF 0.8 ) Pub Date : 2021-01-06 , DOI: 10.1016/j.ic.2021.104689
Daniel Gabric 1 , Štěpán Holub 2 , Jeffrey Shallit 1
Affiliation  

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:

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。

更新日期:2021-01-06
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