Abstract

We consider a certain natural generalization of de Bruijn words, and use it to compute the exact maximum state complexity for the language consisting of the conjugates of a single word. In other words, we determine the state complexity of cyclic shift on languages consisting of a single word.

Highlights

  • In this note we investigate the state complexity of the finite language C(x), over all words x of length N

  • We determine the state complexity of cyclic shift on languages consisting of a single word

  • Our theorem depends on a certain natural generalization of de Bruijn words, of independent interest, which is introduced

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Summary

Generalized de Bruijn Words and the State Complexity of Conjugate Sets

To cite this version: Daniel Gabric, Štěpán Holub, Jeffrey Shallit. Generalized de Bruijn Words and the State Complexity of Conjugate Sets. 21th International Conference on Descriptional Complexity of Formal Systems (DCFS), Jul 2019, Košice, Slovakia. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés

Introduction
Generalized de Bruijn words
State complexity
Final comments

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