On the simplest centralizer of a language

Massazza, Paolo; Salmela, Petri

doi:10.1051/ita:2006014

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On the simplest centralizer of a language

Massazza, Paolo ; Salmela, Petri

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 40 (2006) no. 2, pp. 295-301

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Résumé

Given a finite alphabet $Σ$ and a language $L \subseteq Σ^{+}$ , the centralizer of $L$ is defined as the maximal language commuting with it. We prove that if the primitive root of the smallest word of $L$ (with respect to a lexicographic order) is prefix distinguishable in $L$ then the centralizer of $L$ is as simple as possible, that is, the submonoid $L^{☆}$ . This lets us obtain a simple proof of a known result concerning the centralizer of nonperiodic three-word languages.

MR Zbl

DOI : 10.1051/ita:2006014

Classification : 68Q70, 68R15
Keywords: commutation equation, centralizer, lexicographic order

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     title = {On the simplest centralizer of a language},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {295--301},
     publisher = {EDP-Sciences},
     volume = {40},
     number = {2},
     year = {2006},
     doi = {10.1051/ita:2006014},
     mrnumber = {2252640},
     zbl = {1112.68097},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ita:2006014/}
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Massazza, Paolo; Salmela, Petri. On the simplest centralizer of a language. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 40 (2006) no. 2, pp. 295-301. doi: 10.1051/ita:2006014

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