On the simplest centralizer of a language
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 40 (2006) no. 2, pp. 295-301.

Given a finite alphabet Σ and a language L⊆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.

DOI : 10.1051/ita:2006014
Classification : 68Q70, 68R15
Mots-clés : commutation equation, centralizer, lexicographic order 
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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. http://www.numdam.org/articles/10.1051/ita:2006014/

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