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commutation equation

RAIRO - Theoretical Informatics and Applications (1)

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On the simplest centralizer of a language
Paolo Massazza, Petri Salmela
Journal:

RAIRO - Theoretical Informatics and Applications / Volume 40 / Issue 2 / April 2006

Published online by Cambridge University Press:

20 July 2006, pp. 295-301

Print publication:

April 2006
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Given a finite alphabet Σ and a language L ⊆ ∑+, 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.