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On the simplest centralizer of a language

Published online by Cambridge University Press:  20 July 2006

Paolo Massazza  and
Petri Salmela
Paolo Massazza
Affiliation:
Dipartimento di Informatica e Comunicazione, Università degli Studi dell'Insubria, via Mazzini 5, 21100 Varese, Italy; paolo.massazza@uninsubria.it
Petri Salmela
Affiliation:
Department of Mathematics and TUCS, University of Turku, 20014 Turku, Finland; pesasa@utu.fi
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Abstract

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.

Keywords

Commutation equationcentralizerlexicographic order.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 40 , Issue 2: Alberto Bertoni: Climbing summits , April 2006 , pp. 295 - 301
Copyright
© EDP Sciences, 2006

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