| Issue |
RAIRO-Theor. Inf. Appl.
Volume 40, Number 2, April-June 2006
Alberto Bertoni: Climbing summits
|
|
|---|---|---|
| Page(s) | 295 - 301 | |
| DOI | https://doi.org/10.1051/ita:2006014 | |
| Published online | 20 July 2006 | |
On the simplest centralizer of a language
1
Dipartimento di Informatica e Comunicazione,
Università degli Studi dell'Insubria,
via Mazzini 5, 21100 Varese, Italy;
paolo.massazza@uninsubria.it
2
Department of Mathematics and TUCS,
University of Turku,
20014 Turku, Finland; pesasa@utu.fi
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.
Mathematics Subject Classification: 68Q70 / 68R15
Key words: Commutation equation / centralizer / lexicographic order.
© EDP Sciences, 2006
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