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Uniformly bounded duplication codes

Published online by Cambridge University Press:  17 August 2007

Peter Leupold  and
Victor Mitrana
Peter Leupold
Affiliation:
Research Group in Mathematical Linguistics, Rovira i Virgili University, Pça. Imperial Tàrraco 1, 43005 Tarragona, Catalunya, Spain; klauspeter.leupold@urv.cat; victor.mitrana1@urv.cat
Victor Mitrana
Affiliation:
Research Group in Mathematical Linguistics, Rovira i Virgili University, Pça. Imperial Tàrraco 1, 43005 Tarragona, Catalunya, Spain; klauspeter.leupold@urv.cat; victor.mitrana1@urv.cat Faculty of Mathematics and Computer Science, Bucharest University, Str. Academiei 14, 70109 Bucureşti, Romania.
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Abstract

Duplication is the replacement of a factor w within a word by ww. This operation can be used iteratively to generate languages starting from words or sets of words. By undoing duplications, one can eventually reach a square-free word, the original word's duplication root. The duplication root is unique, if the length of duplications is fixed. Based on these unique roots we define the concept of duplication code. Elementary properties are stated, then the conditions under which infinite duplication codes exist are fully characterized; the relevant parameters are the duplication length and alphabet size. Finally, some properties of the languages generated by duplication codes are investigated.

Keywords

Duplicationduplication primitive wordduplication rootduplication code
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 41 , Issue 4 , October 2007 , pp. 411 - 424
Copyright
© EDP Sciences, 2007

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