Document Theoret. Informatics Appl. 41, 411-424 (2007)
DOI: 10.1051/ita:2007021
Uniformly bounded duplication codes
Peter Leupold1 and Victor Mitrana1, 21 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
2 Faculty of Mathematics and Computer Science, Bucharest University, Str. Academiei 14, 70109 Bucuresti, Romania.
(Received September 8, 2005. Accepted November 14, 2006. Published online 17 August 2007.)
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.
Mathematics Subject Classification. 68R15, 68Q45, 94B60
Key words: Duplication -- duplication primitive word -- duplication root -- duplication code
© EDP Sciences 2007