Uniformly bounded duplication languages

Authors:
Peter Leupold;Carlos Martín-Vide;Victor Mitrana
Affiliations:
Research Group in Mathematical Linguistics, Rovira i Virgili University, Tarragona, Spain;Research Group in Mathematical Linguistics, Rovira i Virgili University, Tarragona, Spain;Research Group in Mathematical Linguistics, Rovira i Virgili University, Tarragona, Spain and Faculty of Mathematics and Computer Science, Institute of Mathematics, Bucharest University, Bucure ...
Venue:
Discrete Applied Mathematics
Year:
2005

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Abstract

We consider a new type of language defined by a word through iterative factor duplications, inspired by the process of tandem repeats production in the evolution of DNA. We investigate the effect of restricting the factor length to a constant. We prove that all these languages are regular, any word has a unique uniformly bounded duplication root, and show how this root can be computed in linear time and memory. We also address the problem of computing the uniformly bounded duplication distance between two words.