# Uniformly bounded duplication codes

RAIRO - Theoretical Informatics and Applications (2007)

- Volume: 41, Issue: 4, page 411-424
- ISSN: 0988-3754

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topLeupold, Peter, and Mitrana, Victor. "Uniformly bounded duplication codes." RAIRO - Theoretical Informatics and Applications 41.4 (2007): 411-424. <http://eudml.org/doc/249927>.

@article{Leupold2007,

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.
},

author = {Leupold, Peter, Mitrana, Victor},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Duplication; duplication primitive word; duplication root; duplication code; square-free word},

language = {eng},

month = {8},

number = {4},

pages = {411-424},

publisher = {EDP Sciences},

title = {Uniformly bounded duplication codes},

url = {http://eudml.org/doc/249927},

volume = {41},

year = {2007},

}

TY - JOUR

AU - Leupold, Peter

AU - Mitrana, Victor

TI - Uniformly bounded duplication codes

JO - RAIRO - Theoretical Informatics and Applications

DA - 2007/8//

PB - EDP Sciences

VL - 41

IS - 4

SP - 411

EP - 424

AB - 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.

LA - eng

KW - Duplication; duplication primitive word; duplication root; duplication code; square-free word

UR - http://eudml.org/doc/249927

ER -

## References

top- J. Berstel and D. Perrin, Theory of Codes. Academic Press, Orlando (1985). Zbl0587.68066
- J. Dassow, V. Mitrana and Gh. Păun, On the Regularity of Duplication Closure. Bull. EATCS69 (1999) 133–136. Zbl0941.68605
- N. Fine and H. Wilf, Uniqueness Theorems for Periodic Functions. Proc. Amer. Math. Soc.16 (1965) 109–114. Zbl0131.30203
- International Human Genome Sequencing Consortium, Finishing the Euchromatic Sequence of the Human Genome. Nature431 (2004) 931–945.
- P. Leupold, V. Mitrana and J. Sempere, Languages Arising from Gene Repeated Duplication, in Aspects of Molecular Computing. Essays Dedicated to Tom Head on the Occasion of his 70th Birthday. Lect. Notes Comput. Sci.2950 (2004) 297–308. Zbl1200.68146
- P. Leupold, C. Martín Vide and V. Mitrana, Uniformly Bounded Duplication Languages. Discrete Appl. Math.146 (2005) 301–310. Zbl1077.68047
- M. Lothaire, Combinatorics on Words. Addison-Wesley, Reading, MA (1983). Zbl0514.20045
- R. Ross and K. Winklmann, Repetitive Strings are not Context-Free. RAIRO-Theor. Inf. Appl.16 (1982) 191–199. Zbl0489.68071
- A. Salomaa, Formal Languages. Academic Press, Orlando (1973). Zbl0262.68025
- H.J. Shyr, Free Monoids and Languages. Hon Min Book Company, Taichung (1991). Zbl0746.20050
- M.-W. Wang, On the Irregularity of the Duplication Closure. Bull. EATCS70 (2000) 162–163. Zbl0983.68111

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