Duplication in DNA Sequences

  • Masami Ito
  • Lila Kari
  • Zachary Kincaid
  • Shinnosuke Seki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5257)


Duplication and repeat-deletion are the basic models of errors occurring during DNA replication from the viewpoint of formal languages. During DNA replication, subsequences of a strand of DNA may be copied several times (duplication) or skipped (repeat-deletion). Iterated duplication and repeat-deletion have been well-studied, but little is known about single-step duplication and repeat-deletion. In this paper, we investigate properties of these operations, such as closure properties of language families in the Chomsky hierarchy, language equations involving these operations. We also make progress towards a characterization of regular languages that are generated by duplicating a regular language.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Dassow, J., Mitrana, V., Păun, G.: On the regularity of duplication closure. Bull. EATCS 69, 133–136 (1999)zbMATHGoogle Scholar
  2. 2.
    Dassow, J., Mitrana, V., Salomaa, A.: Operations and language generating devices suggested by the genome evolution. Theoretical Computer Science 270, 701–738 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Garcia-Diaz, M., Kunkel, T.A.: Mechanism of a genetic glissando: structural biology of indel mutations. Trends in Biochemical Sciences 31(4), 206–214 (2006)CrossRefGoogle Scholar
  4. 4.
    Ito, M.: Algebraic Theory of Automata and Languages. World Scientific Pub. Co. Inc., Singapore (2004)zbMATHGoogle Scholar
  5. 5.
    Ito, M., Leupold, P., S-Tsuji, K.: Closure of language classes under bounded duplication. In: Ibarra, O.H., Dang, Z. (eds.) DLT 2006. LNCS, vol. 4036, pp. 238–247. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Leupold, P.: Duplication roots. In: Harju, T., Karhumäki, J., Lepistö, A. (eds.) DLT 2007. LNCS, vol. 4588, pp. 290–299. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  7. 7.
    Leupold, P.: Languages generated by iterated idempotencies and the special case of duplication. Ph.D. thesis, Department de Filologies Romaniques, Facultat de Lletres, Universitat Rovira i Virgili, Tarragona, Spain (2006)Google Scholar
  8. 8.
    Leupold, P., Mitrana, V., Sempere, J.: Formal languages arising from gene repeated duplication. In: Jonoska, N., Păun, G., Rozenberg, G. (eds.) Aspects of Molecular Computing. LNCS, vol. 2950, pp. 297–308. Springer, Heidelberg (2003)Google Scholar
  9. 9.
    Leupold, P., M-Vide, C., Mitrana, V.: Uniformly bounded duplication languages. Discrete Applied Mathematics 146(3), 301–310 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Lothaire, M.: Combinatorics on Words, Encyclopedia of Mathematics and its Applications 17. Addison-Wesley Publishing Co., Reading (1983)Google Scholar
  11. 11.
    Lyndon, R.C., Schützenberger, M.P.: On the equation a M = b N c P in a free group. Michigan Mathematical Journal 9, 289–298 (1962)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    M-Vide, C., Păun, G.: Duplication grammars. Acta Cybernetica 14, 151–164 (1999)MathSciNetGoogle Scholar
  13. 13.
    Mitrana, V., Rozenberg, G.: Some properties of duplication grammars. Acta Cybernetica 14, 165–177 (1999)zbMATHMathSciNetGoogle Scholar
  14. 14.
    Reis, C.M., Shyr, H.J.: Some properties of disjunctive languages on a free monoid. Information and Control 37, 334–344 (1978)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Ross, R., Winklmann, K.: Repetitive strings are not context-free. R.A.I.R.O informatique théorique / Theoretical Informatics 16(3), 191–199 (1982)zbMATHMathSciNetGoogle Scholar
  16. 16.
    Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages. Springer, Heidelberg (1997)zbMATHGoogle Scholar
  17. 17.
    Searls, D.B.: The computational linguistics of biological sequences. In: Hunter, L. (ed.) Artificial Intelligence and Molecular Biology, pp. 47–120. AAAI Press, The MIT Press (1993)Google Scholar
  18. 18.
    Yu, S.S.: Languages and Codes. Lecture Notes, Department of Computer Science, p. 402. National Chung-Hsing University, Taichung (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Masami Ito
    • 1
  • Lila Kari
    • 2
  • Zachary Kincaid
    • 2
  • Shinnosuke Seki
    • 2
  1. 1.Department of Mathematics, Faculty of ScienceKyoto Sangyo UniversityKyotoJapan
  2. 2.Department of Computer ScienceUniversity of Western OntarioLondonCanada

Personalised recommendations