Abstract
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.
This research was supported by Grant-in-Aid for Scientific Research No. 19-07810 by Japan Society for the Promotion of Sciences and Research Grant No. 015 by Kyoto Sangyo University to M. I., and The Natural Sciences and Engineering Council of Canada Discovery Grant and Canada Research Chair Award to L.K.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Dassow, J., Mitrana, V., Păun, G.: On the regularity of duplication closure. Bull. EATCS 69, 133–136 (1999)
Dassow, J., Mitrana, V., Salomaa, A.: Operations and language generating devices suggested by the genome evolution. Theoretical Computer Science 270, 701–738 (2002)
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)
Ito, M.: Algebraic Theory of Automata and Languages. World Scientific Pub. Co. Inc., Singapore (2004)
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)
Leupold, P.: Duplication roots. In: Harju, T., Karhumäki, J., Lepistö, A. (eds.) DLT 2007. LNCS, vol. 4588, pp. 290–299. Springer, Heidelberg (2007)
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)
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)
Leupold, P., M-Vide, C., Mitrana, V.: Uniformly bounded duplication languages. Discrete Applied Mathematics 146(3), 301–310 (2005)
Lothaire, M.: Combinatorics on Words, Encyclopedia of Mathematics and its Applications 17. Addison-Wesley Publishing Co., Reading (1983)
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)
M-Vide, C., Păun, G.: Duplication grammars. Acta Cybernetica 14, 151–164 (1999)
Mitrana, V., Rozenberg, G.: Some properties of duplication grammars. Acta Cybernetica 14, 165–177 (1999)
Reis, C.M., Shyr, H.J.: Some properties of disjunctive languages on a free monoid. Information and Control 37, 334–344 (1978)
Ross, R., Winklmann, K.: Repetitive strings are not context-free. R.A.I.R.O informatique théorique / Theoretical Informatics 16(3), 191–199 (1982)
Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages. Springer, Heidelberg (1997)
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)
Yu, S.S.: Languages and Codes. Lecture Notes, Department of Computer Science, p. 402. National Chung-Hsing University, Taichung (2005)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ito, M., Kari, L., Kincaid, Z., Seki, S. (2008). Duplication in DNA Sequences. In: Ito, M., Toyama, M. (eds) Developments in Language Theory. DLT 2008. Lecture Notes in Computer Science, vol 5257. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85780-8_33
Download citation
DOI: https://doi.org/10.1007/978-3-540-85780-8_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85779-2
Online ISBN: 978-3-540-85780-8
eBook Packages: Computer ScienceComputer Science (R0)