Skip to main content
SpringerLink
Log in
Book cover

Aspects of Molecular Computing pp 297–308Cite as

Formal Languages Arising from Gene Repeated Duplication

  • Chapter

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2950))

Abstract

We consider two types of languages defined by a string through iterative factor duplications, inspired by the process of tandem repeats production in the evolution of DNA. We investigate some decidability matters concerning the unbounded duplication languages and then fix the place of bounded duplication languages in the Chomsky hierarchy by showing that all these languages are context-free. We give some conditions for the non-regularity of these languages. Finally, we discuss some open problems and directions for further research.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bean, D.R., Ehrenfeucht, A., Mc Nulty, G.F.: Avoidable patterns in strings of symbols. Pacific. J. of Math. 85, 261–294 (1979)

    MATH  MathSciNet  Google Scholar 

  2. Charlesworth, B., Sniegowski, P., Stephan, W.: The evolutionary dynamics of repetitive DNA in eukaryotes. Nature 371, 215–220 (1994)

    Article  Google Scholar 

  3. Dassow, J., Mitrana, V.: On some operations suggested by the genome evolution. In: Altman, R., Dunker, K., Hunter, L., Klein, T. (eds.) Pacific Symposium on Biocomputing 1997, pp. 97–108 (1997)

    Google Scholar 

  4. Dassow, J., Mitrana, V.: Evolutionary grammars: a grammatical model for genome evolution. In: Hofestädt, R., Löffler, M., Schomburg, D., Lengauer, T. (eds.) GCB 1996. LNCS, vol. 1278, pp. 199–209. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  5. Dassow, J., Mitrana, V., Salomaa, A.: Context-free evolutionary grammars and the language of nucleic acids. BioSystems 4, 169–177 (1997)

    Article  Google Scholar 

  6. Dassow, J., Mitrana, V.: Self cross-over systems. In: Păun, G. (ed.) Computing with Bio-Molecules, pp. 283–294. Springer, Singapore (1998)

    Google Scholar 

  7. Dassow, J., Mitrana, V., P˘aun, G.: On the regularity of duplication closure. Bull EATCS 69, 133–136 (1999)

    MATH  MathSciNet  Google Scholar 

  8. Head, T.: Formal language theory and DNA: an analysis of the generative capacity of specific recombinant behaviours. Bull. Math. Biology 49, 737–759 (1987)

    MATH  MathSciNet  Google Scholar 

  9. Head, T., Păun, G., Pixton, D.: Language theory and molecular genetics. Generative mechanisms suggested by DNA recombination. In: [16] (1997)

    Google Scholar 

  10. Levinson, G., Gutman, G.: Slipped-strand mispairing: a major mechanism for DNA sequence evolution. Molec. Biol. Evol. 4, 203–221 (1987)

    Google Scholar 

  11. Manaster Ramer, A.: Some uses and misuses of mathematics in linguistics. In: Martín-Vide, C. (ed.) Issues from Mathematical Linguistics: A Workshop, pp. 70–130. John Benjamins, Amsterdam (1999)

    Google Scholar 

  12. Martín-Vide, C., Păun, G.: Duplication grammars. Acta Cybernetica 14, 101–113 (1999)

    Google Scholar 

  13. Ming-wei, W.: On the irregularity of the duplication closure. Bull. EATCS 70, 162–163 (2000)

    MATH  Google Scholar 

  14. Mitrana, V., Rozenberg, G.: Some properties of duplication grammars. Acta Cybernetica 14, 165–177 (1999)

    MATH  MathSciNet  Google Scholar 

  15. Păun, G., Rozenberg, G., Salomaa, A.: DNA Computing. In: New Computing Paradigms. Springer, Berlin (1998)

    Google Scholar 

  16. Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages, vol. I-III. Springer, Berlin (1997)

    MATH  Google Scholar 

  17. Rounds, W.C., Manaster Ramer, A., Friedman, J.: Finding natural languages a home in formal language theory. In: Manaster Ramer, A. (ed.) Mathematics of Language, pp. 349–360. John Benjamins, Amsterdam (1987)

    Google Scholar 

  18. Schlotterer, C., Tautz, D.: Slippage synthesis of simple sequence DNA. Nucleic Acids Res. 20, 211–215 (1992)

    Article  Google Scholar 

  19. Searls, D.B.: The computational linguistics of biological sequences. In: Hunter, L. (ed.) Artificial Intelligence and Molecular Biology, pp. 47–120. AAAI Press/MIT Press, Menlo Park, CA/Cambridge, MA (1993)

    Google Scholar 

  20. Strand, M., Prolla, T., Liskay, R., Petes, T.: Destabilization of tracts of simple repetitive DNA in yeast by mutations affecting DNA mismatch repair. Nature 365, 274–276 (1993)

    Article  Google Scholar 

  21. Thue, A.: Uber unendliche Zeichenreihen. Norske Videnskabers Selskabs Skrifter Mat.-Nat. Kl (Kristiania) 7, 1–22 (1906)

    Google Scholar 

  22. Thue, A.: Uber die gegenseitige Lage gleicher Teile gewiisser Zeichenreihen. Norske Videnskabers Selskabs Skrifter Mat.-Nat. Kl (Kristiania) 1, 1–67 (1912)

    Google Scholar 

  23. Weitzmann, M., Woodford, K., Usdin, K.: DNA secondary structures and the evolution of hyper-variable tandem arrays. J. of Biological Chemistry 272, 9517–9523 (1997)

    Article  Google Scholar 

  24. Wells, R.: Molecular basis of genetic instability of triplet repeats. J. of Biological Chemistry 271, 2875–2878 (1996)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Research Group on Mathematical Linguistics, Rovira i Virgili University, Pça. Imperial Tàrraco 1, 43005, Tarragona, Spain

    Peter Leupold & Victor Mitrana

  2. Faculty of Mathematics and Computer Science, Bucharest University, Str. Academiei 14, 70109, Bucureşti, Romania

    Victor Mitrana

  3. Departamento de Sistemas Informáticos y Computación, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022, Valencia, Spain

    José M. Sempere

Authors
  1. Peter Leupold
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Victor Mitrana
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. José M. Sempere
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of South Florida, 4202 E. Fowler Ave, 33620, Tampa, Fl, USA

    Nataša Jonoska

  2. Institute of Mathematics of the Romanian Academy, PO Box 1-764, 014700, Bucureşti, Romania

    Gheorghe Păun

  3. Leiden Center of Advanced Computer Science (LIACS), Leiden University, Niels Bohrweg 1, 2333, Leiden, CA, The Netherlands

    Grzegorz Rozenberg

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Leupold, P., Mitrana, V., Sempere, J.M. (2003). Formal Languages Arising from Gene Repeated Duplication. In: Jonoska, N., Păun, G., Rozenberg, G. (eds) Aspects of Molecular Computing. Lecture Notes in Computer Science, vol 2950. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24635-0_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-24635-0_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20781-8

  • Online ISBN: 978-3-540-24635-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation