Skip to main content

Inner Palindromic Closure

  • Conference paper
  • 761 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7907))

Abstract

We introduce the inner palindromic closure as a new operation \(\spadesuit\), which consists in expanding a factor u to the left or right by v such that vu or uv, respectively, is a palindrome of minimal length. We investigate several language theoretic properties of the iterated inner palindromic closure \(\spadesuit^*(w)=\bigcup_{i\geq 0} \spadesuit^i(w)\) of a word w.

The work of Florin Manea and Mike Müller is supported by the DFG grant 582014. The work of Robert Mercaş is supported by Alexander von Humboldt Foundation.

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

Buying options

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. Bovet, D.P., Varricchio, S.: On the regularity of languages on a binary alphabet generated by copying systems. Inf. Process. Lett. 44, 119–123 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  2. Cheptea, D., Martín-Vide, C., Mitrana, V.: A new operation on words suggested by DNA biochemistry: Hairpin completion. Trans. Comput., 216–228 (2006)

    Google Scholar 

  3. Dassow, J., Holzer, M.: Language families defined by a ciliate bio-operation: hierarchies and decision problems. Int. J. Found. Comput. Sci. 16(4), 645–662 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  4. Dassow, J., Mitrana, V., Păun, G.: On the regularity of duplication closure. Bulletin of the EATCS 69, 133–136 (1999)

    MATH  Google Scholar 

  5. Dassow, J., Mitrana, V., Salomaa, A.: Context-free evolutionary grammars and the structural language of nucleic acids. BioSystems 43, 169–177 (1997)

    Article  Google Scholar 

  6. Ehrenfeucht, A., Rozenberg, G.: On regularity of languages generated by copying systems. Discrete Appl. Math. 8, 313–317 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  7. Higman, G.: Ordering by divisibility in abstract algebras. Proc. London Math. Soc. 3(2), 326–336 (1952)

    Article  MathSciNet  Google Scholar 

  8. Kari, L., Konstantinidis, S., Losseva, E., Sosík, P., Thierrin, G.: Hairpin structures in DNA words. In: Carbone, A., Pierce, N.A. (eds.) DNA 2005. LNCS, vol. 3892, pp. 158–170. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  9. Kari, L., Mahalingam, K.: Watson–Crick palindromes in DNA computing. Natural Computing 9(2), 297–316 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  10. Leupold, P.: Languages Generated by Iterated Idempotencies. Ph.D. thesis, Univeritat Rovira y Virgili, Tarragona, Spain (2006)

    Google Scholar 

  11. Leupold, P., Mitrana, V.: Uniformly bounded duplication codes. RAIRO Theor. Inf. Appl. 41, 411–427 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  12. de Luca, A.: Sturmian words: Structure, combinatorics, and their arithmetics. Theor. Comput. Sci. 183, 45–82 (1997)

    Article  MATH  Google Scholar 

  13. Martín-Vide, C., Păun, G.: Duplication grammars. Acta Cybernet 14, 151–164 (1999)

    MathSciNet  MATH  Google Scholar 

  14. Pansiot, J.J.: A propos d’une conjecture de F. Dejean sur les répétitions dans les mots. Discrete Appl. Math. 7, 297–311 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  15. Rampersad, N., Shallit, J., Wang, M.-W.: Avoiding large squares in infinite binary words. Theor. Comput. Sci. 339(1), 19–34 (2005)

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  17. Rozenberg, G., Salomaa, A.: Handbook of Formal Languages. Springer-Verlag New York, Inc. (1997)

    Google Scholar 

  18. Searls, D.B.: The computational linguistics of biological sequences. In: Artificial Intelligence and Molecular Biology, pp. 47–120. AAAI Press, Cambridge (1993)

    Google Scholar 

  19. Wang, M.W.: On the irregularity of the duplication closure. Bulletin of the EATCS 70, 162–163 (2000)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dassow, J., Manea, F., Mercaş, R., Müller, M. (2013). Inner Palindromic Closure. In: Béal, MP., Carton, O. (eds) Developments in Language Theory. DLT 2013. Lecture Notes in Computer Science, vol 7907. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38771-5_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-38771-5_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38770-8

  • Online ISBN: 978-3-642-38771-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics