Involution Solid and Join Codes | SpringerLink
Skip to main content

Involution Solid and Join Codes

  • Conference paper
Developments in Language Theory (DLT 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4036))

Included in the following conference series:

Abstract

In this paper we study a generalization of the classical notions of solid codes and comma-free codes: involution solid codes (θ-solid) and involution join codes (θ-join). These notions are motivated by DNA strand design where Watson-Crick complementarity can be formalized as an antimorphic involution. We investigate closure properties of these codes, as well as necessary conditions for θ-solid codes to be maximal. We show how the concept of θ-join can be utilized such that codes that are not themselves θ-comma free can be split into a union of subcodes that are θ-comma free.

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

Access this chapter

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
JPY 3498
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
JPY 5719
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
JPY 7149
Price includes VAT (Japan)
  • 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Baum, E.B.: DNA sequences useful for computation (unpublished article, 1996), available at: http://www.neci.nj.nec.com/homepages/eric/seq.ps

  2. Berstel, J., Perrin, D.: Theory of Codes. Academis Press, Inc., Orlando Florida (1985)

    MATH  Google Scholar 

  3. Deaton, R., Chen, J., Bi, H., Garzon, M., Rubin, H., Wood, D.F.: A PCR based protocol for in vitro selection of non-crosshybridizing oligonucleotides, DNA Computing. In: Hagiya, M., Ohuchi, A. (eds.) DNA 2002. LNCS, vol. 2568, pp. 196–204. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  4. Deaton, R., Chen, J., Garzon, M., Kim, J., Wood, D., Bi, H., Carpenter, D., Wang, Y.: Characterization of Non-Crosshybridizing DNA Oligonucleotides Manufactured in Vitro, DNA computing. In: Ferretti, C., Mauri, G., Zandron, C. (eds.) DNA 2004. LNCS, vol. 3384, pp. 50–61. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  5. Deaton, R., et al.: A DNA based implementation of an evolutionary search for good encodings for DNA computation. In: Proc. IEEE Conference on Evolutionary Computation ICEC-1997, pp. 267–271 (1997)

    Google Scholar 

  6. Faulhammer, D., Cukras, A.R., Lipton, R.J., Landweber, L.F.: Molecular computation: RNA solutions to chess problems. Proceedings of the National Academy of Sciences, USA 97(4), 1385–1389 (2000)

    Article  Google Scholar 

  7. Ferreti, C., Mauri, G.: Remarks on Relativisations and DNA Encodings. In: Jonoska, N., Păun, G., Rozenberg, G. (eds.) Aspects of Molecular Computing. LNCS, vol. 2950, pp. 132–138. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  8. Garzon, M., Deaton, R., Reanult, D.: Virtual test tubes: a new methodology for computing. In: Proc. 7th. Int. Symposium on String Processing and Information retrieval, A Corun̆a, Spain, pp. 116–121. IEEE Computing Society Press, Los Alamitos (2000)

    Chapter  Google Scholar 

  9. Head, T.: Unique decipherability relative to a language. Tamkang J. Math. 11, 59–66 (1980)

    MATH  MathSciNet  Google Scholar 

  10. Head, T.: Relativized code concepts and multi-tube DNA dictionaries. In: Calude, C.S., Paun, G. (eds.) Finite vs Infinite, pp. 175–186 (2000)

    Google Scholar 

  11. Hussini, S., Kari, L., Konstantinidis, S.: Coding properties of DNA languages. In: Jonoska, N., Seeman, N.C. (eds.) DNA 2001. LNCS, vol. 2340, pp. 57–69. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  12. Jonoska, N., Kephart, D., Mahalingam, K.: Generating DNA code words. Congressus Numerantium 156, 99–110 (2002)

    MathSciNet  Google Scholar 

  13. Jonoska, N., Mahalingam, K.: Languages od DNA based code words. In: Chen, J., Reif, J.H. (eds.) DNA 2003. LNCS, vol. 2943, pp. 61–73. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  14. Jonoska, N., Mahalingam, K., Chen, J.: Involution codes: with application to DNA coded languages. Natural Computing 4-2, 141–162 (2005)

    Article  MathSciNet  Google Scholar 

  15. Jürgensen, H., Yu, S.S.: Solid Codes. Journal of Information Processing Cybernatics, EIK 26 10, 563–574 (1990)

    Google Scholar 

  16. Jürgensen, H., Konstantinidis, S.: Codes. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 1, pp. 511–608. Springer, Heidelberg (1997)

    Google Scholar 

  17. Jürgensen, H., Katsura, M., Konstantinidis, S.: Maximal solid codes. Journal of Automata, Languages and Combinatorics 6(1), 25–50 (2001)

    MATH  MathSciNet  Google Scholar 

  18. Kari, L., Konstantinidis, S., Losseva, E., Wozniak, G.: Sticky-free and overhang-free DNA languages. Acta Informatica 40, 119–157 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  19. Kari, L., Mahalingam, K.: DNA Codes and their properties (submitted)

    Google Scholar 

  20. Kari, L., Konstantinidis, S., Sosik, P.: Bond-free languages: formalizations, maximality and construction methods. In: Ferretti, C., Mauri, G., Zandron, C. (eds.) DNA 2004. LNCS, vol. 3384, pp. 169–181. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  21. Kari, L., Konstantinidis, S., Sosik, P.: Preventing undesirable bonds between DNA codewords. In: Ferretti, C., Mauri, G., Zandron, C. (eds.) DNA 2004. LNCS, vol. 3384, pp. 182–191. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  22. Mahalingam, K.: Involution Codes: With Application to DNA Strand Design. Ph.d. Thesis, University of South Florida, Tampa, FL (2004)

    Google Scholar 

  23. Marathe, A., Condon, A.E., Corn, R.M.: On combinatorial word design. In: Preproceedings of the 5th International Meeting on DNA Based Computers, Boston, pp. 75–88 (1999)

    Google Scholar 

  24. Mauri, G., Ferretti, C.: Word design for molecular computing: a survey. In: Chen, J., Reif, J.H. (eds.) DNA 2003. LNCS, vol. 2943, pp. 37–47. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  25. Shyr, H.J., Yu, S.S.: Solid codes and disjunctive domains. Semigroup Forum 41, 23–37 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  26. Shyr, H.J.: Free Monoids and Languages. Hon Min Book Company (2001)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Jonoska, N., Kari, L., Mahalingam, K. (2006). Involution Solid and Join Codes. In: Ibarra, O.H., Dang, Z. (eds) Developments in Language Theory. DLT 2006. Lecture Notes in Computer Science, vol 4036. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11779148_18

Download citation

  • DOI: https://doi.org/10.1007/11779148_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35428-4

  • Online ISBN: 978-3-540-35430-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics