Involution Solid and Join Codes

  • Nataša Jonoska
  • Lila Kari
  • Kalpana Mahalingam
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4036)


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.


Regular Language Code Word Closure Property Formal Language Theory Springer LNCS 
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  1. 1.
    Baum, E.B.: DNA sequences useful for computation (unpublished article, 1996), available at:
  2. 2.
    Berstel, J., Perrin, D.: Theory of Codes. Academis Press, Inc., Orlando Florida (1985)zbMATHGoogle Scholar
  3. 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)CrossRefGoogle Scholar
  4. 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)CrossRefGoogle Scholar
  5. 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. 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)CrossRefGoogle Scholar
  7. 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)CrossRefGoogle Scholar
  8. 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)CrossRefGoogle Scholar
  9. 9.
    Head, T.: Unique decipherability relative to a language. Tamkang J. Math. 11, 59–66 (1980)zbMATHMathSciNetGoogle Scholar
  10. 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. 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)CrossRefGoogle Scholar
  12. 12.
    Jonoska, N., Kephart, D., Mahalingam, K.: Generating DNA code words. Congressus Numerantium 156, 99–110 (2002)MathSciNetGoogle Scholar
  13. 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)CrossRefGoogle Scholar
  14. 14.
    Jonoska, N., Mahalingam, K., Chen, J.: Involution codes: with application to DNA coded languages. Natural Computing 4-2, 141–162 (2005)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Jürgensen, H., Yu, S.S.: Solid Codes. Journal of Information Processing Cybernatics, EIK 26 10, 563–574 (1990)Google Scholar
  16. 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. 17.
    Jürgensen, H., Katsura, M., Konstantinidis, S.: Maximal solid codes. Journal of Automata, Languages and Combinatorics 6(1), 25–50 (2001)zbMATHMathSciNetGoogle Scholar
  18. 18.
    Kari, L., Konstantinidis, S., Losseva, E., Wozniak, G.: Sticky-free and overhang-free DNA languages. Acta Informatica 40, 119–157 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Kari, L., Mahalingam, K.: DNA Codes and their properties (submitted)Google Scholar
  20. 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)CrossRefGoogle Scholar
  21. 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)CrossRefGoogle Scholar
  22. 22.
    Mahalingam, K.: Involution Codes: With Application to DNA Strand Design. Ph.d. Thesis, University of South Florida, Tampa, FL (2004)Google Scholar
  23. 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. 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)CrossRefGoogle Scholar
  25. 25.
    Shyr, H.J., Yu, S.S.: Solid codes and disjunctive domains. Semigroup Forum 41, 23–37 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Shyr, H.J.: Free Monoids and Languages. Hon Min Book Company (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Nataša Jonoska
    • 1
  • Lila Kari
    • 2
  • Kalpana Mahalingam
    • 2
  1. 1.Department of MathematicsUniversity of South FloridaTampa
  2. 2.Department of Computer ScienceUniversity of Western OntarioLondonCanada

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