Skip to main content
SpringerLink
Log in

Some properties of involution binary relations

  • Original Article
  • Published:
Acta Informatica Aims and scope Submit manuscript

Abstract

This paper aims to investigate properties of involution binary relations, which are some particular binary relations. We study the concepts of involution spanning sets and give some examples related to different involution binary relations. Moreover, some relationships among the involution independent sets, codes, and involution codes are studied when the mapping function is either a morphic or an antimorphic involution of \(X^*\).

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Berstel, J., Perrin, D.: Theory of Codes. Academic Press, Orlando, TO (1985)

    MATH  Google Scholar 

  2. Cohn, P.M.: Universal Algebra, revised ed., Harper and Row, New York, 1965. D. Reidel Publishing Co., Dordrecht (1981)

    Google Scholar 

  3. Fan, C.-M., Huang, C.C.: Some properties of involution palindrome languages. Int. J. Comput. Math. 87(15), 3397–3404 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  4. Fan, C.-M., Wang, T.-T., Huang, C.-C.: The involution binary relations. In: Proceedings of the 29th Workshop on Combinatorial Mathematics and Computation Theory, National Taipei College of Business, Institute of Information and Decision Sciences, Taipei, Taiwan, pp. 254–258 (2012)

  5. Gécseg, F., Jürgensen, H.: Dependence in algebra. Fundam. Infor. 25, 247–256 (1996)

    MATH  Google Scholar 

  6. Hsiao, H.K., Yeh, Y.T., Yu, S.S.: Dependences related to strict binary relations. Theor. Comput. Sci. 347, 306–324 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  7. Hussini, S., Kari, L., Konstantinidis, S.: Coding properties of DNA languages. Theor. Comput. Sci. 209, 1557–1579 (2003)

    Article  MathSciNet  Google Scholar 

  8. Jonoska, N., Mahalingam, K.: Languages of DNA based code words. In: Chen, J., Reif, J. (eds.) DNA Computing: 9th International Workshop on DNA Based Computers, LNCS, pp 61–73 (2004)

  9. Jonoska, N., Mahalingam, K.: Methods for constructing coded DNA languages. In: Jonoska, N., Paun, G., Rozenberg, G. (eds.) Aspects of Molecular Computing: Essays Dedicated to Tom Head, on the Occasion of his 70th Birthday, LNCS, 2950, pp. 241–253 (2004)

  10. Jonoska, N., Mahalingam, K., Chen, J.: Involution codes: with application to DNA coded languages. Nat. Comput. 4(2), 141–162 (2005)

    Article  MathSciNet  Google Scholar 

  11. Jürgensen, H., Yu, S.S.: Relations on free monoids, their independent sets, and codes. Int. J. Comput. Math. 40, 17–46 (1991)

    Article  MATH  Google Scholar 

  12. Kari, L.: DNA computing: arrival of biological mathematics. Math. Intell. 19(2), 9–22 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  13. Kari, L., Kitto, R., Thierrin, G.: Codes, involutions, and DNA encoding. Formal Nat. Comput. LNCS 2300, 376–393 (2002)

    Article  MathSciNet  Google Scholar 

  14. Kari, L., Mahalingam, K.: DNA codes and their properties. DNA Comput. LNCS 4287, 127–142 (2006)

    Article  Google Scholar 

  15. Kari, L., Mahalingam, K.: Involutively bordered words. Int. J. Found. Comput. Sci. 18(5), 1089–1106 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  16. Kari, L., Mahalingam, K.: Watson–Crick conjugate and commutative words. DNA Comput. LNCS 4848, 273–283 (2008)

    Article  Google Scholar 

  17. Luca, A.D., Luca, A.D.: Pseudopalindrome closure operators in free monoids. Theor. Comput. Sci. 362, 282–300 (2006)

    Article  MATH  Google Scholar 

  18. Shyr, H.J., Thierrin, G.: Codes and binary relations. In: Séminaire d’Algébra Paul Dubreil Paris 1975–1976, LNM 586, pp. 180–188 (1977)

  19. Shyr, H.J., Thierrin, G.: Codes, languages and MOL schemes. RAIRO-Theor. Inform. Appl. 11(4), 293–301 (1977)

    MATH  MathSciNet  Google Scholar 

  20. Shyr, H.J.: Free Monoids and Languages, 3rd edn. Hon-Min Book Company, Taichung (2001)

    Google Scholar 

Download references

Acknowledgments

This paper was supported by the National Science Council, R.O.C., under Grant NSC 100-2115-M-025-002. The authors would like to thank the referees for their careful reading of the manuscript and useful suggestions.

Author information

Authors and Affiliations

  1. Department of Information Management, National Chin-Yi University of Technology, Taichung, 411, Taiwan

    Chen-Ming Fan

  2. Department of Information Management, Hsiuping Institute of Technology, Taichung, 412, Taiwan

    Jen-Tse Wang

  3. Center for General Education, National Taichung University of Science and Technology, Taichung, 403, Taiwan

    Cheng-Chih Huang

Authors
  1. Chen-Ming Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jen-Tse Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Cheng-Chih Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Cheng-Chih Huang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fan, CM., Wang, JT. & Huang, CC. Some properties of involution binary relations. Acta Informatica 52, 483–495 (2015). https://doi.org/10.1007/s00236-014-0208-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00236-014-0208-8

Search

Navigation