Advertisement

The Power of Networks of Watson-Crick D0L Systems

  • Erzsébet Csuhaj-Varjú
  • Arto Salomaa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2950)

Abstract

The notion of a network of Watson-Crick D0L systems was recently introduced, [7]. It is a distributed system of deterministic language defining devices making use of Watson-Crick complementarity. The research is continued in this paper, where we establish three results about the power of such networks. Two of them show how it is possible to solve in linear time two well-known NP-complete problems, the Hamiltonian Path Problem and the Satisfiability Problem. Here the characteristic feature of DNA computing, the massive parallelism, is used very strongly. As an illustration we use the propositional formula from the celebrated recent paper, [3]. The third one shows how in the very simple case of four-letter DNA alphabets we can obtain weird (not even Z-rational) patterns of population growth.

Keywords

Hamiltonian Path Propositional Formula Node Versus Derivation Step Massive Parallelism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Adleman, L.M.: Molecular computation of solutions to combinatorial problems. Science 266, 1021–1024 (1994)CrossRefGoogle Scholar
  2. 2.
    Amos, M., Păun, G., Rozenberg, G., Salomaa, A.: DNA-based computing: a survey. Theoretical Computer Science 287, 3–38 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Braich, S., Chelyapov, N., Johnson, C., Rothemund, P.W.K., Adleman, L.: Solution of a 20-variable 3-SAT problem on a DNA computer. Sciencexpress, March 14, 10.1126/science.1069528 (2002)Google Scholar
  4. 4.
    Csima, J., Csuhaj-Varjú, E., Salomaa, A.: Power and size of extended Watson- Crick L systems. Theoretical Computer Science 290, 1665–1678 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Csuhaj-Varjú, E.: Networks of Language Processors. EATCS Bulletin 63, 120–134 (1997); Păun, G., Rozenberg, G., Salomaa, A. (eds.): Current Trends in Theoretical Computer Science, pp. 771–790. World Scientific, Singapore (2001)Google Scholar
  6. 6.
    Csuhaj-Varjú, E., Salomaa, A.: Networks of parallel language processors. In: Păun, G., Salomaa, A. (eds.) New Trends in Formal Languages. LNCS, vol. 1218, pp. 299–318. Springer, Heidelberg (1997)Google Scholar
  7. 7.
    Csuhaj-Varjú, E., Salomaa, A.: Networks of Watson-Crick D0L systems. TUCS Report 419, Turku Centre for Computer Science, Turku (2001); To appear in Ito, M., Imaoka, T. (eds.): Words, Languages, Combinatorics III. Proceedings of the Third International Colloquium in Kyoto, Japan. World Scientific Publishing Company, Singapore (2003)Google Scholar
  8. 8.
    Honkala, J., Salomaa, A.: Watson-Crick D0L systems with regular triggers. Theoretical Computer Science 259, 689–698 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Kuich, W., Salomaa, A.: Semirings, Automata, Languages. EATCS Monographs on Theoretical Computer Science. Springer, Heidelberg (1986)Google Scholar
  10. 10.
    Mihalache, V., Salomaa, A.: Language-theoretic aspects of DNA complementarity. Theoretical Computer Science 250, 163–178 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Păun, G., Rozenberg, G., Salomaa, A.: DNA Computing. New Computing Paradigms. Springer, Heidelberg (1998)zbMATHGoogle Scholar
  12. 12.
    Rozenberg, G., Salomaa, A.: The Mathematical Theory of L Systems. Academic Press, New York (1980)zbMATHGoogle Scholar
  13. 13.
    Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages, vol. I-III. Springer, Heidelberg (1997)zbMATHGoogle Scholar
  14. 14.
    Salomaa, A.: Formal Languages. Academic Press, New York (1973)zbMATHGoogle Scholar
  15. 15.
    Salomaa, A.: Computation and Automata. Cambridge University Press, Cambridge (1985)zbMATHGoogle Scholar
  16. 16.
    Salomaa, A.: Watson-Crick walks and roads in D0L graphs. Acta Cybernetica 14, 179–192 (1999)zbMATHMathSciNetGoogle Scholar
  17. 17.
    Salomaa, A.: Uni-transitional Watson-Crick D0L systems. Theoretical Computer Science 281, 537–553 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Salomaa, A.: Iterated morphisms with complementarity on the DNA alphabet. In: Ito, M., Păun, G., Yu, S. (eds.) Words, Semigroups, Transductions, pp. 405–420. World Scientific, Singapore (2001)CrossRefGoogle Scholar
  19. 19.
    Salomaa, A., Soittola, M.: Automata-Theoretic Aspects of Formal Power Series. Text and Monographs in Computer Science. Springer, Heidelberg (1978)zbMATHGoogle Scholar
  20. 20.
    Salomaa, A., Sosík, P.: Watson-Crick D0L systems: the power of one transition. Theoretical Computer Science 301, 187–200 (2003)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Erzsébet Csuhaj-Varjú
    • 1
  • Arto Salomaa
    • 2
  1. 1.Computer and Automation Research InstituteHungarian Academy of SciencesBudapestHungary
  2. 2.Turku Centre for Computer ScienceTurkuFinland

Personalised recommendations