Advertisement

Accepting Networks of Splicing Processors

  • Florin Manea
  • Carlos Martín-Vide
  • Victor Mitrana
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3526)

Abstract

We present linear time solutions to two NP-complete problems, namely SAT and the directed Hamiltonian Path Problem (HPP), based on accepting networks of splicing processors (ANSP) having all resources (size, number of rules and symbols) linearly bounded by the size of the given instance. The underlying structure of these ANSPs does not depend on the number of clauses, in the case of SAT, and the number of edges, in the case of HPP. Furthermore, the running time of the ANSP solving HPP does not depend on the number of edges of the given graph and this network provides all solutions, if any, of the given instance of HPP.

Keywords

Turing Machine Hamiltonian Path Mathematical Linguistics Correct Word Input Formula 
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.
    Castellanos, J., Martin-Vide, C., Mitrana, V., Sempere, J.: Solving NP-complete problems with networks of evolutionary processors. In: Mira, J., Prieto, A.G. (eds.) IWANN 2001. LNCS, vol. 2084, pp. 621–628. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  2. 2.
    Castellanos, J., Martin-Vide, C., Mitrana, V., Sempere, J.: Networks of evolutionary processors. Acta Informatica 39, 517–529 (2003)zbMATHMathSciNetGoogle Scholar
  3. 3.
    Castellanos, J., Leupold, P., Mitrana, V.: Descriptional and computational complexity aspects of hybrid networks of evolutionary processors. Theoretical Computer Science (in press)Google Scholar
  4. 4.
    Csuhaj-Varjú, E., Kari, L., Păun, G.: Test tube distributed systems based on splicing. Computers and AI 15(2-3), 211–232 (1996)zbMATHGoogle Scholar
  5. 5.
    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
  6. 6.
    Csuhaj-Varjú, E., Mitrana, V.: Evolutionary systems: a language generating device inspired by evolving communities of cells. Acta Informatica 36, 913–926 (2000)zbMATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Errico, L., Jesshope, C.: Towards a new architecture for symbolic processing. In: Plander, I. (ed.) Artificial Intelligence and Information-Control Systems of Robots 1994, pp. 31–40. World Sci. Publ., Singapore (1994)Google Scholar
  8. 8.
    Fahlman, S.E., Hinton, G.E., Seijnowski, T.J.: Massively parallel architectures for AI: NETL, THISTLE and Boltzmann machines. In: Proc. AAAI National Conf. on AI, pp. 109–113. William Kaufman, Los Altos (1983)Google Scholar
  9. 9.
    Garey, M., Johnson, D.: Computers and Intractability. A Guide to the Theory of NP-completeness. Freeman, San Francisco (1979)zbMATHGoogle Scholar
  10. 10.
    Hartmanis, J., Lewis II, P.M., Stearns, R.E.: Hierarchies of memory limited computations. In: Proc. 6th Annual IEEE Symp. on Switching Circuit Theory and Logical Design, pp. 179–190 (1965)Google Scholar
  11. 11.
    Hartmanis, J., Stearns, R.E.: On the computational complexity of algorithms. Trans. Amer. Math. Soc. 117, 533–546 (1965)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Hillis, W.D.: The Connection Machine. MIT Press, Cambridge (1985)Google Scholar
  13. 13.
    Manea, F., Martín-Vide, C., Mitrana, V.: Solving 3CNF-SAT and HPP in Linear Time Using WWW. In: Margenstern, M. (ed.) MCU 2004. LNCS, vol. 3354, pp. 269–280. Springer, Heidelberg (2005) (in press)CrossRefGoogle Scholar
  14. 14.
    Martin-Vide, C., Mitrana, V., Perez-Jimenez, M., Sancho-Caparrini, F.: Hybrid networks of evolutionary processors. In: Cantú-Paz, E., Foster, J.A., Deb, K., Davis, L., Roy, R., O’Reilly, U.-M., Beyer, H.-G., Kendall, G., Wilson, S.W., Harman, M., Wegener, J., Dasgupta, D., Potter, M.A., Schultz, A., Dowsland, K.A., Jonoska, N., Miller, J., Standish, R.K. (eds.) GECCO 2003. LNCS, vol. 2723, pp. 401–412. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  15. 15.
    Păun, G.: Distributed architectures in DNA computing based on splicing: Limiting the size of components. Unconventional Models of Computation, pp. 323–335. Springer, Berlin (1998)Google Scholar
  16. 16.
    Sankoff, D., et al.: Gene order comparisons for phylogenetic inference:Evolution of the mitochondrial genome. Proc. Natl. Acad. Sci. USA 89, 6575–6579 (1992)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Florin Manea
    • 1
  • Carlos Martín-Vide
    • 2
  • Victor Mitrana
    • 1
    • 2
  1. 1.Faculty of Mathematics and Computer ScienceUniversity of BucharestBucharestRomania
  2. 2.Research Group in Mathematical LinguisticsRovira i Virgili UniversityTarragonaSpain

Personalised recommendations