Advertisement

The P Versus NP Problem Through Cellular Computing with Membranes

  • Mario J. Pérez-Jiménez
  • Alvaro Romero-Jiménez
  • Fernando Sancho-Caparrini
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2950)

Abstract

We study the P versus NP problem through membrane systems. Language accepting P systems are introduced as a framework allowing us to obtain a characterization of the P ≠ NP relation by the polynomial time unsolvability of an NP–complete problem by means of a P system.

Keywords

Polynomial Time Turing Machine Evolution Rule Complete Problem Input Alphabet 
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.
    Berry, G., Boudol, G.: The chemical abstract machine. Theoretical Computer Science 96, 217–248 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Cook, S.: The P versus NP problem. Manuscript prepared for the Clay Mathematics Institute for the Millennium Prize Problems (revised November 2000)Google Scholar
  3. 3.
    Manca, V.: String rewriting and metabolism: A logical perspective. In: Păun, G. (ed.) Computing with Bio-Molecules. Theory and Experiments, pp. 36–60. Springer, Singapore (1998)Google Scholar
  4. 4.
    Păun, G.: Membrane Computing. An Introduction. Springer, Berlin (2002)zbMATHGoogle Scholar
  5. 5.
    Păun, G.: Computing with membranes. Journal of Computer and System Sciences 61(1), 108–143 (2000); Turku Center for Computer Science-TUCS Report Nr. 208 (1998)Google Scholar
  6. 6.
    P˘aun, G., Rozenberg, G.: A guide to membrane computing. Theoretical Computer Science 287, 73–100 (2002)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Pérez–Jiménez, M.J., Romero-Jiménez, A., Sancho-Caparrini, F.: Teoría de la Complejidad en Modelos de Computación con Membranas. In: Kronos, Sevilla, eds. (2002)Google Scholar
  8. 8.
    Romero-Jiménez, A.: Complexity and Universality in Cellular Computing Models, PhD. Thesis. University of Seville, Spain (2003)Google Scholar
  9. 9.
    Romero-Jiménez, A., Pérez Jiménez, M.J.: Simulating Turing machines by P systems with external output. Fundamenta Informaticae 49(1-3), 273–287 (2002)zbMATHMathSciNetGoogle Scholar
  10. 10.
    Turing, A.: On computable numbers with an application to the Entscheidnungsproblem. Proceeding London Mathematical Society, serie 2(42), 230–265 (1936-1937)Google Scholar
  11. 11.
    Zandron, C., Ferreti, C., Mauri, G.: Solving NP-complete problems using P systems with active membranes. In: Antoniou, I., Calude, C., Dinneen, M.J. (eds.) Unconventional Models of Computation, UMC 2000, pp. 289–301. Springer, Berlin (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Mario J. Pérez-Jiménez
    • 1
  • Alvaro Romero-Jiménez
    • 1
  • Fernando Sancho-Caparrini
    • 1
  1. 1.Dpt. Computer Science and Artificial Intelligence, E.T.S. Ingeniería InformáticaUniversity of SevilleSevillaSpain

Personalised recommendations