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Natural Computing

, Volume 2, Issue 3, pp 265–285 | Cite as

Complexity classes in models of cellular computing with membranes

  • Mario J. Péerez Jiménez
  • Álvaro Romero Jiménez
  • Fernando Sancho Caparrini
Article

Abstract

In this paper we introduce four complexity classes for cellularcomputing systems with membranes: the first and the second ones containall decision problems solvable in polynomial time by a family ofdeterministic P systems, without and with an input membrane,respectively; the third and fourth classes contain all decision problemssolvable in polynomial time by a family of non-deterministic P systems,without and with an input membrane, respectively. We illustrate theusefulness of these classes by solving two NP–completeproblems, namely HPP and SAT, in both variants of Psystems.

complexity classes membrane computing P systems 

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References

  1. Păun G (2000) Computing with membranes. Journal of Computer and System Sciences 61(1): 108–143Google Scholar
  2. Păun G (2002) Membrane Computing. An Introduction. Springer-Verlag, BerlinGoogle Scholar
  3. Pérez Jiménez MJ, Romero Jiménez A and Sancho Caparrini F (2002) Teoría de la complejidad en modelos de computaciôn celular con membranas. Editorial Kronos, SevillaGoogle Scholar
  4. Pérez Jiménez MJ, Romero Jiménez Á and Sancho Caparrini F (2003) Decision P systems and the PNP conjecture. In: Păun G, Rozenberg G, Salomaa A and Zandron C (eds) Membrane Computing (International Workshop, WMC-CdeA 2002, Curtea de Arges, Romania, 19-23 August 2002, Revised Papers), pp. 388–399. LNCS 2597, Springer-VerlagGoogle Scholar
  5. Pérez Jiménez MJ, Romero Jiménez A and Sancho Caparrini F (2003) Solving the VALIDITY problem by active membranes with input. In: Cavalieri M, Martín-Vide C and Păun G (eds) Proceedings of the Brainstorming Week on Membrane Computing, pp. 279–290. GRLM Report 26/03, Rovira i Virgili Unoversity of TarragonaGoogle Scholar
  6. Romero Jiménez A (2003) Complejidad y Universalidad en Modelos de Computaciôn Celular. Ph.D. thesis, Universidad de Sevilla.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Mario J. Péerez Jiménez
    • 1
  • Álvaro Romero Jiménez
    • 1
  • Fernando Sancho Caparrini
    • 1
  1. 1.Dpto. de Ciencias de la Computación e Inteligencia Artificial, E.T.S. Ingeniería InformáticaUniversidad de SevillaSevillaSpain

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