Universality of Minimal Symport/Antiport: Five Membranes Suffice

  • Francesco Bernardini
  • Andrei Păun
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2933)

Abstract

P systems with symport/antiport rules of a minimal size (only one object passes in any direction in a communication step) have been recently proved to be computationally universal. The result originally reported in [2] has been subsequently improved in [6] by showing that six membranes suffice. In [6] it has been also conjectured that at least one membrane can be saved. Here we prove that conjecture: P systems with five membranes and symport/antiport rules of a minimal size are computationally complete. The optimality of this result remains open.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alberts, B., Johnson, A., Lewis, J., Raff, M., Roberts, K., Walter, P.: The Molecular Biology of The Cell, 4th edn. Garland Publ. Inc., London (2002)Google Scholar
  2. 2.
    Bernardini, F., Gheorghe, M.: On the Power of Minimal Symport/Antiport. In: Alhazov, A., Martin-Vide, C., Păun, Gh. (eds.): Workshop on Membrane Computing, WMC-2003, Tarragona, July 17–22, Technical Report N. 28/03, Research Group on Mathematical Linguistics, Universitat Rovira i Virgili, Tarragona, pp. 72–83 (2003)Google Scholar
  3. 3.
    Freund, R., Păun, A.: Membrane Systems with Symport/Antiport: Universality Results. In: Păun, G., Rozenberg, G., Salomaa, A., Zandron, C. (eds.) WMC 2002. LNCS, vol. 2597, pp. 270–287. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  4. 4.
    Frisco, P., Hoogeboom, J.H.: Simulating Counter Automata by P Systems with Symport/Antiport. In: Păun, G., Rozenberg, G., Salomaa, A., Zandron, C. (eds.) WMC 2002. LNCS, vol. 2597, pp. 288–301. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  5. 5.
    Hopcroft, J., Ulmann, J.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading (1979)MATHGoogle Scholar
  6. 6.
    Kari, L., Martin-Vide, C., Păun, A.: On the Universality of P Systems with Minimal Symport/Antiport Rules (2003) (submitted)Google Scholar
  7. 7.
    Martin-Vide, C., Păun, A., Păun, G.: On the Power of P Systems with Symport and Antiport Rules. Journal of Universal Computer Science 8, 317–331 (2002)Google Scholar
  8. 8.
    Păun, A., Păun, G.: The Power of Communication: P Systems with Symport/ Antiport. New Generation Computing 20, 295–305 (2002)MATHCrossRefGoogle Scholar
  9. 9.
    Păun, G.: Computing with Membranes. Journal of Computer and System Sciences 61, 108–143 (2000)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Păun, G.: Membrane Computing. An Introduction. Springer, Berlin (2002)MATHGoogle Scholar
  11. 11.
    Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages, vol. 1–3. Springer, Berlin (1997)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Francesco Bernardini
    • 1
  • Andrei Păun
    • 2
  1. 1.Department of Computer ScienceThe University of SheffieldSheffieldUK
  2. 2.Department of Computer ScienceLouisiana Tech UniversityRustonUSA

Personalised recommendations