Communicative P Systems with Minimal Cooperation

  • Artiom Alhazov
  • Maurice Margenstern
  • Vladimir Rogozhin
  • Yurii Rogozhin
  • Sergey Verlan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3365)

Abstract

We prove that two classes of communicative P systems with 3 membranes and with minimal cooperation, namely P systems with symport/antiport rules of size 1 and and P systems with symport rules of size 2, are computationally complete: they generate all recursively enumerable sets of vectors of nonnegative integers. The result of computation is obtained in the elementary membrane.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bernardini, F., Gheorghe, M.: On the Power of Minimal Symport/Antyport. Pre-proceedings of Workshop on Membrane Computing, WMC 2003, Tarragona, July 17–22 (2003), Technical Report No 28/03, RGML, Universitat Rovira i Virgili, Tarragona, 72–83 (2003)Google Scholar
  2. 2.
    Bernardini, F., Păun, A.: Universality of Minimal Symport/Antiport: Five Membranes Suffice. In: Martín-Vide, C., Mauri, G., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2003. LNCS, vol. 2933, pp. 43–45. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  3. 3.
    Freund, R., Oswald, M.: GP Systems with Forbidding Contexts. Fundamenta Informaticae 49(1-3), 81–102 (2002)MATHMathSciNetGoogle Scholar
  4. 4.
    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
  5. 5.
    Frisco, P.: About P Systems with Symport/Antiport. In: Proceedings of the Second Brainstorming Week on Membrane Computing, TR 01/2004, RGNC, Sevilla University, pp. 224–236 (2004)Google Scholar
  6. 6.
    Frisco, P., Hoogeboom, J.H.: Simulating Counter Automata by P Systems with Symport/Antypot. In: Păun, G., Rozenberg, G., Salomaa, A., Zandron, C. (eds.) WMC 2002. LNCS, vol. 2597, pp. 288–301. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Kari, L., Martin-Vide, C., Păun, A.: On the universality of P systems with Minimal Symport/Antiport Rules. In: Jonoska, N., Păun, G., Rozenberg, G. (eds.) Aspects of Molecular Computing. LNCS, vol. 2950, pp. 254–265. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  8. 8.
    Margenstern, M., Rogozhin, V., Rogozhin, Y., Verlan, S.: About P Systems with Minimal Symport/Antiport Rules and Four Membranes. In: Pre-Proceedings of Fifth Workshop on Membrane Computing, WMC5, Milano-Bicocca, Italy, pp. 283–294 (2004)Google Scholar
  9. 9.
    Martin-Vide, C., Păun, A., Păun, G.: On the Power of P systems with Symport and Antiport rules. Journal of Universal Computer Science 8, 295–305 (2002)Google Scholar
  10. 10.
    Minsky, M.L.: Finite and Infinite Machines. Prentice Hall, Englewood Cliffs (1967)MATHGoogle Scholar
  11. 11.
    Păun, A., Păun, G.: The Power of Communication: P systems with Symport/Antiport. New Generation Computing 20, 295–305 (2002)MATHCrossRefGoogle Scholar
  12. 12.
    Păun, G.: Computing with Membranes. Journal of Computer and Systems Sciences 61, 108–143 (2000)MATHCrossRefGoogle Scholar
  13. 13.
    Păun, G.: Membrane Computing. An Introduction. Springer, Heidelberg (2002)MATHGoogle Scholar
  14. 14.
    Vaszil, G.: On the size of P systems with minimal symport/antiport. In: Pre-Proceedings of Fifth Workshop on Membrane Computing, WMC5, Milano-Bicocca, Italy, pp. 422–431 (2004)Google Scholar
  15. 15.
    The P systems web page, http://psystems.disco.unimib.it/

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Artiom Alhazov
    • 1
    • 2
  • Maurice Margenstern
    • 3
  • Vladimir Rogozhin
    • 4
  • Yurii Rogozhin
    • 1
  • Sergey Verlan
    • 3
  1. 1.Institute of Mathematics and Computer ScienceAcademy of Sciences of MoldovaChişinăuMoldova
  2. 2.Research Group on Mathematical LinguisticsRovira i Virgili UniversityTarragonaSpain
  3. 3.LITAUniversité de MetzFrance
  4. 4.State University of MoldovaChişinăuMoldova

Personalised recommendations