P Systems with Cutting/Recombination Rules Assigned to Membranes

  • Franziska Freund
  • Rudolf Freund
  • Marion Oswald
  • Maurice Margenstern
  • Yurii Rogozhin
  • Sergey Verlan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2933)


We introduce a new variant of splicing P systems, where the rules are directly assigned to the membranes and not to the regions as this is usually observed in the area of membrane systems. The strings involved in the splicing operation are either taken from inside or from outside the membrane and the strings resulting from the splicing operation also may go inside or outside the membrane. Instead of the splicing operation, also the operations of cutting and recombination are used as rules assigned to membranes. For the application of rules leading from one configuration of the system to the succeeding configuration we consider a sequential model and do not use the model of maximal parallelism. We will show that for such sequential P systems using splicing rules or cutting/recombination rules assigned to the skin membrane we already obtain universal computational power with only one membrane.


Membrane System Evolution Rule Terminal Symbol Terminal Object Membrane Computing 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Adleman, L.M.: Molecular computation of solutions to combinatorial problems. Science 226, 1021–1024 (1994)CrossRefGoogle Scholar
  2. 2.
    Csuhaj-Varjú, E., Kari, L., Păun, G.: Test tube distributed systems based on splicing. Computers and Artificial Intelligence 15(2), 211–232 (1996)zbMATHMathSciNetGoogle Scholar
  3. 3.
    Dassow, J., Păun, G.: On the power of membrane computing. Journal of Universal Computer Science 5(2), 33–49 (1999), MathSciNetGoogle Scholar
  4. 4.
    Dassow, J., Păun, G.: Regulated Rewriting in Formal Language Theory. Springer, Heidelberg (1989)Google Scholar
  5. 5.
    Freund, R.: Generalized P-systems. In: Ciobanu, G., Păun, G. (eds.) FCT 1999. LNCS, vol. 1684, pp. 281–292. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  6. 6.
    Freund, R., Csuhaj-Varjú, E., Wachtler, F.: Test tube systems with cutting/ recombination operations. In: Proceedings PSB 1997, pp. 163–174. World Scientific, Singapore (1997)Google Scholar
  7. 7.
    Freund, R., Freund, F.: Molecular computing with generalized homogenous Psystems, DNA Computing. In: Condon, A., Rozenberg, G. (eds.) DNA 2000. LNCS, vol. 2054, pp. 130–144. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  8. 8.
    Freund, R., Freund, F.: Test tube systems: When two tubes are enough. In: Rozenberg, G., Thomas, W. (eds.) Developments in Language Theory, Foundations, Applications and Perspectives, pp. 338–350. World Scientific Publishing Co., Singapore (2000)Google Scholar
  9. 9.
    Freund, R., Kari, L.: DNA computing based on splicing: The existence of universal computers. Theory of Computing Systems 32, 69–112 (1999)zbMATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    Freund, R., Oswald, M.: P systems with conditional communication rules assigned to membranes. In: Martín-Vide, C., Mauri, G., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2003. LNCS, vol. 2933, pp. 191–202. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  11. 11.
    Freund, R., Wachtler, F.: Universal systems with operations related to splicing. Computers and Artificial Intelligence 15(4), 273–294 (1996)zbMATHMathSciNetGoogle Scholar
  12. 12.
    Păun, G.: Computing with membranes. Journal of Computer and System Sciences 61(1), 108–143 (2000),; and TUCS Research Report 208 (1998) zbMATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Păun, G.: Computing with membranes: an introduction. Bulletin EATCS 67, 139–152 (1999)zbMATHGoogle Scholar
  14. 14.
    Păun, G.: Membrane Computing: An Introduction. Springer, Berlin (2002)zbMATHGoogle Scholar
  15. 15.
    Păun, G.: Regular extended H systems are computationally universal. Journal of Automata, Languages and Combinatorics 1(1), 27–37 (1996)zbMATHMathSciNetGoogle Scholar
  16. 16.
    Păun, G., Rozenberg, G., Salomaa, A.: DNA Computing. In: New Computing Paradigms. Springer, Berlin (1998)Google Scholar
  17. 17.
    Pixton, D.: Splicing in abstract families of languages. Theoretical Computer Science 234, 135–166 (2000)zbMATHMathSciNetCrossRefGoogle Scholar
  18. 18.
    Priese, L., Rogozhin, Y., Margenstern, M.: Finite H-systems with 3 test tubes are not predictable. In: Altman, R.B., Dunker, A.K., Hunter, L., Klein, T.E. (eds.) Proceedings of Pacific Symposium on Biocomputing, Kapalua, Maui, January 1998, pp. 545–556. World Scientific Publishing Co., Singapore (1998)Google Scholar
  19. 19.
    Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages. Springer, Berlin (1997)zbMATHGoogle Scholar
  20. 20.
    Verlan, S.: About splicing P systems with immediate communication and non-extended splicing P systems. In: Martín-Vide, C., Mauri, G., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2003. LNCS, vol. 2933, pp. 369–382. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  21. 21.
    The P Systems Web Page,

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Franziska Freund
    • 1
  • Rudolf Freund
    • 2
  • Marion Oswald
    • 2
  • Maurice Margenstern
    • 3
  • Yurii Rogozhin
    • 4
  • Sergey Verlan
    • 3
  1. 1.Gymnasium der SchulbrüderWienAustria
  2. 2.Department of Computer ScienceTechnical University WienWienAustria
  3. 3.LITA, UFR MIM, Ile du SaulcyUniversité de MetzMetz CedexFrance
  4. 4.Institute of Mathematics and Computer ScienceAcademy of Sciences of Moldova RepublicChişinăuMoldova

Personalised recommendations