Counting Time in Computing with Cells

  • Oscar H. Ibarra
  • Andrei Păun
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3892)


We consider models of P systems using time either as the output of a computation or as a means of synchronizing the hugely complex processes that take place in a cell. In the first part of the paper, we introduce and study the properties of “timed symport/antiport systems”. In the second part we introduce several new features for P systems: the association/deassociation of molecules (modeling for example the protein-protein interactions), ion channel rules and gene activation rules. We show that such timed systems are universal. We also prove several properties concerning these systems.


Mathematical Linguistics Membrane Computing Skin Membrane Endoplasmic Retic Stop Rule 
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 266, 1021–1024 (1994)CrossRefGoogle Scholar
  2. 2.
    Alberts, B.: Essential Cell Biology. An Introduction to the Molecular Biology of the Cell. Garland Publ. Inc., New York (1998)Google Scholar
  3. 3.
    Bernardini, F., Gheorghe, M.: On the Power of Minimal Symport/Antiport. In: Alhazov, A., et al. (eds.) WMC 2003. Workshop on Membrane Computing, July 17-22 (2003); Technical Report N. 28/03, Research Group on Mathematical Linguistics, Universitat Rovira i Virgili, Tarragona, pp. 72–83 (2003)Google Scholar
  4. 4.
    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. 43–54. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  5. 5.
    Cavaliere, M.: Towards Asynchronous P Systems. In: Mauri, G., Păun, G., Jesús Pérez-Jímenez, M., Rozenberg, G., Salomaa, A. (eds.) WMC 2004. LNCS, vol. 3365, pp. 161–173. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Cavaliere, M., Freund, R., Păun, Gh.: Event–Related Outputs of Computations in P Systems, personal communication (manuscript)Google Scholar
  7. 7.
    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
  8. 8.
    Frisco, P., Hogeboom, 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
  9. 9.
    Friso, P.: About P Systems with Symport/Antiport, Second Brainstorming Week in Membrane Computing, Sevilla, Technical Report 01/2004 of the Research Group in Natural Computing, University of Sevilla, Spain, pp. 224–236 (February 2004)Google Scholar
  10. 10.
    Hopcroft, J., Ulmann, J.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading (1979)Google Scholar
  11. 11.
    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
  12. 12.
    Maas, W.: Computing with Spikes. Spec. Iss. on Found. of Inf. Processing of TELEMATIK 8(1), 32–36 (2002)Google Scholar
  13. 13.
    Minsky, M.L.: Recursive Unsolvability of Post’s Problem of “Tag” and Other Topics in Theory of Turing Machines. Annals of Mathematics 74, 437–455 (1961)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Sburlan, D.: Clock-free P Systems. In: Pre-proceedings of the Fifth Workshop on Membrane Computing (WMC5), Milano, Italy, June 14-16, pp. 372–383 (2004)Google Scholar
  15. 15.
    Păun, A., Păun, G.: The Power of Communication: P Systems with Symport/Antiport. New Generation Computing 20(3), 295–306 (2002)CrossRefMATHGoogle Scholar
  16. 16.
    Păun, G.: Membrane Computing – An Introduction. Springer, Berlin (2002)CrossRefMATHGoogle Scholar
  17. 17.
    Păun, G., Perez-Jimenez, M., Sancho-Caparrini, F.: On the Reachability Problem for P Systems with Symport/Antiport. In: Proc. Automata and Formal Languages Conf., Debrecen, Hungary (2002)Google Scholar
  18. 18.
    Păun, Gh.: Further Twenty-six Open Problems in Membrane Computing. In: Third Brainstorming Meeting on Membrane Computing, Sevilla, Spain (February 2005)Google Scholar
  19. 19.
    Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages, 3 volumes. Springer, Berlin (1997)MATHGoogle Scholar
  20. 20.
    Vazil, G.: On the Size of P Systems with Minimal Symport/Antiport. In: Mauri, G., Păun, G., Jesús Pérez-Jímenez, M., Rozenberg, G., Salomaa, A. (eds.) WMC 2004. LNCS, vol. 3365, pp. 422–431. Springer, Heidelberg (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Oscar H. Ibarra
    • 1
  • Andrei Păun
    • 2
  1. 1.Department of Computer ScienceUniversity of California – Santa BarbaraSanta BarbaraUSA
  2. 2.Department of Computer Science/IfMLouisiana Tech UniversityRustonUSA

Personalised recommendations