On Pure Catalytic P Systems

  • Shankara Narayanan Krishna
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4135)


Catalytic P systems is one of the basic classes of P systems. The number of catalysts required for optimal universality results (both in pure catalytic systems and catalytic systems) has been a problem of extensive research [3],[5],[6],[7],[12]. The differences that can give universality/non-universality are very small in these systems, and finding this borderline is one of the ‘jewel’ problems in P systems [12]. In this paper, we try to figure out this borderline and have obtained some interesting results. We have proved that with 2 catalysts, if λ-rules are not used, then universality cannot be obtained. We also consider two restricted variants of pure catalytic systems and prove that they are also not universal. Finally, we look at mobile catalytic systems and solve two open problems.


Catalytic System Register Machine Membrane Computing Applicable Rule Formal Language Theory 
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.
    Dassow, J., Păun, Gh.: Regulated Rewriting in Formal Language Theory. Springer, Berlin (1989)Google Scholar
  2. 2.
    Dassow J.: Grammars with Regulated Rewriting, Handout given during the Ph.D school at Terragona (2003), theo.cs.uni-magdeburg.de/dassow/tarraphd.pdf
  3. 3.
    Freund, R., Kari, L., Oswald, M., Sosik, P.: Computationally universal P systems without priorities: two catalysts are sufficient. Theoretical Computer Science 330, 251–266 (2005)CrossRefMathSciNetMATHGoogle Scholar
  4. 4.
    Freund, R., Oswald, M., Sosik, P.: Reducing the number of catalysts required in computationally universal systems without priorities. In: Proceedings of DCFS 2003, pp. 102–113 (2003)Google Scholar
  5. 5.
    H. Ibarra, O., Yen, H.-C.: On Deterministic Catalytic Systems. In: Farré, J., Litovsky, I., Schmitz, S. (eds.) CIAA 2005. LNCS, vol. 3845, pp. 163–175. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    H. Ibarra, O., Dang, Z., Egecioglu, O., Saxena, G.: Characterizations of Catalytic Membrane Computing Systems. In: Rovan, B., Vojtáš, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 480–489. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Krishna, S.N., Păun, A.: Results on catalytic and evolution-communication P systems. New Generation Computing (22)4, 377–394 (2004)CrossRefGoogle Scholar
  8. 8.
    Krishna, S.N.: On Pure Catalytic P Systems. Technical Report, IIT Bombay (2006), www.cse.iitb.ac.in/~krishnas/uc06.ps
  9. 9.
    Minsky, M.L.: Computation: Finite and Infinite Machines. Prentice-Hall, Englewood Cliffs (1967)MATHGoogle Scholar
  10. 10.
    Papadimitriou, C.: Computational Complexity, 1st edn. Addison-Wesley, Reading (1993)Google Scholar
  11. 11.
    Păun, Gh.: Membrane Computing – An Introduction. Springer, Berlin (2002)MATHGoogle Scholar
  12. 12.
    Păun, Gh.: 2006 Research Topics in Membrane Computing (manuscript, 2006)Google Scholar
  13. 13.
    Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages. Springer, Heidelberg (1997)MATHGoogle Scholar
  14. 14.
    Sosik, P.: The power of catalysts and priorities in membrane computing. Grammars 6(1), 13–24 (2003)CrossRefMathSciNetMATHGoogle Scholar
  15. 15.
    Sosik, P., Freund, R.: P Systems without Priorities Are Computationally Universal. In: Păun, G., Rozenberg, G., Salomaa, A., Zandron, C. (eds.) WMC 2002. LNCS, vol. 2597, pp. 400–409. Springer, Heidelberg (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Shankara Narayanan Krishna
    • 1
  1. 1.Department of Computer Science and EngineeringIndian Institute of Technology, BombayPowai, MumbaiIndia

Personalised recommendations