Advertisement

The Number of Membranes Matters

  • Oscar H. Ibarra
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2933)

Abstract

We look at a restricted model of a communicating P system, called RCPS, whose environment does not contain any object initially. The system can expel objects into the environment but only expelled objects can be retrieved from the environment. Such a system is initially given an input \(a_1^{i_1} ... a_n^{i_n}\) (with each i j representing the multiplicity of distinguished object a i , 1 ≤ i ≤ n) and is used as an acceptor. We show that RCPS’s are equivalent to two-way multihead finite automata over bounded languages (i.e., subsets of \(a_1^* ... a_n^*\), for some distinct symbols a 1, ..., a n ). We then show that there is an infinite hierarchy of RCPS’s in terms of the number of membranes. In fact, for every r, there is an s> r and a unary language L accepted by an RCPS with s membranes that cannot be accepted by an RCPS with r membranes. This provides an answer to an open problem in [12] which asks whether there is a nonuniversal model of a membrane computing system which induces an infinite hierarchy on the number of membranes. We also consider variants/generalizations of RCPS’s, e.g., acceptors of languages; models that allow a “polynomial bounded” supply of objects in the environment initially; models with tentacles, etc. We show that they also form an infinite hierarchy with respect to the number of membranes (or tentacles). The proof techniques can be used to obtain similar results for other restricted models of P systems, like symport/antiport systems.

Keywords

Turing Machine Restricted Model Input String Input Tape Counter Machine 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Berry, G., Boudol, G.: The chemical abstract machine. In: POPL 1990, pp. 81–94. ACM Press, New York (1990)CrossRefGoogle Scholar
  2. 2.
    Csuhaj-Varju, E., Vaszil, G.: P automata. In: Păun, G., Rozenberg, G., Salomaa, A., Zandron, C. (eds.) WMC 2002. LNCS, vol. 2597, pp. 177–192. Springer, Heidelberg (2002)Google Scholar
  3. 3.
    Freund, R.: Special variants of P systems inducing an infinite hierarchy with respect to the number of membranes. Bulletin of the EATCS (75), 209–219 (2001)Google Scholar
  4. 4.
    Freund, R., Oswald, M.: A short note on analyzing P systems with antiport rules. Bulletin of EATCS 78, 231–236 (2002)zbMATHMathSciNetGoogle Scholar
  5. 5.
    Ibarra, O.H., 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
  6. 6.
    Ibarra, O.H.: On the computational complexity of membrane computing systems (2003) (submitted)Google Scholar
  7. 7.
    Krishna, S.: Infinite hierarchies on some variants of P systems (2002) (submitted)Google Scholar
  8. 8.
    Monien, B.: Two-way multihead automata over a one-letter alphabet. RAIRO Informatique theorique 14(1), 67–82 (1980)zbMATHMathSciNetGoogle Scholar
  9. 9.
    Paun, A., Paun, G.: The power of communication: P systems with symport/ antiport. New Generation Computing 20(3), 295–306 (2002)zbMATHCrossRefGoogle Scholar
  10. 10.
    Paun, Gh.: List of problems circulated before the Brainstorming Week in Membrane Computing held in Tarragona, Spain, February 5-11 (2003)Google Scholar
  11. 11.
    Paun, G.: Computing with membranes. Journal of Computer and System Sciences 61(1), 108–143 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Paun, G.: Membrane Computing: An Introduction. Springer, Heidelberg (2002)zbMATHGoogle Scholar
  13. 13.
    Paun, Gh., Perez-Jimenez, M., Sancho-Caparrini, F.: On the reachability problem for P systems with symport/antiport (2002) (submitted)Google Scholar
  14. 14.
    Paun, G., Rozenberg, G.: A guide to membrane computing. TCS 287(1), 73–100 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Sosik, P.: P systems versus register machines: two universality proofs. In: Păun, G., Rozenberg, G., Salomaa, A., Zandron, C. (eds.) WMC 2002. LNCS, vol. 2597, pp. 371–376. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  16. 16.
    Sosik, P., Matysek, J.: Membrane computing: when communication is enough. In: Calude, C.S., Dinneen, M.J., Peper, F. (eds.) UMC 2002. LNCS, vol. 2509, pp. 264–275. Springer, Heidelberg (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Oscar H. Ibarra
    • 1
  1. 1.Department of Computer ScienceUniversity of CaliforniaSanta BarbaraUSA

Personalised recommendations