Skip to main content
SpringerLink
Log in
SpringerLink
Log in

Towards a Characterization of P Systems with Minimal Symport/Antiport and Two Membranes

  • Conference paper
Membrane Computing (WMC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4361))

Included in the following conference series:

Abstract

We prove that any set of numbers containing zero generated by symport/antiport P systems with two membranes and minimal cooperation is finite (for both symport/antiport P systems and for purely symport P systems). On the other hand, one additional object in the output membrane allows symport/antiport P systems (purely symport P systems) with two membranes and minimal cooperation generate any recursively enumerable sets of natural numbers without zero. Thus we improve our previous results for symport/antiport P systems with two membranes and minimal cooperation from three “garbage” objects down to one object and for purely symport P systems from six objects down to one object. Thus we show the optimality of these results.

The authors acknowledge the project 06.411.03.04P from the Supreme Council for Science and Technological Development of the Academy of Sciences of Moldova.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alhazov, A., Freund, R., Rogozhin, Y.: Computational Power of Symport/Antiport: History, Advances, and Open Problems. In: Freund, R., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2005. LNCS, vol. 3850, pp. 1–30. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  2. Alhazov, A., Freund, R., Rogozhin, Y.: Some Optimal Results on Communicative P Systems with Minimal Cooperation. In: Gutiérrez-Naranjo, M.A., Păun, G., Pérez-Jiménez, M.J. (eds.) Cellular Computing (Complexity Aspects), ESF PESC Exploratory Workshop, Fénix Editora, Sevilla, pp. 23–36 (2005)

    Google Scholar 

  3. Alhazov, A., Margenstern, M., Rogozhin, V., Rogozhin, Y., Verlan, S.: Communicative P Systems with Minimal Cooperation. In: Mauri, G., Păun, G., Jesús Pérez-Jímenez, M., Rozenberg, G., Salomaa, A. (eds.) WMC 2004. LNCS, vol. 3365, pp. 161–177. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  4. Alhazov, A., Rogozhin, Y.: Minimal Cooperation in Symport/Antiport P Systems with One Membrane. In: Gutiérrez-Naranjo, M.A., Riscos-Núñez, A., Romero-Campero, F.J., Sburlan, D. (eds.) Third Brainstorming Week on Membrane Computing, RGNC TR 01/2005, University of Seville, Fénix Editora, Sevilla, pp. 29–34 (2005)

    Google Scholar 

  5. Alhazov, A., Rogozhin, Y.: Towards a characterization of P systems with minimal symport/Antiport and two membranes. In: Hoogeboom, H.J., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2006. LNCS, vol. 4361, pp. 135–153. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  6. Alhazov, A., Rogozhin, Y., Verlan, S.: Symport/Antiport Tissue P Systems with Minimal Cooperation. In: Gutiérrez-Naranjo, M.A., Păun, G., Pérez-Jiménez, M.J. (eds.) Cellular Computing (Complexity Aspects), ESF PESC Exploratory Workshop, Fénix Editora, Sevilla, pp. 37–52 (2005)

    Google Scholar 

  7. Bernardini, F., Gheorghe, M.: On the Power of Minimal Symport/Antiport. In: Alhazov, A., Martín-Vide, C., Păun, G.(eds.) Workshop on Membrane Computing, WMC 2003, Tarragona, TR 28/03, Research Group on Mathematical Linguistics, Universitat Rovira i Virgili, Tarragona, pp. 72–83 (2003)

    Google Scholar 

  8. 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)

    Chapter  Google Scholar 

  9. Freund, R., Oswald, M.: GP Systems with Forbidding Context. Fundamenta Informaticae 49(1-3), 81–102 (2002)

    MATH  MathSciNet  Google Scholar 

  10. Freund, R., Oswald, M.: P Systems with Activated/Prohibited Membrane Channels. In: Păun, G., Rozenberg, G., Salomaa, A., Zandron, C. (eds.) WMC 2002. LNCS, vol. 2597, pp. 261–269. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  11. Freund, R., Păun, A.: Membrane Systems with Symport/Antiport Rules: Universality Results. In: Păun, G., Rozenberg, G., Salomaa, A., Zandron, C. (eds.) WMC 2002. LNCS, vol. 2597, pp. 270–287. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  12. Frisco, P.: About P Systems with Symport/Antiport. In: Păun, G., Riscos-Núñez, A., Romero-Jiménez, A., Sancho-Caparrini, F. (eds.) Second Brainstorming Week on Membrane Computing, TR 01/2004, Research Group on Natural Computing, University of Seville, pp. 224–236 (2004)

    Google Scholar 

  13. Frisco, P., Hoogeboom, H.J.: P Systems with Symport/Antiport Simulating Counter Automata. Acta Informatica 41(2-3), 145–170 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  14. Frisco, P., Hoogeboom, H.J.: 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)

    Chapter  Google Scholar 

  15. Kari, L., Martín-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)

    Chapter  Google Scholar 

  16. Margenstern, M., Rogozhin, V., Rogozhin, Y., Verlan, S.: About P Systems with Minimal Symport/Antiport Rules and Four Membranes. In: Mauri, G., Păun, G., Zandron, C. (eds.) Fifth Workshop on Membrane Computing (WMC5), Universitá di Milano-Bicocca, Milan, pp. 283–294 (2004)

    Google Scholar 

  17. Martín-Vide, C., Păun, A., Păun, G.: On the Power of P Systems with Symport Rules. Journal of Universal Computer Science 8(2), 317–331 (2002)

    MathSciNet  Google Scholar 

  18. Minsky, M.L.: Finite and Infinite Machines. Prentice-Hall, Englewood Cliffs (1967)

    MATH  Google Scholar 

  19. Păun, A., Păun, G.: The Power of Communication: P Systems with Symport/Antiport. New Generation Computing 20, 295–305 (2002)

    Article  MATH  Google Scholar 

  20. Păun, G.: Computing with Membranes. Journal of Computer and Systems Science 61, 108–143 (2000)

    Article  MATH  Google Scholar 

  21. Păun, G.: Membrane Computing. An Introduction. Springer, Berlin (2002)

    MATH  Google Scholar 

  22. Păun, G.: Further Twenty Six Open Problems in Membrane Computing. In: Gutiérrez-Naranjo, M.A., Riscos-Núñez, A., Romero-Campero, F.J., Sburlan, D. (eds.) Third Brainstorming Week on Membrane Computing, RGNC TR 01/2005, University of Seville, Fénix Editora, Sevilla, pp. 249–262 (2005)

    Google Scholar 

  23. Păun, G.: 2006 Research Topics in Membrane Computing. In: Gutiérrez-Naranjo, M.A., Păun, G., Riscos-Núñez, A., Romero-Campero, F.J. (eds.) Fourth Brainstorming Week on Membrane Computing, vol. 1, pp. 235–251. Fénix Edit., Sevilla (2006)

    Google Scholar 

  24. Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages (3 volumes). Springer, Berlin (1997)

    Google Scholar 

  25. Vaszil, G.: On the size of P systems with minimal symport/Antiport. In: Mauri, G., Păun, G., Jesús Pérez-Jímenez, M., Rozenberg, G., Salomaa, A., Zandron, C. (eds.) WMC 2004. LNCS, vol. 3365, pp. 422–431. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  26. Verlan, S.: Optimal Results on Tissue P Systems with Minimal Symport/ Antiport. In: EMCC meeting, Lorentz Center, Leiden (2004)

    Google Scholar 

  27. Verlan, S.: Tissue P Systems with Minimal Symport/Antiport. In: Calude, C.S., Calude, E., Dinneen, M.J. (eds.) DLT 2004. LNCS, vol. 3340, pp. 418–429. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  28. P Systems Webpage: http://psystems.disco.unimib.it

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics and Computer Science, Academy of Sciences of Moldova,  

    Artiom Alhazov & Yurii Rogozhin

  2. Research Group on Mathematical Linguistics, Rovira i Virgili University, Tarragona, Spain

    Artiom Alhazov

Authors
  1. Artiom Alhazov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yurii Rogozhin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Leiden Institute of Advanced Computer Science, Universiteit Leiden, Niels Bohrweg 1, 2333, Leiden, CA, The Netherlands

    Hendrik Jan Hoogeboom

  2. Institute of Mathematics of the Romanian Academy, PO Box 1-764, 014700, Bucureşti, Romania

    Gheorghe Păun

  3. Leiden Center of Advanced Computer Science (LIACS), Leiden University, Niels Bohrweg 1, 2333, Leiden, CA, The Netherlands

    Grzegorz Rozenberg

  4. Turku Centre for Computer Science (TUCS), Leminkäisenkatu 14, 20520, Turku, Finland

    Arto Salomaa

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Alhazov, A., Rogozhin, Y. (2006). Towards a Characterization of P Systems with Minimal Symport/Antiport and Two Membranes. In: Hoogeboom, H.J., Păun, G., Rozenberg, G., Salomaa, A. (eds) Membrane Computing. WMC 2006. Lecture Notes in Computer Science, vol 4361. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11963516_9

Download citation

  • DOI: https://doi.org/10.1007/11963516_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69088-7

  • Online ISBN: 978-3-540-69090-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation