Advertisement

Properties of Membrane Systems

  • Artiom Alhazov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7184)

Abstract

The goal of this survey is to overview some important properties of membrane systems that are referred to as “promising” or dynamic. It is sometimes quite desirable to achieve them, although they are mostly undecidable. We summarize how some of these properties affect the computational power or the descriptional complexity of membrane systems. A number of variants of the dynamic systems is also discussed. Finally, a few self-stabilization properties are proposed.

Keywords

Membrane System Correct State Deterministic System Syntactic Property Register 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.
    Alhazov, A.: Minimizing Evolution-Communication P Systems and Automata. New Generation Computing 22(4), 299–310 (2004)MATHCrossRefGoogle Scholar
  2. 2.
    Alhazov, A.: Number of Protons/Bi-stable Catalysts and Membranes in P Systems. Time-Freeness. In: Freund, R., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2005. LNCS, vol. 3850, pp. 79–95. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  3. 3.
    Alhazov, A.: On Determinism of Evolution-Communication P Systems. Journal of Universal Computer Science 10(5), 502–508 (2004)MathSciNetGoogle Scholar
  4. 4.
    Alhazov, A.: P Systems without Multiplicities of Symbol-Objects. Information Processing Letters 100(3), 124–129 (2006)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Alhazov, A.: Solving SAT by Symport/Antiport P Systems with Membrane Division. In: Gutiérrez-Naranjo, M.A., Păun, G., Pérez-Jiménez, M.J. (eds.) Cellular Computing (Complexity Aspects), ESF PESC Exploratory Workshop, pp. 1–6. Fénix Editora, Sevilla (2005)Google Scholar
  6. 6.
    Alhazov, A., Cavaliere, M.: Evolution-Communication P Systems: Time-Freeness. In: Proceedings of the Third Brainstorming Week on Membrane Computing, pp. 11–18. Fénix Editora, Sevilla (2005)Google Scholar
  7. 7.
    Alhazov, A., Freund, R., Morita, K.: Determinism and Reversibility in P Systems with One Membrane. Kasseler Informatikschriften (KIS), Tagungsband zum 20. Theorietag der GI-Fachgruppe Automaten und Formale Sprachen, Technical report urn:nbn:de:hebis:34-2010110534894, 39–44 (2010)Google Scholar
  8. 8.
    Alhazov, A., Morita, K.: On Reversibility and Determinism in P Systems. In: Păun, G., Pérez-Jiménez, M.J., Riscos-Núñez, A., Rozenberg, G., Salomaa, A. (eds.) WMC 2009. LNCS, vol. 5957, pp. 158–168. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  9. 9.
    Alhazov, A., Freund, R., Morita, K.: Reversibility and Determinism in Sequential Multiset Rewriting. In: Calude, C.S., Hagiya, M., Morita, K., Rozenberg, G., Timmis, J. (eds.) UC 2010. LNCS, vol. 6079, pp. 21–31. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  10. 10.
    Alhazov, A., Freund, R., Morita, K.: Sequential and Maximally Parallel Multiset Rewriting: Reversibility and Determinism. Natural Computing (accepted, 2011)Google Scholar
  11. 11.
    Alhazov, A., Freund, R., Oswald, M.: Cell/Symbol Complexity of Tissue P Systems with Symport/Antiport Rules. International Journal of Foundations of Computer Science 17(1), 3–26 (2006)MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Alhazov, A., Freund, R., Oswald, M.: Symbol/Membrane Complexity of P Systems with Symport/Antiport Rules. In: Freund, R., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2005. LNCS, vol. 3850, pp. 96–113. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  13. 13.
    Alhazov, A., Freund, R., Riscos-Núñez, A.: Membrane Division, Restricted Membrane Creation and Object Complexity in P Systems. International Journal of Computer Mathematics 83(7), 529–548 (2006)MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Alhazov, A., Freund, R., Rogozhin, Y.: Some Optimal Results on Communicative P Systems with Minimal Cooperation. In: Proceedings of the ESF Exploratory Workshop on Cellular Computing (Complexity Aspects), Sevilla, pp. 23–36 (2005)Google Scholar
  15. 15.
    Alhazov, A., Ishdorj, T.-O.: Membrane Operations in P Systems with Active Membranes. In: Păun, G., Riscos-Núñez, A., Romero-Jiménez, A., Sancho-Caparrini, F. (eds.) Second Brainstorming Week on Membrane Computing, Sevilla, RGNC report 01/2004, University of Seville, pp. 37–44 (2004)Google Scholar
  16. 16.
    Alhazov, A., Rogozhin, Y.: Skin Output in P Systems with Minimal Symport/Antiport and Two Membranes. In: Eleftherakis, G., Kefalas, P., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2007. LNCS, vol. 4860, pp. 97–112. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  17. 17.
    Alhazov, A., Rogozhin, Y., Verlan, S.: Minimal Cooperation in Symport/Antiport Tissue P Systems. International Journal of Foundations of Computer Science 18(1), 163–180 (2007)MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    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)CrossRefGoogle Scholar
  19. 19.
    Alhazov, A., Sburlan, D.: Ultimately Confluent Rewriting Systems. Parallel Multiset–Rewriting with Permitting or Forbidding Contexts. In: Mauri, G., Păun, G., Jesús Pérez-Jímenez, M., Rozenberg, G., Salomaa, A. (eds.) WMC 2004. LNCS, vol. 3365, pp. 178–189. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  20. 20.
    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, Technical Report N. 28/03, Research Group on Mathematical Linguistics, Universitat Rovira i Virgili, Tarragona, pp. 72–83 (2003)Google Scholar
  21. 21.
    Binder, A., Freund, R., Lojka, G., Oswald, M.: Implementation of Catalytic P Systems. In: Domaratzki, M., Okhotin, A., Salomaa, K., Yu, S. (eds.) CIAA 2004. LNCS, vol. 3317, pp. 45–56. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  22. 22.
    Busi, N.: Using Well-Structured Transition Systems to Decide Divergence for Catalytic P Systems. Theoretical Computer Science 372(2-3), 125–135 (2007)MathSciNetMATHCrossRefGoogle Scholar
  23. 23.
    Calude, C.S., Păun, G.: Bio-Steps Beyond Turing. BioSystems 77(1-3), 175–194 (2004)CrossRefGoogle Scholar
  24. 24.
    Cavaliere, M.: Towards Asynchronous P systems. In: Pre-proceedings of the Fifth Workshop on Membrane Computing (WMC5), Milano, pp. 161–173 (2004)Google Scholar
  25. 25.
    Cavaliere, M., Deufemia, V.: Further Results on Time-Free P Systems. International Journal of Foundations of Computer Science 71(1), 69–89 (2006)MathSciNetMATHCrossRefGoogle Scholar
  26. 26.
    Cavaliere, M., Sburlan, D.: Time–Independent P Systems. In: Mauri, G., Păun, G., Jesús Pérez-Jímenez, M., Rozenberg, G., Salomaa, A. (eds.) WMC 2004. LNCS, vol. 3365, pp. 239–258. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  27. 27.
    Csuhaj-Varjú, E., Vaszil, G., Verlan, S.: On Generalized Communicating P Systems with One Symbol. In: Gheorghe, M., Hinze, T., Păun, G., Rozenberg, G., Salomaa, A. (eds.) CMC 2010. LNCS, vol. 6501, pp. 160–174. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  28. 28.
    Freund, R.: Asynchronous P Systems and P Systems Working in the Sequential Mode. In: Mauri, G., Păun, G., Jesús Pérez-Jímenez, M., Rozenberg, G., Salomaa, A. (eds.) WMC 2004. LNCS, vol. 3365, pp. 36–62. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  29. 29.
    Freund, R., Alhazov, A., Rogozhin, Y., Verlan, S.: Communication P Systems. In: ch. 5 of [41], pp. 118–143Google Scholar
  30. 30.
    Freund, R., Kari, L., Oswald, M., Sosík, P.: Computationally Universal P Systems without Priorities: Two Catalysts are Sufficient. Theoretical Computer Science 330(2), 251–266 (2005)MathSciNetMATHCrossRefGoogle Scholar
  31. 31.
    Freund, R., Păun, G.: On Deterministic P Systems (2003); see [46] (manuscript)Google Scholar
  32. 32.
    Freund, R., Verlan, S.: A Formal Framework for Static (Tissue) P Systems. In: Eleftherakis, G., Kefalas, P., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2007. LNCS, vol. 4860, pp. 271–284. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  33. 33.
    Ibarra, O.H.: On Strong Reversibility in P Systems and Related Problems. International Journal of Foundations of Computer Science 22(1), 7–14 (2011)MathSciNetMATHCrossRefGoogle Scholar
  34. 34.
    Ibarra, O.H., Yen, H.-C.: Deterministic Catalytic Systems are not Universal. Theoretical Computer Science 363(2), 149–161 (2006)MathSciNetMATHCrossRefGoogle Scholar
  35. 35.
    Kleijn, J., Koutny, M.: Synchrony and Asynchrony in Membrane Systems. In: Hoogeboom, H.J., Paun, G., Rozenberg, G. (eds.) Pre-proceedings of Membrane Computing, International Workshop, WMC7, Leiden, pp. 21–39 (2006)Google Scholar
  36. 36.
    Oswald, M.: P Automata. PhD thesis, Vienna University of Technology (2003)Google Scholar
  37. 37.
    Leporati, A., Zandron, C., Mauri, G.: Reversible P Systems to Simulate Fredkin Circuits. Fundamenta Informaticae 74(4), 529–548 (2006)MathSciNetMATHGoogle Scholar
  38. 38.
    Pan, L., Alhazov, A., Ishdorj, T.-O.: Further Remarks on P Systems with Active Membranes, Separation, Merging, and Release Rules. Soft Computing - A Fusion of Foundations, Methodologies and Applications 9(9), 686–690 (2005)MATHGoogle Scholar
  39. 39.
    Păun, G.: Membrane Computing. An Introduction. Springer, Heidelberg (2002)MATHCrossRefGoogle Scholar
  40. 40.
    Păun, A., Păun, G.: The Power of Communication: P Systems with Symport / Antiport. New Generation Computing 20, 295–305 (2002)MATHCrossRefGoogle Scholar
  41. 41.
    Păun, G., Rozenberg, G., Salomaa, A.: The Oxford Handbook of Membrane Computing. Oxford University Press (2010)Google Scholar
  42. 42.
    Verlan, S.: Look-Ahead Evolution for P Systems. In: Păun, G., Pérez-Jiménez, M.J., Riscos-Núñez, A., Rozenberg, G., Salomaa, A. (eds.) WMC 2009. LNCS, vol. 5957, pp. 479–485. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  43. 43.
    Verlan, S., Bernardini, F., Gheorghe, M., Margenstern, M.: Computational Completeness of Tissue P Systems with Conditional Uniport. In: Hoogeboom, H.J., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2006. LNCS, vol. 4361, pp. 521–535. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  44. 44.
    Verlan, S., Rogozhin, Y.: New Choice for Small Universal Devices: Symport / Antiport P Systems. In: Neary, T., Woods, D., Seda, A.K., Murphy, N. (eds.) Proceedings International Workshop on The Complexity of Simple Programs, CSP 2008, Cork (2008); Electronic Proceedings in Theoretical Computer Science 1, 235–241 (2009)Google Scholar
  45. 45.
  46. 46.
    P systems webpage, http://ppage.psystems.eu

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Artiom Alhazov
    • 1
    • 2
  1. 1.Institute of Mathematics and Computer ScienceAcademy of Sciences of MoldovaChişinăuMoldova
  2. 2.Dipartimento di Informatica Sistemistica e ComunicazioneUniversità degli Studi di Milano-BicoccaMilanoItaly

Personalised recommendations