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Matter and Anti-Matter in Membrane Systems

  • Artiom Alhazov
  • Bogdan Aman
  • Rudolf Freund
  • Gheorghe Păun
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8614)

Abstract

The concept of a matter object being annihilated when meeting its corresponding anti-matter object is investigated in the context of membrane systems, i.e., of (distributed) multiset rewriting systems applying rules in the maximally parallel way. Computational completeness can be obtained with using only non-cooperative rules besides these matter/anti-matter annihilation rules if these annihilation rules have priority over the other rules. Without this priority condition, in addition catalytic rules with one single catalyst are needed to get computational completeness. Even deterministic systems are obtained in the accepting case. Universal P systems with a rather small number of rules – 57 for computing systems, 59 for generating and 53 for accepting systems – can be constructed when using non-cooperative rules together with matter/anti-matter annihilation rules having weak priority.

Keywords

Membrane System Evolution Rule Register Machine Membrane Computing Skin Membrane 
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.

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References

  1. 1.
    Alhazov, A., Sburlan, D.: Static Sorting P Systems. In: Ciobanu, G., Păun, G., Pérez-Jiménez, M.J. (eds.) Applications of Membrane Computing. Natural Computing Series, pp. 215–252. Springer (2005)Google Scholar
  2. 2.
    Csuhaj-Varjú, E., Vaszil, G.: P Automata or Purely Communicating Accepting P Systems. In: Păun, G., Rozenberg, G., Salomaa, A., Zandron, C. (eds.) WMC-CdeA 2002. LNCS, vol. 2597, pp. 219–233. Springer, Heidelberg (2003)Google Scholar
  3. 3.
    Dassow, J., Păun, G.: Regulated Rewriting in Formal Language Theory. Springer (1989)Google Scholar
  4. 4.
    Freund, R., Kari, L., Oswald, M., Sosík, P.: Computationally Universal P Systems without Priorities: Two Catalysts Are Sufficient. Theoretical Computer Science 330, 251–266 (2005)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Freund, R., Oswald, M.: A Small Universal Antiport P System with Forbidden Context. In: Leung, H., Pighizzini, G. (eds.) 8th International Workshop on Descriptional Complexity of Formal Systems, DCFS 2006, June 21-23. Proceedings DCFS, pp. 259–266. New Mexico State University, Las Cruces (2006)Google Scholar
  6. 6.
    Freund, R., Oswald, M.: Catalytic and Purely Catalytic P Automata: Control Mechanisms for Obtaining Computational Completeness. In: Bensch, S., Drewes, F., Freund, R., Otto, F. (eds.) Fifth Workshop on Non-Classical Models of Automata and Applications (NCMA 2013), pp. 133–150. OCG, Wien (2013)Google Scholar
  7. 7.
    Freund, R.: Gh. Păun: How to Obtain Computational Completeness in P Systems with One Catalyst. In: Proceedings Machines, Computations and Universality, MCU 2013, Zürich, Switzerland, September 9-11. EPTCS, vol. 128, pp. 47–61 (2013)Google Scholar
  8. 8.
    Korec, I.: Small Universal Register Machines. Theoretical Computer Science 168, 267–301 (1996)CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Minsky, M.L.: Computation: Finite and Infinite Machines. Prentice Hall, Englewood Cliffs (1967)MATHGoogle Scholar
  10. 10.
    Pan, L., Păun, G.: Spiking Neural P Systems with Anti-Matter. International Journal of Computers, Communications & Control 4(3), 273–282 (2009)Google Scholar
  11. 11.
    Păun, G.: Computing with Membranes. Journal of Computer and System Sciences 61(1), 108–143 (2000); (Turku Center for Computer Science-TUCS Report 208 (November 1998), www.tucs.fi)
  12. 12.
    Păun, G.: Membrane Computing. An Introduction. Springer (2002)Google Scholar
  13. 13.
    Păun, G., Rozenberg, G., Salomaa, A. (eds.): The Oxford Handbook of Membrane Computing. Oxford University Press (2010)Google Scholar
  14. 14.
    Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages, vol. 3. Springer (1997)Google Scholar
  15. 15.
    The P Systems Website, www.ppage.psystems.eu

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Artiom Alhazov
    • 1
  • Bogdan Aman
    • 2
  • Rudolf Freund
    • 3
  • Gheorghe Păun
    • 4
  1. 1.Institute of Mathematics and Computer ScienceAcademy of Sciences of MoldovaChişinăuMoldova
  2. 2.Institute of Computer ScienceRomanian AcademyIaşiRomania
  3. 3.Faculty of InformaticsVienna University of TechnologyViennaAustria
  4. 4.Institute of MathematicsRomanian AcademyBucharestRomania

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