Advertisement

P Systems with Generalized Multisets Over Totally Ordered Abelian Groups

  • Rudolf Freund
  • Sergiu Ivanov
  • Sergey Verlan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9504)

Abstract

In this paper we extend the definition of a multiset by allowing elements to have multiplicities from an arbitrary totally ordered Abelian group instead of only using natural numbers. We consider P systems with such generalized multisets and give well-founded notations for the applicability of rules and for different derivation modes. These new definitions raise challenging mathematical questions and we propose several solutions yielding models sometimes having quite unexpected behavior. Another interesting application of our results is the possibility to consider complex objects and to manipulate them directly in a P system instead of their numerical encodings.

References

  1. 1.
    Alexandru, A., Ciobanu, G.: Algebraic properties of generalized multisets. In: Proceedings of the 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), pp. 367–374. IEEE (2013)Google Scholar
  2. 2.
    Alhazov, A., Aman, B., Freund, R., Paun, Gh.: Matter and anti-matter in membrane systems. In: Macías-Ramos, L.F., Martínez-del-Amor, M.Á., Paun, Gh., Riscos-Núñez, A., Valencia-Cabrera, L. (eds.) Proceedings of the Twelfth Brainstorming Week on Membrane Computing, pp. 1–26. Fénix Editora, Sevilla (2014)Google Scholar
  3. 3.
    Blizard, W.D.: Multiset theory. Notre Dame J. Formal Logic 30(1), 36–66 (1989)zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Blizard, W.D.: Real-valued multisets and fuzzy sets. Fuzzy Sets Syst. 33, 77–97 (1989)zbMATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Blizard, W.D.: Negative membership. Notre Dame J. Formal Logic 31(1), 346–368 (1990)zbMATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Dassow, J., Paun, Gh.: Regulated Rewriting in Formal Language Theory. Springer, Heidelberg (1989)Google Scholar
  7. 7.
    Holt, D.F., Eick, B., O’Brien, E.A.: Handbook of Computational Group Theory. CRC Press, Boca Raton (2005)zbMATHCrossRefGoogle Scholar
  8. 8.
    Minsky, M.L.: Computation: Finite and Infinite Machines. Prentice Hall, Englewood Cliffs (1967)zbMATHGoogle Scholar
  9. 9.
    Pan, L., Paun, Gh.: Spiking neural P systems with anti-matter. Int. J. Comput. Commun. Control 4(3), 273–282 (2009)Google Scholar
  10. 10.
    Paun, Gh.: Computing with membranes. J. Comput. Syst. Sci. 61(1), 108–143 (2000). Turku Center for Computer Science-TUCS Report 208, November 1998. http://www.tucs.fi
  11. 11.
    Paun, Gh.: Membrane Computing: An Introduction. Springer, Heidelberg (2002)Google Scholar
  12. 12.
    Paun, Gh., Rozenberg, G., Salomaa, A. (eds.): The Oxford Handbook of Membrane Computing. Oxford University Press, Oxford (2010)Google Scholar
  13. 13.
    Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages. Springer, Heidelberg (1997). 3 VolumeszbMATHGoogle Scholar
  14. 14.
    Paun, Gh.: Some quick research topics. http://www.gcn.us.es/files/OpenProblems_bwmc15.pdf
  15. 15.
    The P Systems Website. http://www.ppage.psystems.eu

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Faculty of InformaticsTU WienViennaAustria
  2. 2.LACLUniversité Paris Est – Créteil Val de MarneCréteilFrance

Personalised recommendations