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Generalized Membrane Systems with Dynamical Structure, Petri Nets, and Multiset Approximation Spaces

  • Péter Battyányi
  • Tamás Mihálydeák
  • György VaszilEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11493)

Abstract

We study generalized P systems with dynamically changing membrane structure by considering different ways to determine the existence of communication links between the compartments. We use multiset approximation spaces to define the dynamic notion of “closeness” of regions by relating the base multisets of the approximation space to the notion of chemical stability, and then use it to allow communication between those regions only which are close to each other, that is, which contain elements with a certain chemical “attraction” towards each other. As generalized P systems are computationally complete in general, we study the power of weaker variants. We show that without taking into consideration the boundaries of regions, unsynchronized systems do not gain much with such a dynamical structure: They can be simulated by ordinary place-transition Petri nets. On the other hand, when region boundaries also play a role in the determination of the communication structure, the computational power of generalized P systems is increased.

Notes

Acknowledgments

T. Mihálydeák and G. Vaszil was supported by the project TÉT_16-1-2016-0193 of the National Research, Development and Innovation Office of Hungary (NKFIH). G. Vaszil was also supported by grant K 120558 of the National Research, Development and Innovation Office of Hungary (NKFIH), financed under the K 16 funding scheme.

References

  1. 1.
    Bernardini, F., Gheorgue, M., Margenstern, M., Verlan, S.: Networks of cells and Petri nets. In: Díaz-Pernil, D., Graciani, C., Gutiérrez-Naranjo, M.A., Păun, G., Pérez-Hurtado, I., Riscos-Núñez, A. (eds.) Proceedings of the Fifth Brainstorming Week on Membrane Computing, pp. 33–62. Fénix Editora, Sevilla (2007)Google Scholar
  2. 2.
    Ciobanu, G., Pérez-Jiménez, M.J., Păun, G. (eds.): Applications of Membrane Computing. Natural Computing Series. Springer, Heidelberg (2006).  https://doi.org/10.1007/3-540-29937-8CrossRefzbMATHGoogle Scholar
  3. 3.
    Csajbók, Z., Mihálydeák, T.: Partial approximative set theory: a generalization of the rough set theory. Int. J. Comput. Inf. Syst. Ind. Manag. Appl. 4, 437–444 (2012)zbMATHGoogle Scholar
  4. 4.
    Csuhaj-Varjú, E., Gheorghe, M., Stannett, M.: P systems controlled by general topologies. In: Durand-Lose, J., Jonoska, N. (eds.) UCNC 2012. LNCS, vol. 7445, pp. 70–81. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-32894-7_8CrossRefGoogle Scholar
  5. 5.
    Csuhaj-Varjú, E., Gheorghe, M., Stannett, M., Vaszil, G.: Spatially localised membrane systems. Fundam. Inform. 138(1–2), 193–205 (2015)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Mihálydeák, T., Csajbók, Z.E.: Membranes with boundaries. In: Csuhaj-Varjú, E., Gheorghe, M., Rozenberg, G., Salomaa, A., Vaszil, G. (eds.) CMC 2012. LNCS, vol. 7762, pp. 277–294. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-36751-9_19CrossRefGoogle Scholar
  7. 7.
    Mihálydeák, T., Csajbók, Z.E.: On the membrane computations in the presence of membrane boundaries. J. Autom. Lang. Comb. 19(1), 227–238 (2014)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Mihálydeák, T., Vaszil, G.: Regulating rule application with membrane boundaries in P systems. In: Rozenberg, G., Salomaa, A., Sempere, J.M., Zandron, C. (eds.) CMC 2015. LNCS, vol. 9504, pp. 304–320. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-28475-0_21CrossRefzbMATHGoogle Scholar
  9. 9.
    Minsky, M.L.: Computation: Finite and Infinite Machines. Prentice-Hall, Inc., Upper Saddle River (1967)zbMATHGoogle Scholar
  10. 10.
    Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11(5), 341–356 (1982)CrossRefGoogle Scholar
  11. 11.
    Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)CrossRefGoogle Scholar
  12. 12.
    Peterson, J.L.: Petri Net Theory and the Modeling of Systems. Prentice Hall PTR, Upper Saddle River (1981)zbMATHGoogle Scholar
  13. 13.
    Popova-Zeugmann, L.: Time and Petri Nets. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-41115-1CrossRefzbMATHGoogle Scholar
  14. 14.
    Păun, G.: Computing with membranes. J. Comput. Syst. Sci. 61(1), 108–143 (2000)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Păun, G.: Membrane Computing: An Introduction. Springer, Heidelberg (2002).  https://doi.org/10.1007/978-3-642-56196-2CrossRefzbMATHGoogle Scholar
  16. 16.
    Păun, G., Rozenberg, G., Salomaa, A.: The Oxford Handbook of Membrane Computing. Oxford University Press, Inc., New York (2010)CrossRefGoogle Scholar
  17. 17.
    Zhang, G., Pérez-Jiménez, M.J., Gheorghe, M.: Real-life Applications with Membrane Computing. ECC, vol. 25. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-55989-6CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Péter Battyányi
    • 1
  • Tamás Mihálydeák
    • 1
  • György Vaszil
    • 1
    Email author
  1. 1.Department of Computer Science, Faculty of InformaticsUniversity of DebrecenDebrecenHungary

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