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