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.