Modelling Symport/Antiport P Systems with a Class of Hierarchical Petri Nets

A model of P systems with symport/antiport rules is given in terms of hypernets, a generalization of a class of hierarchical Petri nets introduced for modeling mobility inside the nets-within-nets paradigm. The hierarchical structure of a P system is reflected by the associated hypernet, where molecules are modeled by unstructured agents (simple tokens) and membranes by agents. Each agent is modeled by a net which may contain in its places unstructured agents or other agents. Agents can exchange tokens with their sub- or super-agents and thus the hierarchy may change. The main result of the paper shows a correspondence between reachable configurations of the P system and reachable hypermarkings of the related hypernet, in such a way that if the P system can evolve from one configuration to another one then in the hypernet there exists a corresponding transformation of hypermarkings.