Towards Structured Modelling with Hyperdag P Systems

Although P systems are computationally complete, many real world models, such as socio-economic systems, databases, operating systems and distributed systems, seem to require more expressive power than provided by tree structures. Many such systems have a primary tree-like structure augmented with shared or secondary communication channels. Modelling these as tree-based systems, while theoretically possible, is not very appealing, because it typically needs artificial extensions that introduce additional complexities, inexistent in the originals. In this paper, we propose and define a new model called hyperdag P systems, in short, hP systems, which extend the definition of conventional P systems, by allowing dags, interpreted as hypergraphs, instead of trees, as models for the membrane structure. We investigate the relation between our hP systems and neural P systems. Despite using an apparently restricted structure, i.e., a dag instead of a general graph, we argue that hP systems have essentially the same computational power as tissue and neural P systems. We argue that hP systems offer a structured approach to membranebased modelling that is often closer to the behavior and underlying structure of the modelled objects.