Towards structured modelling with hyperdag P systems

Abstract

begin{abstract} 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 \emph{hyperdag P~systems}, in short, \emph{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 membrane-based modelling that is often closer to the behavior and underlying structure of the modelled objects. \end{abstract}