Synchrony and Asynchrony in Membrane Systems

We consider synchrony and asynchrony in the behavior of various models of membrane systems, which may differ in the way individual reactions are defined as well as in the way multisets of these reactions can be executed in a single computational step. We concentrate on the properties of ongoing computations, including the unbounded ones. Our focus is on the properties of system states involved in such computations as well as on concurrency and causality relationships between executed reactions. This should be contrasted with the approach which investigates different notions of ‘results’ produced through halting computations of membrane systems. As a formal behavioral model we use Petri nets and their processes which are very well suited to capture the notion of an execution in a concurrent context. We continue our earlier work reported in [15], where a systematic and structural link has been established between a basic class of membrane systems and Petri nets. Here, we look at some natural extensions of this basic class of membrane systems and investigate the ways in which they can be represented within the behavioral model provided by Petri nets.