Synchrony and Asynchrony in Membrane Systems

Abstract

Abstract. We consider synchrony and asynchrony in the behaviour 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 behavioural model we use Petri nets and their processes which capture the notion of an execution in concurrent contexts. We continue our earlier work reported in [14], 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 behavioural model provided by Petri nets.

Processes of membrane systems with promoters and inhibitors

“…The reader might wonder whether similar one-to-one translations are also possible for other extensions of the basic membrane system model. An initial investigation is reported in [14] where membrane systems with reaction rules that may become obsolete or available depending on the changing structure of the cells are discussed, as are membrane systems with permeable or with dissolving membranes. It appears that such extensions do not lend themselves to one-to-one translations to Petri nets, although there is a way of modelling of their salient features using the translation to PTLAI-nets in combination with special control structures.…”

Modelling of Multi-Agent Systems: Experiences with Membrane Computing and Future Challenges

“…We have also attempted a number of transformations between Communicating X-Machines and P Systems and vice-versa [19,23]. Others in the P system research community showed more interest in other transformations, such as from P Systems to Petri nets [25], process algebra [6], cellular automata [7] etc. These have not only demonstrated the equivalence of these methods but created a temptation to try out several techniques known for one method to the other.…”

Mobile Membranes

“…One of the research line in membrane systems is to connect mobile membranes with process calculi; e.g., [31], Petri nets [2], [45], cellular automata [34] and communicating X-machines [44]. Several studies focused on the relationships between these models in order to use their techniques and results: e.g., model checking of process calculi, invariants of Petri nets, testing methods of X-Machines.…”