Maximal Parallelism in Membrane Systems with Generated Membrane Boundaries

In membrane systems, the maximal parallelism is a useful tool for modeling real biotic/chemical interactions. After all, there are many attempts to relax maximal parallelism at the definition level, e.g. minimal parallelism, bounded parallelism etc., or even at the system level as the metabolic P system. By the help of topological means, membrane computations and maximal parallelism can be controlled. Besides, in natural processes, the events represented by communication rules take place in the vicinity of the membranes. The authors, motivated by natural phenomena, propose a framework in which the abstract notion of boundaries along membranes is modeled. In this paper, behaviors of communication rules restricted to these membrane boundaries are presented, in particular, showing how these restrictions affect the maximal parallelism.

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