A Programming Perspective of the Membrane Systems

Abstract

Abstract:We present an operational semantics of the membrane systems, using an appropriate notion of configurations and sets of inference rules corresponding to the three stages of an evolution step in membrane systems: maximal parallel rewriting step, parallel communication of objects through membranes, and parallel membrane dissolving. We define various arithmetical operations over multisets in the framework of membrane systems, indicating their complexity and presenting the membrane systems which implement the arithmetic operations. Finally we discuss and compare various sequential and parallel software simulators of the membrane systems, emphasizing their specific features. Keywords: membrane systems, operational semantics, arithmetical operations over multisets. Membrane SystemsMembrane systems represent a computational model inspired by cell compartments and molecular membranes. Essentially, such a system is composed of various compartments, each compartment with a different task, and all of them working simultaneously to accomplish a more general task of the whole system. A detailed description of the membrane systems (also called P systems) can be found in [17]. A membrane system consists of a hierarchy of membranes that do not intersect, with a distinguishable membrane, called the skin membrane, surrounding them all. The membranes produce a delimitation between regions. For each membrane there is a unique associated region. Regions contain multisets of objects, evolution rules and possibly other membranes. Only rules in a region delimited by a membrane act on the objects in that region. The multiset of objects from a region corresponds to the "chemicals swimming in the solution in the cell compartment", while the rules correspond to the "chemical reactions possible in the same compartment". Graphically, a membrane structure is represented by a Venn diagram in which two sets can be either disjoint, or one is a subset of the other. More details (concepts, results) and several variants of membrane systems are presented in [17].A P system consists of several membranes that do not intersect, and a skin membrane, surrounding them all. The membranes delimit regions, and contain multisets of objects, as well as evolution rules. Each membrane has a unique associated region. The space outside the skin membrane is called the outer region (or the environment). Because of the one-to-one correspondence between the membranes and the regions, we usually use the word membrane instead of region. Only rules in a region delimited by a membrane act on the objects in that region. Moreover, the rules must contain target indications, specifying the membrane where objects are sent after applying the rule. The objects can either remain in the same region, or pass through membranes in two directions: they can be sent out of the membrane which delimits a region from outside, or can be sent in one of the membranes which delimit a region from inside, precisely identified by its label. The membranes can also be dissolved. When such a...

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