Encodings and Arithmetic Operations in Membrane Computing

Membrane systems represent a new abstract model inspired by cell compartments and molecular membranes. 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 [7]. 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 multisets of objects from a region correspond 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. We refer mainly to the so-called transition membrane systems. Other variants and classes are introduced [7]. The membrane systems represent a new abstract machine. For each abstract machine, the theory of programming introduces and studies various paradigms of computation. For instance, Turing machines and register machines are mainly related to imperative programming, and λ-calculus is related to functional programming. Looking at the membrane systems from the point of view of programming theory, we intend to provide useful results for future definitions and implementations of P system-based programming languages, that is, programming languages that generate P systems as an executable form. The authors of such languages will certainly have to face the problem of number encoding using multisets, since the multiset is the support structure of P systems. We attempt to show that the problem of number encoding using multisets is an interesting