A Study of the Application of Multiset to Membrane Computing: A Discrete Approach to Representing Membrane Structures for Implementation in a Programming Environment

Simulating membrane computing in digital computers cannot be without the mathematical modelling of a membrane structure and its inherent inter- and intra-regional molecular interactions together with the rules governing such interactions. Before now there has not been a flexible representation of membrane structure. This thesis opens up a new dimension in the study of membrane computing by providing current synthesis of knowledge concerning the structure of membranes. The main aim of the thesis is to design a mathematical tool for representing a membrane structure, called a tree structure. It uses a suitable multiset permutation rather than a Venn diagram or a tree diagram for the representation in a one-to-one correspondence. Since a Venn diagram or a tree diagram representation of a membrane structure is not readily available to the computer at programming level, the use of tree structures can be exploited.