Multiset-based Tree Model for Membrane Computing

In this paper, we introduce a new paradigm multiset-based tree model. We show that trees can be represented in the form of wellfounded multisets. We also show that the conventional approach for this representation is not injective from a set of trees to the class of multisets representing such trees. We establish a oneto-one correspondence between trees and suitable permutations of a wellfounded multiset, which we call tree structures. We give formal definitions of a tree structure and a subtree structure of a tree structure. Finally, we represent membrane structures in the form of tree structures – a form in which membrane structures can suitably be represented at programming level.