Multiset-based Tree Model for Membrane Computing

Abstract

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 one-to-one correspondence between trees and suitable permutations of a wellfounded multiset, which we call \textit{tree structures}. We give formal definitions of a \textit{tree structure} and a \textit{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.

Keywords

• wellfounded multiset
• saw-like structure
• multi\-set-based tree structure
• membrane structure
• multiset-based tree structure