A Study of the Application of Multiset to Membrane Computing
A Study of the Application of Multiset to Membrane Computing.
ABSTRACT
We present a Venn diagram model, a tree-based model, and a multiset-based model for membrane structure and point out some of their limitations.
We construct a multiset-based tree model of membrane structure to resolve some of the limitations mentioned earlier. We also construct a saw-like structure to embed into it the multiset-based tree model of membrane structure.
INTRODUCTION
A quasi-generally accepted schematic comprehension of a biological system can be described as a hierarchical structure in which deterministic or non-deterministic or stochastic (or random) interactions among its various substructures characterized by a set of basic components take place.
It is also presumed that the said interactions do take place cooperatively and competitively leading to equilibrium (or emergent) or unstable or chaotic state.
Having the aforesaid orientation in mind, a biological system can be viewed as a multiset object space that evolves by means of the application of rewriting rules. Thus, it seems plausible to construct a multiset model to mimic the biological evolution, such as a P system or its variant – a transition P system.
Essentially, the interactions between substructures of a bio-system can be mimicked by suitably formulated relations with bound multiplicities.
In the sequel, the rule-based multiset programming paradigm (Krishinamwithy, 2006) has been found of immense importance in the construction of algorithms for Deoxyribonucleic acid (DNA), (more generally, molecular) and membrane computing, augmenting programmable living machines, comprehending evolutionary processes.
In recent years, a good number of researches (Păun 2002, Rogozhin et al., 2004 and Amos 1997) have been undertaken in this direction.
It is difficult to trace the origin of a multiset. In recent years, the notion of multiset has been re-discovered, analyzed, and employed in various areas of mathematics, computer science, linguistics, and logic.
We will present a brief account of the application of multiset in our literature review. In course of doing this, we will specify the main area of our research in this thesis vis-à-vis: application of multiset to membrane computing.
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