TOC Chapter 14

Chapter 14. New Models of Computation

 

14.1. DNA Computing

Mathematical biology is a highly interdisciplinary area of research that lies at the intersection of mathematics and biology. So far, in this area, mathematical results have been used to solve biological problems. The development of stochastic processes and statistical methods are examples of such a development. In contrast, an instance of the directed Hamilton path problem was solved solely by manipulating DNA strings by Leonard Adleman. Hence, one can see that biological technique is used to solve a mathematical problem, thus paving way for a new line of research ‘DNA computing.’ The resemblance between mathematics and biology is that in both, simple operations are applied to initial information to obtain a result. Hence, the use of biology to solve a mathematical problem was demonstrated by a mathematician with adequate knowledge in biology, to bring together these two fields. Adleman thought that DNA strings can be used to encode an information while enzymes can be employed to simulate simple computations.

Molecules that play central roles in molecular biology and genetics, are DNA, RNA, and the polypeptides. The recombinant behaviors of double-stranded DNA molecules is made possible by the presence of restricted enzymes. Hence, DNA computing is a fast-growing research area concerned with the use of DNA molecules for the implementation of computational processes.

14.2. Membrane Computing

Membrane computing is a new computability technique which is inspired from biochemistry. The model used for any computation here resembles a membrane structure and it is a highly parallel, distributed computing model. Several cell-like membranes are recurrently placed inside a unique membrane called “skin” membrane. The structure of this model may be placed as a Venn diagram without intersected sets and with unique superset. Hence, the structure or compartment of the computing model can be diagrammatically represented as below: