Study On Arithmetic P System Based On DNA Computing

According to the "Moore’s law", the traditional computer speed is close to the bottleneck. Scientists began to search for the computation model instead of the traditional electronic computer. So far, many models have been abstracted from a variety of biological phenomena, such as Biological Computing. DNA Computing and Membrane Computing are the two branches of Biological Computing. DNA Computing is a parallel computing model which is abstracted from the DNA molecule Watson-Crick complementarity and high parallelism of the biochemical reactions. Many NP problems can be solved in polynomial time by DNA Computing. Membrane Computing(also called P system) establishments a distributed parallel computing model of good computing performance through referencing to and simulating the way cells, tissues, organs or other biological structures process chemical substances. The computation ability of Membrane Computing has been proved to be equivalent to the one of Turing machine. Many NP hard problems can be solved in polynomial time by Membrane Computing.How to implement arithmetical operations is the primary problem in a computing model. So far, there are some certain research results about the implementation of arithmetical operations in DNA Computing and Membrane Computing. However, the parallelism of arithmetic operations, especially division operation, attracts rare attention in the research on Biological Computing. So we design the arithmetic formulas table and arithmetic processes for better use of the parallelism of Biological Computing. In this paper, we respectively design and implement two systems of the four basic arithmetic operations based on arithmetic formulas table in DNA Computing and Membrane Computing and improve the parallelism of arithmetic operations. And combining the arithmetic operations in DNA Computing and those in Membrane Computing, we design an arithmetic P system based on structured objects of DNA strands.The following is a brief introduction to the work of completed study in this paper:① In order to improve the parallelism of arithmetic operations in DNA Computing, we design the arithmetic formulas table for four basic arithmetic operations(including addition, subtraction, multiplication and division) of single digit x(0￡x￡9). Based on Adleman-Lipton model, we design two DNA encoding methods respectively for decimal number and arithmetic formulas table. On the above basis, we design and implement the four basic arithmetic operations of decimal number which make use of the parallelism of DNA Computing well.② A new arithmetic P system is designed based on the above arithmetic formulas table. In this P system, the evolution rules for basic arithmetic operations of single digit are designed based on arithmetic formulas table. Compared with the present arithmetic P system, the new one based on arithmetic formulas table reduces complexity in arithmetic operations of multiplication and division.③ Based on the structured object P system, we instantiate the structured object as a DNA strand and design an arithmetic P system based on DNA structured objects. The P system combines the characteristics of Watson-Crick complementarity of DNA strands and the distributed computing in membrane area of P system. And it simplifies the complexity of evolution rules and the structure of arithmetic P system.Research results of this paper are to further enrich the theory of four basic arithmetic operations in the Membrane Computing and DNA Computing. And based on arithmetic formulas table, we combine DNA Computing with Membrane Computing and design a DNA Computing-based arithmetic P system. It extends the types and application of the structured object P system, so it is able to be the reference when we solve other problems in future.