| Membrane computingalso called P systems is a new branch of natural computing and abstract parallel computing models by studying the architecture and the functioning of living cells, as well as from the organization of cells in tissues, organs(brain included) or other higher order structures such as colonies of cells; One of the biggest advantages of membrane computing is that it has great parallelism,It has been proved that membrane computing has the same equivalent computing power as Turing machine, and could solve the NP problem in polynomial time.Currently, the research on numerical calculation based on the membrane computing is not involved, and arithmetic operation is the basis of solving numerical calculations problems, the research of arithmetic operation based on membrane computing has mad a lot of achievements. So based on the arithmetic operation system in membrane computing, this paper firstly study the numerical calculation in the membrane computing, which includes solving system of linear equation and matrix-vector multiplication, and lay a solid foundation for the research of membrane computing in the field of numerical calculation. Besides, we also study the division parallel computing based on division famula table, and enrich theoretical research on the arithmetic operation in membrane computing. The following is an introduction to the work of completed studied in this paper:(1) Based on the research on the arithmetic operation in membrane computing and principle of multi processor parallel computing for electronic computer, an algorithm is proposed which is suitable to be implemented in P system, and according to this algorithm, we firstly design a family of P systems ΠLE, an example is given to illustrates the execution process of P systems, and verify the correctness of the rules and the feasibility of the P systems ΠLE by the simulation program.(2) Disscusses the parallel computing method of matrix vector multiplication and the parallel computing algorithm which suitable for implementation in P systems, and according to this algorithm, we design the matrix vector multiplication P system ΠMT, and firstly implement the matrix operation in P systems. Finally, through an example to illustrate the execution process of the rules, and design the simulation program to verify the correctness of the rules and the feasibility of the P system.(3) In order to improve the efficiency of division operation in the arithmetic P systems, this paper proposed division parallel computing algorithm and division table, and design a P systems ΠPD based on division formula tables. By giving an example to illustrate the implementation process of the rules, and through simulation program to verify the correctness of the rules and the feasibility of based on the division table P systems to implement the division parallel computation.Results of this paper not only expand the application of membrane computing in the field of numerical calculation, but also enrich the theory of arithmetic operations in the membrane computing. Using multilayer P systems to implements the solving linear equations and matrix operations, and it expanded the range of application of the P systems. The results of this paper can be used as a reference for future research in the field of numerical computation. |
