Research On Signed Numbers Arithmetic Operations With Membrane Computing

Membrane structure consists of several cell-like membranes, recurrently placed inside a unique"skin"membrane. In the regions delimited by the membranes there placed a variety of objects, they can evolve in several ways: one object can be transformed in other objects, can arrive a specifically membrane. During the evolution, new membranes can be generated; the existed membranes can be dissolved. Simulating these characteristics of membranes, we obtain a computing model that is distributed, parallel and based on the evolution of objects in a membrane structure, called a P system. Currently, Arithmetic problems play an important role in the algorithmic problems, so research on the basic arithmetic operations in the membrane system can be used as the basis for more complex applications.The start of the research on P system is the Romania Professor Gheorghe Paun's famous paper "Computing with membranes" in 2000. Because P systems are highly parallel and distributed computing, so using P systems to solve the NP complete problems are very popular. However, researchs on the basic arithmetic operations don't be noticed, only focused on the arithmetic of positive numbers and don't form a unified computing framework.Based on active membrane model to solve the signed arithmetic operations, major research in the following areas have benn carried out:1) According to biological characteristics, design uniform APS (arithmetic P system) unit. Uniform APS make the system have the same membrane construction and can be executed in a uniform framework.2) According to principles of computer binary arithmetic, and through the complement principles to solve the signed arithmetic operations. Using the biological characteristics to design the evolution rules, and make the arithmetic operations and data processing can be executed in parallel.3) In arithmetic multiplication, the shift of multiplicand to achieve the multiplication, relative to the cumulative multiplicand, improve the computational efficiency.4) According to certain substances can not enter the same membrane, we solve the problem about calculation of arithmetic expressions. Membrane computing is a kind of molecular computing, currently, membrane computing only focused on building mathematical model, and through observing the biological properties, using mathematics, computer knowledges to research the relevant theory. This paper extends the theory of solving the signed arithmetic operations based on P systems, expands the scope of application. And we can use this result to solve other problems.