Rational Expression Evaluation With Membrane Computing

According to the description of Moore’s Law, the number of transistors that can beplaced inexpensively on an integrated circuit doubles approximately every18months.However, the number of transistors can not be increased unlimitedly, and it willeventually reach a limit. Additionally, computing performance about computer haslimitations (The computation process about computer is essentially a serial work), so ithas become to need to immediately study and solve problem which selects a newcomputational model to replace the computer. And it which chooses biologicalcomputer as an alternative model possesses a large number of supporters, and the reasonwhy chooses biological computer is based on two obvious advantages: very low energyconsumption, very high parallelism.Membrane Computing is a new branch of biological computing, by researching theevolution of life of the cell membrane, and thereby it is able to abstract from thecalculation model. Membrane Computing can also be known as the P System, thedirection of the study was founded in1998by Romanian scientists Gheorghe.P un, andit has rapidly developed into a field of science with great potential, and it brings newsolution ideas to many areas of difficult issues. In this paper, our study direction is oneof directions in the Membrane Computing, and that is the arithmetic and expressionevaluation in the rational field. By studying the arithmetic and expression evaluation inthe Membrane Computing, and then it lays a solid foundation for the realization of theMembrane Computing.Because of it which researches the arithmetic in the Membrane Computing stayscurrently in the integer field, by studying the rational field arithmetic P System, thispaper able to extend use of arithmetic P System, and enhance further the biologicalcomputing performance. The following is a brief introduction to the work ofcompleted studies in this paper:1) According to the basic ideas and execution feature of the MembraneComputing, priority rule-based rational arithmetic operations P System isdesigned, and it lays a foundation for the realization of rational expressionevaluation in the Membrane Computing.2) According to the rational arithmetic P System, it designs a constructionalgorithm about rational expression evaluation in the Membrane Computing and the execution algorithm in the Membrane Computing.3) Achieved to simulation of the rational expression evaluation by using ofcomputer and it verifies correctness.4) By researching reduction of a fraction, it achieves a simplified form of the finalresults.Result of this paper is to further enrich the theory that rational arithmeticoperations and expression evaluation in the Membrane Computing and it extendsapplication of arithmetic P System, so it is able to become the references that improvethe other problems.