Research On Arithmetic Operations System Based On Membrane Computing

Membrane computing is a new branch of natural computing and abstracts computingmodels from the architecture and the functioning of living cells. One of the biggestadvantages of membrane computing is that it can achieve calculations in maximumdegree of parallelism. It was proved that the computing power of membrane computingis equivalent to that of Turning machine, and membrane computing’s powerful parallelcomputing ability can effectively solve the bottleneck that current computer faced. Inthis paper, our study direction is arithmetic operation systems in membrane computing,which includes hybrid encoding over multisets, fraction reduction and primedecomposition, and then lays a solid foundation for the realization of the biologicalcomputer.Because of the arithmetic operation remains to be studied, by studying hybridencoding over multisets, fraction reduction and prime decomposition, this paper able toverify the feasibility of solving complex arithmetic problems. The following is anintroduction to the work of completed studied in this paper:1) Most of existing P systems are proposed to perform arithmetic operations withthe operands encoded by positional or non-positional encodings over multisets.According to the shortcoming of these encodings, this paper presents a family ofcell-like P systems for primary arithmetic operations based on hybrid encoding,implementing arithmetic operations for large numbers by P systems. At the same time,we give examples to describe the implementation process of the rules in detail, andachieve to simulation of the P system respectively for hybrid encoding over multisets byusing computer, which is used to virify the constructed P systems.2) Propose and prove a method of fraction reduction and discuss how to carry it outin cell-like P systems with the membrane structure and the rules with priority designedaccording to the proposed algorithm. Then we give example to describe theimplementation process of the rules in detail, and achieve to simulation of the P systemfor fraction reduction by using computer, which is used to virify the constructed Psystems.3) Discuss the theoretical basis of prime decomposition and the method of primedecomposition which is suitable in cell-like P systems. Then design the primedecomposition P system based on hybrid encoding and give example to describe the implementation process of the rules in detail.Results of this paper is to further enrich the theory of arithmetic operations in the membranecomputing, and it extends application of arithmetic P systems through studying hybridencoding over multisets, fraction reduction and prime decomposition, so it is able tobecome the references that improve the other problems.