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Abstract
P- system or membrane computation created by paun [1998] is a branch of natural computing which is a research filed that investigates both the computation designed by human being and computation taking place in nature. This model of computation is based on the processes done by the living cells and its computations are defined as applications of rules and transitions of objects. In this way, we have the same behavior of computational power as turing machine. This kind of systems computes by passing from a configuration to another by applying rules and the computation is considered complete when it halts. P-systems have two phases of computation application and communication phase, P- systems are massively parallel and distributed model of computation, there are some models of simulation has been developed but do not usually allow this parallel. This thesis investigates an alternative system to the P- system model using the persistent turing machine (PTM). The proposed system likewise P- systems has two phases of computation application and communication phases. We introduce the design of the application phase and leave the communication phase for another research. Our design considers each membrane in the system membrane structure as a machine and the design of this machine will be explained using state transition graphs. Also the thesis simulating transition P- system using persistent turing machine Model under condition which is the rules are applied in predefine order (priority), where the rules applied in an ascending order according to the rules execution priorities. According to this view, the P Systems has the same relevance of PTM, and each membrane in the P- system can be considered as the simplest machine in the transition P- systems