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P systems or membrane systems provide a high level computational modeling framework that combines the structural and dynamic aspects of biological systems in a relevant and understandable way. P systems are massively parallel distributed, and non-deterministic systems. In this paper, we describe the implementation of a simulator for the class of recognizer P systems with active membranes by using the GPU (graphics processing unit). We compare the high performance parallel simulator for the GPU to the simulator developed on a single CPU (central processing unit), and we show that the GPU is better suited than the CPU to simulate P systems due to its highly parallel nature.