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The research in biology has been transformed by the products of interdisciplinary research. Many works attempt to model, simulate and analyze biological processes. These studies are structured by various modeling formalisms. Among the diversity of approaches, our research focuses on deterministic finite automata as a central subject. In this research paper we used finite automata (FA) as a modeling tool to model, simulate and analyze the process of protein production. There is tremendous potential for mathematical and computational approaches in leading to fundamental insights and important practical benefits in research on biological systems. Mathematical and computational approaches have long been appreciated in physics and in the last twenty years have played an ever-increasing role in chemistry. Now more and more molecular biologist and biochemists are interested in using computer science applications and mathematical approaches in their work. In the first section, we introduce the basic concept of bioinformatics and modeling tools in biology. In the second and third sections the molecular events of protein production process is explained and then based on the molecular events, a finite automata model is constructed.