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This paper presents a novel approach to implementation of finite state automaton (FSA) using fatiguing Leaky Integrate and Fire (fLIF) neurons. This approach uses fLIF neurons because they are a model of biological neurons that closely approximates the basic functions of neurons. FSAs are an important mechanism for processing information. In this paper, the creation and implementation of two FSA models is described; the results show that all input sentences are correctly marked as acceptable or unacceptable.