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We propose a new method for the use of genetic algorithm to synthesize a finite state machine (FSM) consistent with a given input/output sequence set. Our approach improves the method previously used by many researchers based on omitting the evolution of the complete FSM, but rather evolve only the state transition function. The output is later inferred from the input/output sequence set. The results show that our method is able to solve a much larger problem size than the previous approach.