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Two-level fractional factorial design is an efficient technique for experiments considering a large number of factors. To evaluate the efficiency and analyze the data for such a design, we need to know the generators for the design, so that, using the generators, we can generate its defining relation and alias structure. Although knowing the generators is important for a two-level fractional factorial design, it is not unusual in actual industrial situations for the generators used in the design to be lost or overlooked while the design is performed. Since Taguchi methods has been widely applied in industry, in this research, an efficient algorithm based on Taguchi orthogonal arrays (OA's) and interaction tables is developed to identify the generators for given designs. Furthermore, with the investigation of the insights of Taguchi OA's and interaction tables, this research may provide ideas for making Taguchi methods a simple tool for developing optimal designs for 2^{k - p} experiments.