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This paper presents a new method to express functional permissibilities for look-up table (LUT) based field programmable gate arrays (FPGAs). The method represents functional permissibilities by using sets of pairs of functions, not by incompletely specified functions. It makes good use of the properties of LUTs such that their internal logics can be freely changed. The permissibilities expressed by the proposed method have the desired property that at many points of a network they can be simultaneously treated. Applications of the proposed method are also presented; a method to optimize networks and a method to remove connections that are obstacles at the routing step. Preliminary experimental results are given to show the effectiveness of our proposed method.