在开关网络(包括移位寄存器)的分析和综合,数字系统的故障检测等问题中都要涉及开关函数与某一变元无关的条件,关于这个问题文章〔1〕〔2〕都给出一些判别条件。本文通过实例指出开关函数的一个特性,给出开关函数与某一变量无关的一个新的条件,并给出这结论的数学证明,在证明中对充分性给出两种方法。设f(x_1,x_2…,X_n)是定义在V_n(F_2)=GTF(2)×G_1F(2)×…G_1F(2)X…上的一个开关函数。称f(x_1,x_2,…,x_n)与x无关,如果f(x_1…,x_(i-1),o,x_(i+1),…,x_n)=f(x_1,…,x_(i-),1,x_(i+),…,x_i)Ax_1,…,x_(i-1),x_(+1),…,x_n,EGF_((2))我们定义f(x_1,x_2,…,x_n)的重量W_((f))为 In the analysis and synthesis of the switch network (including the shift register), digital system fault detection and other issues involve the switch function has nothing to do with a certain argument, on this issue [1] 〔2〕 are given some Discriminant conditions. In this paper, a characteristic of the switch function is pointed out by an example, a new condition that the switch function is irrelevant to a certain variable is given, and the mathematical proof of this conclusion is given. In the proof, two methods are given for the sufficiency. Let f (x_1, x_2 ..., X_n) be a switching function defined on V_n (F_2) = GTF (2) × G_1F (2) × ... G_1F (2) X .... Let f (x_1, x_2, ..., x_n) be independent of x if f (x_1 ..., x_ (i-1), o, x_ (i + 1), ..., x_n) = f we define f (x_1, x_2, ..., x_i) Ax_1, ..., x_i-1, x_ (+1), ..., x_n, ..., x_n) is given by W _ ((f))