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Boole函数的线性可分和线性不可分问题，一直是前向人工神经网络的一个比较困难的问题，目前仅对变量数n≤7的线性可分问题给予过讨论。本文在文献［1］中所提出的n-维Boole函数分类复杂度定义的基础上，提出了n－维Boole函数容错分类复杂度的概念，并讨论了n-维超立方体的一些计数性质，给出了计数结果，从而为进一步讨论容错分类复杂度为2的Boole函数及其计数问题做了理论上的准备。
The linear separable and linear inseparable problems of Boole function have always been a difficult problem for the forward artificial neural network. At present, only the linear separable problems with n ≤ 7 variables are discussed. Based on the definition of classification complexity of n-dimensional Boole function proposed in [1], this paper proposes the concept of fault-tolerant classification complexity of n-dimensional Boole function and discusses some counting properties of n-dimensional hypercubes. The result of counting is given, which provides a theoretical preparation for further discussing the Boole function with fault-tolerant classification complexity of 2 and its counting problem.