Boole函数的非线性可分性──n-维超立方体的一些计数性质

The Non-linear Separability of Boolean Functions──Some Counting Properties for n-dimensional Hypercubes

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 and non-linear separability of Boolean functions are difficult problems, in which only linearly separable problem for dimension n ≤7 had ever been discussed. This paper, on the bases of classification complexity of n-dimensional Boo1ean functions, presents a concept of to1erantly lineat c1assification of n-dimensional Boolean functions , and discusses some counting properties of n-dimensional hypercubes with the counting results presented' A1l of these are refered as the theoretical preparation for the further discussion of Boolean functions of tolerantly linear separability to be 2.