m值逻辑函数的相关度和相关系数

Correlation Degree and Correlation Coefficient of m valued Logical Functions

本文提出了ｍ（ｍ≥２为正整数）值逻辑函数的相关度和相关系数的概念；给出了任一ｍ值逻辑函数与仿射函数相关度的概率表示式及谱表示式；讨论了独立性和相关性的关系。特别在本文的定义下，ｍ值逻辑函数的相关系数圆满地保留了实值随机变量相关系数的性质。

This paper presents the concept of the correlation degree and correlation coefficient of m valued logical functions,where m is a positive integer (m≥2),gives the probabilistic and Chrestenson spectral representations of a m valued logical function with a m valued affine function,and discusses the relation between independence and correlativity.Especially,based on the definition in this paper,the correlation coefficient of m valued logical functions retains successfully the properties of the correlation coefficient of real random variables.