相关免疫函数的谱与感知机表示

On the Spectral and Perceptron Representation of Correlation - Immune Functions

本文将ＧＦｎ（２）＝｛０，１｝ｎ上布尔函数的相关免疫（ＣＩ）性概念等价地引入到｛－１，１｝ｎ上，并基于｛－１，１｝ｎ上布尔函数的多项式表示，给出了ＣＩ函数的谱表示及其充要判别条件，首先得出了ｍ阶ＣＩ函数一般不能由ｍ阶感知机所表示这一结论，从而在一定意义上否定了用单展感知机攻击前馈组合函数的可能性。

Based on the polynomial representation of Boolean functions over{ -1,1 }n, the spectral representation and equivalent conditions of CI functions are presented,and the perceptronr epresentation of CI functions is investigated.It is,to certain degree, impossible to attack on the combining functions by perceptrons.