On Analysis and Judgment of Balance for Boolean Functions by E-Derivative

Abstract

Using the derivative of the Boolean function and the e-derivative defined by ourselves as research tools and deeply into the internal structure of Boolean, we study the issues of the analysis and judgment of balance for Boolean functions. We get that the linear functions and the nonzero derivative of the product of two linear functions are balanced functions, and the product of two linear functions are not balanced functions. We also obtain the quadratic homogeneous Booleans are not all balanced function. Besides, we deduce the theorem which determine the sum of linear function and balanced function whether it is a balanced function. What is more, the features of balance of Boolean functions can be reflected easily and effectively by e-derivative.