函数恒等的数值判定及其机器实现问题

Numerical value determinant of function equality and its machine implementation

本文主要介绍了一种判定函数恒等的方法。这种方法的基本思想是 ,对于给定集 X到 Y上的函数集 ,寻找定义域 X中的一点 x,使得对任意 f ,g∈ ,f≡ g当且仅当 f ( x) =g( x) ,从而把 f与g恒等判定问题归结为 f与 g是否在点 x相等的判定问题。本文证明了这种方法对于相当大的一类函数集都成立。同时 ,并对这种方法的失误概率进行了讨论。得出在通常情况下其失误概率为零。

In this paper, a method is introduced to determine whether two functions are equal. The base idea of this mathod is: give a set of functions , from a set X to a set Y , find a point in X , for f,g ∈ , iff f()=g() . Thus simplified the problem of determining f≡g to determining f=g at the point . We proved that this method is efficient for a lot of sets of functions. At the same time, we discussed its failure probability,and we proved that its failure probability is zero at the common case.