归纳定义与递归算法

Inductive Definition and Recursive Algorithm

归纳定义是定义某些概念时常用到的一种定义方法，但是，什么叫做“归纳定义”并没有严格的说法，本文从代数系统的观点出发，对归纳定义进行了严格的数学定义。递归算法是编程时经常使用的一种算法设计方法，其思想就是算法本身调用自己。本文对归纳定义与递归算法之间的联系进行了深入的讨论和研究，结论是：利用归纳定义所定义的概念一定可以利用递归算法进行判定；反之，由递归算法可以判定的概念一定能够进行归纳定义。

Inductive definition is a method which is used to define some concepts, but what is the inductive definition bas not a strict description yet. In this paper the auther, proceeding from the algebra system, gives a strict definition to the inductive definition. Recursive algorithm is B Programming method which is often adOPted in program designs, its basic thinking is to transfer itself by itself. Then, is there any relation between inductive definition and recursive algorithm ? the auther bas studied this problem thoroughly and concludes that a concept that is defined by inductive defiultion can be decided by a recursive algorithm, and the converse is also true.