Abstract:

Introducing the structure of tree into the recursion structure of the inward-recursion information,  the concept of inward-recursion binary tree is proposed. The structure and the characteristics of the tree are obtained. Also, the inward-recursion degree and the recursive loss degree are defined. The existence theorem of the inward-recursion binary tree, the existence and uniqueness theorem of the full binary tree for the inward-recursion binary tree, the theorem of the complete binary tree for the inward-recursion binary tree are given, including the identification theorems and the identification criterion of nodes for the inward-recursion binary tree. The inward-recursion binary tree is an important organization structure for the inward-recursion information. The research way and results provide a new method for information processing which has the characteristics of inward-recursion.

Key words: P-sets; inward-recursion information; inward-recursion binary tree; inward-recursion degree; identification