Accession Number : AD0475421

Title :   SOME INVESTIGATIONS IN MATHEMATICAL LOGIC.

Descriptive Note : Edited translation,

Corporate Author : FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFB OH

Personal Author(s) : K'uei, Mo Shao

Report Date : 18 OCT 1965

Pagination or Media Count : 51

Abstract : Problems in the theory of algorithms and in the theory of recursive functions are investigated. The simplification of algorithms is discussed, and the normal algorithm of Markov is shown not to be sufficiently simple and basic. The concept of middle-transformation calculi is introduced. It is a generalization of the associative calculi. Investigations concerning the problem of recognizing certain properties of calculi, and of algorithms are presented. A discussion is presented on the reductions of compositions and functionals, and a proof is given that, under appropriate restrictions, any composition of the form (m,n) can be reduced to the composition of the form (1,1), and that any set of h functionals of the form (s;n,t) can be reduced to a functional of the form (1;1,1). The problems of reduction regarding sets of recursively generated functions are considered. It is shown that, under proper restrictions and appropriate conditions, to any set S of recursively generated functions and any positive integer n, the set of functions constructed through functons of n variables in S is recursively generated.

Descriptors :   *ALGORITHMS), (*MATHEMATICAL LOGIC, (*RECURSIVE FUNCTIONS, THEORY), MATHEMATICS, CHINA, TRANSFORMATIONS(MATHEMATICS), FUNCTIONAL ANALYSIS.

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE