Equivalence Problems in a Model of Computation

Abstract

A central problem in the mathematical teory of computers and computation is to find a suitable framework for expressing the ececution of a computer program by a computer. Within the framework we want to be alble to provide answers to such questions as; (1) Does a certain program perform a certain task? (2) Are two programs equivalent, i.e., do they perform the same task? (3) Under what conditions, if at all, will a program fail to help? (4) how can a given program be simplified, in some sense, or made more efficient? These kinds of questions are customarily answered by experienced intuition, for simple programs, supplemented by trial and, often error for more complicated ones. We should like to replace such methods by a formalizable procedure, capable of being carried out by a computer program.