Analysis of simple programs over different sets of primitives

Abstract

It is well known that most questions of interest about the behavior of programs--such as equivalence, halting, optimization, and other problems--are undecidable. On the other hand, it is possible to make some or all of these questions decidable by introducing appropriate restrictions on the programming language under consideration. And once such restrictions are made, the next step is to ask how hard it is to solve these problems for programming languages for which they are decidable.This analysis of programming languages has been undertaken by others, in particular by Jones and Muchnick [4], who choose to restrict their programs to operate over finite memory. Our approach starts from the language of loop-programs, as defined by Meyer and Ritchie [1], in which we in fact allow more general arithmetical operations. Unlike Jones and Muchnick, we do not place any restriction on memory here; instead, we (primarily) restrict our attention to loop-programs without nested loops.