Introduction

Abstract

A computer is a large machine capable of solving a wide range of problems. The problems have certain common features, whether they relate to calculation, data processing, or other fields; they must be precisely formulated both to the human solver and to the computer, and it must be possible to find an algorithm, or program, of simple, precise instructions that leads to the solution of the problem. In general, the machine receives an input of information related to the problem (program, data, etc.), which affects the state of the machine and produces an output related to the solution. Both input and output may be represented by finite strings of symbols. A common, though not universal, feature of the programs used is iteration, exemplified by such instructions as ‘repeat until all the data has been used’ or ‘replace x by y and repeat the last 10 lines until |x − y| < 1’; it will be shown that this feature may occur even in very simple machines.