A Theory of Computer Instructions
This paper has arisen from an attempt to determine the nature of computer instructions from a viewpoint of general function and set theory. Mathematical machines, however the term is understood, are not adequate models for the computers of today; this is true whether we are talking about Turning machines, sequential machines, push-down automata, generalized sequential machines, or any of the other numerous machine models that have been formulated I the last fifteen years. Most of these models are either not general enough, as the sequential or Turning machines with their single input and output devices; or capable of accurately reproducing only one important programming feature; or in a sense too general (see discussion of sequential machines in Chapter 10 below). On the other hand, modern computers, whether they are binary, decimal, or mixed, whether they have one or two instructions per word, or one instruction covering several words, have several important common features, All of their instructions have input, output, and affected regions (in the sense of Definitions B and K below). The study of the input and output regions and the structure of affected regions of all the instructions on a given computer can provide a key to its logical efficiency.