Introduction to Computer Theory
CHAPTER 1
BACKGROUND
The twentieth century has been filled with the most incredible shocks and surprises: the theory of relativity, Communist revolutions, psychoanalysis, nuclear war, television, moon walks, genetic engineering, and so on. As astounding as any of these is the advent of the computer and its development from a mere calculating device into what seems like a "thinking machine." The birth of the computer was not wholly independent of the other events of this century. The history of the computer is a fascinating story; however, it is not the subject of this course. We are concerned with the Theory of Computers, which means that we form several abstract mathematical models that will describe with varying degrees of accuracy parts of computers and types of computers and similar machines. Our models will not be used to discuss the practical engineering details of the hardware of computers, but the more abstract questions of the frontiers of capability of these mechanical devices. There are separate courses that deal with circuits and switching theory (computer logic) and with instruction sets and register arrangements (computer ar-chitecture) and with data structures and algorithms and operating systems and compiler design and artificial intelligence and so forth. All of these courses have a theoretical component, but they differ from our study in two basic ways. First, they deal only with computers that already exist; our models, on
3
4
AUTOMATA THEORY
the other hand, will encompass all computers that do exist, will exist, and that can ever be dreamed of. Second, they are interested in how best to do things; we shall not be interested in optimality at all, but rather we shall be concerned with the question of possibility-what can and what cannot be done. We shall look at this from the perspective of what language structures the machines we describe can and cannot accept as input, and what possible meaning their output may have. This
BACKGROUND
The twentieth century has been filled with the most incredible shocks and surprises: the theory of relativity, Communist revolutions, psychoanalysis, nuclear war, television, moon walks, genetic engineering, and so on. As astounding as any of these is the advent of the computer and its development from a mere calculating device into what seems like a "thinking machine." The birth of the computer was not wholly independent of the other events of this century. The history of the computer is a fascinating story; however, it is not the subject of this course. We are concerned with the Theory of Computers, which means that we form several abstract mathematical models that will describe with varying degrees of accuracy parts of computers and types of computers and similar machines. Our models will not be used to discuss the practical engineering details of the hardware of computers, but the more abstract questions of the frontiers of capability of these mechanical devices. There are separate courses that deal with circuits and switching theory (computer logic) and with instruction sets and register arrangements (computer ar-chitecture) and with data structures and algorithms and operating systems and compiler design and artificial intelligence and so forth. All of these courses have a theoretical component, but they differ from our study in two basic ways. First, they deal only with computers that already exist; our models, on
3
4
AUTOMATA THEORY
the other hand, will encompass all computers that do exist, will exist, and that can ever be dreamed of. Second, they are interested in how best to do things; we shall not be interested in optimality at all, but rather we shall be concerned with the question of possibility-what can and what cannot be done. We shall look at this from the perspective of what language structures the machines we describe can and cannot accept as input, and what possible meaning their output may have. This