Part I. Preliminaries
Part II. Methods and Analysis
Part III. Limitations and Robustness
Part IV. Relaxing the Rules
Part V. The Bigger Picture
Read this, I pray thee
This book tells a story. The story concerns the concepts, ideas, methods and results fundamental to computer science. It is not specifically about computer technology, nor is it about computer programming, though obviously it is heavily influenced by both.
The book is intended to fill a rather disturbing gap in the literature related to the computer revolution. Scores of excellent books can be found on computers themselves, with details of their structure, workings, and operation. There are also numerous books about the act of writing programs for the computers in any of a growing number of languages. These books come at a wide range of levels, some aimed at people with no computer-related background at all, and some aimed at the most computer-literate professionals. In addition, there are many books on subjects peripheral to the technology, such as the social and legal aspects of the revolution, as well as books describing the relevance of computers to a variety of application areas. All this comes as no surprise. People are curious about computers, and want to learn how to put them to use. They are typically interested in specific kinds of computers, and often for specific purposes, too.
Then there are textbooks. Indeed, computer science is a fast-growing academic discipline, with ever-larger numbers of potential students knocking at the doors of admission offices. Well-established academic disciplines have a habit of yielding excellent textbooks, and computer science is no exception. Over the years many comprehensive and clearly written textbooks have appeared, containing detailed technical accounts of the subjects deemed appropriate to students of computer science. However, despite the dizzying speed with which some of the technological innovations become obsolete and are replaced by new ones, the fundamentals of the science of computation, and hence many of the basic concepts that are considered important in a computer science curriculum, change slowly, if at all. Of course, new technologies and new languages require revisions in scientific emphasis, which are eventually reflected in the scientific literature. However, by and large, there is almost universal agreement on a core of fundamental topics that computer science students should be taught.
It would appear that anyone associated with computers ought to be aware of these topics, and not only those who have decided to spend three or four years getting a particular kind of academic diploma. Moreover, given that a revolution is indeed taking place before our very eyes, many of these topics, and the special ways of thinking that go with them, ought to be available to the enquiring person even if that person is not directly associated with a computer at all.
Books concerned primarily with computers or programming are intended to fulfill quite different needs. Computers are made of bits and bytes, and programming is carried out using languages with rigid rules of grammar and punctuation. Consequently, computer books often suffer from the "bit/byte syndrome" and programming books from the "semicolon syndrome". In other words, the reader becomes predominantly involved in the principles of a particular computer or the syntactic rules of a particular programming language (or both). It would seem that things cannot be explained without first describing, in detail, either a machine or a medium for communicating with one (or both).
Many advanced textbooks do treat the fundamentals, but by their very nature they concentrate on specific topics, and do so at an advanced technical level that is usually unsuitable for the general reader. Even professional programmers and systems analysts might lack the background or motivation required to get through books aimed at full-time computer science students.
Curiously, there appears to be very little written material devoted to the science of computing and aimed at the technically-oriented general reader as well as the computer professional. This fact is doubly curious in view of the abundance of precisely this kind of literature in most other scientific areas, such as physics, biology, chemistry, and mathematics, not to mention humanities and the arts. There appears to be an acute need for a technically-detailed, expository account of the fundamentals of computer science; one that suffers as little as possible from the bit/byte or semicolon syndromes an their derivatives, one that transcends the technological and linguistic whirlpool of specifics, and one that is useful both to a sophisticated layperson and to a computer expert. It seems that we have all been too busy with the revolution to be bothered with satisfying such a need.
This book is an attempt in this direction. Its objective is to present a readable account of some of the mot important and basic topics of computer science, stressing the fundamental and robust nature of the science in a form that is virtually independent of the details of specific computers, languages, and formalisms.
This book grew out of a series of lectures given by the author on "Galei Zahal", one of Israel's national radio channels, between October 1984 and January 1985. It is about what shall be called algorithmics in this book, that is, the study of algorithms. An algorithm is an abstract recipe, prescribing a process that might be carried out by a human, by a computer, or by other means. It thus represents a very general concept, with numerous applications. Its principal interest and use, however, is in those areas where the process is to be carried out by a computer.
The book could be used as the basis of one-semester introductory course in computer science or a general computer science literacy course in science and engineering schools. Moreover, it can be used as supplementary reading in many kinds of computer-related educational activities, from basic programming courses to advanced graduate or undergraduate degree programs in computer science. The material covered herein, while not directly aimed at producing better programmers or system analysts, can aid people who work with computers by providing an overall picture of some of the most fundamental issues relevant to their work.
The preliminary chapters discuss the concept of an algorithmic problem and the algorithm that solves it, followed by cursory discussions of the structure of algorithms, the data they manipulate, and the languages in which they are programmed. With the stage thus set, the first chapter of Part Two turns to some general methods and paradigms for algorithmic design. This is followed by two chapters on the analysis of algorithms, treating, respectively, their correctness and efficiency (mainly time efficiency), including techniques for establishing the former and estimating the latter. Part Three of the book is devoted to the inherent limitations of effectively executable algorithms, and hence of the computers that implement them. Certain precisely defined problems, including important and practical ones, are shown to be provably not solvable by any computers of reasonable size in any reasonable amount of time (say, the lifetime of a person), and never will be. Worse still, it is shown that some problems are provably not solvable by computers at all, even with unlimited time! In Part Four of the book the requirements are relaxed, for example, by employing concurrent activities or coin tossing, in order to overcome some of these difficulties. These chapters also discuss reactive and distributed systems, and cryptography. Finally, the relationship of computers to human intelligence is discussed, emphasizing the "soft" heuristic, or intuitive, nature of the latter, and the problems involved in relating it to the "hard" scientific subject of algorithmics.
The book is intended to be read or studied sequentially, not be used as a reference. It is organized so that each chapter depends on the previous ones, but with smooth readability in mind. Most of the material in the preliminary Part One should be familiar to people with a background in programming. Thus, Chapters 1 and 2 and parts of Chapter 3 can be browsed through by such readers.
Certain sections contain relatively technical material and can be skipped by the reader without too much loss of continuity. They are indented, set in smaller type and are prefixed by a small square. It is recommended, however, that even those sections be skimmed, at least to get a superficial idea of their contents.
Whenever appropriate, brief discussions of the research topics that are of current interest to computer scientists are included. The text is followed by Bibliographic Notes for each chapter, with "backward" pointers connecting the discussions in the text with the relevant literature.
It is hoped that his book will facilitate communication between the various groups of people who are actively involved in the computer revolution, and between that group, and those who, for the time being, are observers only.
David Harel; Pittsburgh, PA; February 1987
See, this is new; but it has
The first edition of this book was intended to be read from beginning to end; it could also be used as a supplementary reading in a number of courses. Teaching a course based exclusively on it was possible, but would have required that the instructor prepare exercises and add examples and more detail in certain places. The present edition contains numerous exercises, as well as solutions to about a third of them. The solved exercises can thus be used to supplement the text.
Three chapters do not have exercises: Chapter 1 is an introduction, the bulk of Chapter 3 is really just a brief survey of several programming languages, and Chapter 12 is a nontechnical account of some topics in artificial intelligence. In a sense, these chapters are not integral parts of the topic of the book -- algorithmics -- and hence in teaching a course based on the book these should probably be assigned as homework reading.
Apart from the inclusion of exercises and solutions, which mark the most obvious change made in this edition, the text has been revised and updated. The reader may wonder why a more extensive revision of the text was not called for. Have computer scientists been idle during the five years since the first edition was published? Rather than taking this as a criticism of the field, I think that it shows that the topics selected for inclusion in the book are really of fundamental nature, so that no significant changes had to be made. The issues discussed herein are thus probably basic and lasting; maybe the term "classical" is most fitting.
David Harel; Rehovot, Israel; May, 1991
they three were of one measure
This time around, a significant revision was carried out. There are several
important changes in this edition of the book, compared to the first and second
editions, including two brand new chapters, new sections, and more.
a threefold cord is not
Write the vision, and make it
plain upon tablets