"Algebraic Structure Theory of Sequential Machines" will seem hopelessly out of date to some people, but the contemporary interest in concurrency gives the book a new found importance. I have a complete searchable scan of the book that I would post online if I knew how to get permission from Prentice-Hall. Does anyone have any ideas?

Here is the very interesting preface of the book.

The explosive development of information-processing technology during

the last two decades has stimulated the vigorous growth of an Information

Science. This new science is primarily concerned with the study of information

and the laws which govern its processing and transmission. A very

active part of this science is the study of sequential machines or finite automata

which are abstract models of digital computers. The aim of this research

is to provide a basic theoretical background for the study of digital computers

and to contribute to a deeper understanding of discrete or finite

information-processing devices. This area of research was started around

1954 by D. A. Huffman and E. F. Moore and has since undergone a considerable

growth in several diverse directions. In the period from 1960 to

1965, a body of results we call "structure theory" was created and developed

to a considerable degree of completeness and unity. This book is an exposition

on the foundations, techniques, and applications of this theory.

By a structure theory for sequential machines, we mean an organized

body of techniques and results which deal with the problems of how sequential

machines can be realized from sets of smaller component machines, how

these component machines have to be interconnected, and how "information"

flows in and between these machines when they operate. The importance of

machine structure theory lies in the fact that it provides a direct link between

algebraic relationships and physical realizations of machines. Many structure

results describe the organization of physical devices (or component machines)

from which a given machine can be synthesized. Stated differently, the

structure theory describes the patterns of possible realizations of a machine

from smaller units. It should be stressed, however, that although many

structure theory results describe possible physical realizations of machines,

the theory itself is independent of the particular physical components or

technology used in the realization. More specifically, this theory is concerned

with logical or functional dependence in machines and studies the information

flow of the machine independently of how the information is represented

and how the logical functions are to be implemented.

The mathematical foundations of this structure theory rest on an algebraization

of the concept of "information" in a machine and supply the algebraic

formalism necessary to study problems about the flow of this information

in machines as they operate. The formal techniques and results are

very closely related to modern algebra. Many of its results show considerable

similarity with results in universal algebra, and some can be directly derived

from such considerations. Nevertheless, the engineering motivation demands

that this theory go its own way and raises many problems which require

new mathematical techniques to be invented that have no counterpart in

the development of algebra. Thus, this theory has a characteristic flavor and

mathematical identity of its own. It has, we believe, an abstract beauty

combined with the challenge and excitement of physical interpretation and

application. It falls squarely in the interdisciplinary area of applied algebra

which is becoming a part of engineering mathematics.

This book is intended for people interested in information science

who have either an engineering or mathematical background. It can be read

by anyone who has either some mathematical maturity, achieved through

formal study, or engineering intuition developed through work in switching

theory or experience in practical computer design.

Enough concepts of machine theory and machine design are introduced

in the first chapter so that a mathematician may read the book without any

experience with computers or switching theory. A preliminary chapter on

basic algebraic concepts supplies enough mathematics to make the book

self-contained for a non-mathematician. A good number of examples are

given to supply the engineer with an interpretation or application of the

mathematics.

J. HARTMANIS

R. E. STEARNS

## Recent comments

19 weeks 6 days ago

24 weeks 1 day ago

25 weeks 5 days ago

25 weeks 5 days ago

28 weeks 3 days ago

33 weeks 17 hours ago

33 weeks 19 hours ago

33 weeks 3 days ago

33 weeks 3 days ago

36 weeks 2 days ago