Theoretical models of simple computing mahcines, known as automata, play a central role in theoretical computer science. This textbook presents an introduction to the theory of automata and to their connections with the study of languages. At the heart of the book is the notion that by considering a language as a set of words it is possible to construct automata which `recognize' words in the language. Consequently one can generate a
correspondence between a hierarchy of machines and a corresponding hierarchy of grammars and languages. Professor Howie leads the reader from finite state automata through pushdown
automata to Turing machines. He demonstrates clearly and elegantly the fundamental connections between automata and abstract algebra via the notions of syntactic monoid and minimal automaton. The author presupposes a basic familiarity with modern algebra, but beyond this the book is self-contained. As a result, the book will make ideal reading for students of mathematics and computer science approaching this subject for the first time.
'a deeply and rigorously mathematical text'
Mike Holderness, New Scientist
'Highly readable and with many exercises (with solutions).'
'The presentation is clear and rigorous, the precise definitions being preceded by introductory examples that motivate them ... presents two distinguishing features. First, it illustrates very nicely the use of algebraic notation and methods and, second, its final chapter covers important material not easily accessible to students. It is a very welcome addition to the literature and is recommended as a textbook with mathematical sophistication.'
Paulo A.S. Veloso, The Computer Journal, Vol. 36, No. 6, 1993
'One finds all the essential facts on automata and formal languages. Style and form of presentation of this book give evidence of the beauty of applied algebra, not only for those who are interested in semigroup-theory.'
H. Mitsch, Monashefte fur Mathematik, Vol. 116, No. 2, 1993