Automata and Computability

by Dexter C. Kozen

Book Overview

This textbook provides undergraduate students with an introduction to the basic theoretical models of computability, and develops some of the model's rich and varied structure. The first part of the book is devoted to finite automata and their properties. Pushdown automata provide a broader class of models and enable the analysis of context-free languages. In the remaining chapters, Turing machines are introduced and the book culminates in analyses...

• Format: Hardcover
• Language: English
• ISBN: 0387949070
• ISBN13: 9780387949079
• Release Date: August 1997
• Publisher: Springer
• Length: 400 Pages
• Weight: 2.04 lbs.
• Dimensions: 1.3" x 7.1" x 9.7"

Customer Reviews

Rigorous, clear, and concise

I started learning the theory of computation using Sipser's excellent textbook. The goal of his book is to show students "the big picture" of the area by explaining the materials in an intuitive manner. However, when I was reading the first two chapters of his book (i.e. on finite automata), often times I found myself asking questions like "why does this automaton recognize that language, as Sipser claimed?". Sometimes, Sipser gives only intuitive explanations to justify his claim, which in my opinion is not sufficient. This is when Kozen's book comes in. Kozen's book is rigorous, clear, and concise (as some of the previous reviewers have remarked). Everything is explained from the basic. In particular, you will see the value of structural inductions in the theory of computation, as it is used quite often to prove statements like "the automaton L recognizes the language A" and other constructive proofs in the book. The reader will also learn how abstract algebra (more precisely, monoid and semigroup theory) can be used to prove important results in the theory of computation, e.g., Parikh's theorem and it's consequence that context-free languages over a singleton alphabet must be regular. [As an aside, monoid theory has recently been used in the proof that the problem of determing whether two deterministic pushdown automata recognize the same language is decidable (the author of the paper was rewarded Godel's prize). I believe that some future breakthroughs in the theory of computation will employ tools from monoid and semigroup theory.] Further, Kozen did a superb job in explaining the materials. So long as you have taken some courses on discrete mathematics and know the principle of mathematical induction, the book will be a quite an easy read. The book also has a great set of homework exercises and "miscellaneous" exercises with solutions/hints. I have to admit that some of these exercises are quite tough (but fear not, as they have hints/solutions). On the other hand, Kozen intentionally omitted any chapters on complexity theory in this book. In conclusion, if you are learning the theory of computation and love mathematical rigor (as I do), I strongly recommend this book. This book can also be used as a great supplement to Sipser's excellent textbook.

Very good as a textbook

This is the textbook I used for my Honors Introduction to Theory of Computing course which was taught by Kozen. This book is very well organized, each chapter corresponds exactly to one lecture, so it's almost like a collection of lecture notes in a sense. This book (and the course it's based on) provides a very good introduction to general theoretical aspects of computing. It's divided mainly into 3 sections, each covering a third of the course. First Finite Automata, then Context Free Languages and Pushdown Automata, finally Turing machines and general computability. It covers the basics very well, sprinkled with some optional lectures on more advanced topics such as Kleene Algebra (which is a favorite of Kozen)This course mainly deals with notions and models of computation, a previous reviewer noted that it doesn't include NP-completeness. There is a reason for this, because at Cornell University, this course is the first in a sequence, the second of which covers algorithms and complexity issues. That course covers NP-completeness and all the basic algorithm techniques.For those readers in a similar situation as the previous reviewer, it's difficult to find a more simple introduction to computer theory. I thought DFAs were the easiest part of the book/course, DFAs are the simplest models of computation, you can think of counting fingers as a form of DFA. I'm confident that anyone that can count will be able to understand the explanations of DFA in this book.

Definitely an excellent book

This book has been a great surprise to me. Initially I thought that in about 300 pages (excluding homeworks and exercises) I could not find all I could need for an Automata, Languages and Computation course. I was wrong, definitely. The book is coincise, but also rich and precise. The material is very well chosen, and the writing stile is directly thought with students in mind. Kozen has a pluri-annual experience in teaching at Cornell University, and it seems he has developed an effective style of communication with students, that's perfectly reflected in his books.Some important topics are present in this book and not in both Sipser and Hopcroft-Ullman. If you need (as I did) to learn about Myhill-Nerode Relations and Theorem, this book features the best account I've seen (the other, much shorter, reference can be found in the first editon of Hopcroft-Ullman but not in the second one !).A nice shot of the Lambda-calculus is also featured, and this too lacks in the other two books.The organization in lectures is a very good idea when studying. Lectures are carefully cut and self-contained, so that you can organize your time using this unit, and wherever you choose to stop a study session, you always stop at correct boundary of a topics.As a further (and important) note, the notation used is very clear and elegant. As soon as you get used with it (very soon since its clarity) it becomes very stimulating. Don't understimate this value, since many books feature too-hard-to-follow notations, or no notation at all. Both of which cases are to be avoided, INMH.I have used other books for my course, starting from both the editions of the Hopcroft and Ullman, but one way or the other I found myself always with this book (and Sipser's) in my hands.

Clear and Concise

This book is an excellent introduction to the subject. There is also material that can be taught to students more advanced than the beginning undergraduate. We used this book for one half (roughly) of a first-year grad course on foundations of computer science.The greatest strengths of the book are (1) its exceptionally clear writing. (2) Excellent collection of problems (with hints and solutions to a subset of these).This book follows the "standard" approach to the introduction of notion of effective computability in present day CS curriculum, namely the Turing Machine and formal grammars approach. There is however, thankfully, some introductory material on other formalisms like lamda calculus etc.One topic whose omission is striking is NP Completeness. It is kind of dissappointing to find a treatment of that subject missing from this wonderful text. I really find it hard to believe that Kozen does not deal with this topic in his under grad class. Considering he has a chapter on something as profound and complicated as Godel's Incompleteness Theorem (and its proof), the omission of NPC is inexplicable. (which is why I give it only 4 stars). Personally, I would have liked to see a good discussion of the Post's Correspondence problem too.In our class, we kept going back to Sipser's book on this subject, which is an outstanding book in its own right - having the best qualities of Kozen's book and The Book by Hofcroft & Ullman, for more advanced material.All in all, I think this is a great book for its intended audience.

An absolute choice to learn automata theory

The presentation is in an exceptional style of self contained lectures instead of chapters. Apart from the basic lectures, 11 supplementary lectures that cover special topics in the subject and several exercises make the book an IDEAL TEXT. I feel this recently published text is an excellent and an absolute choice to learn automata theory bit by bit, lecture by lecture!