Introduction to the Theory of Computation

As a teacher of the subject, I have had the chance to evaluate numerous books on the theory of computation. Of all the available texts, I think this one is the most appropriate for CS students. In the past I taught out of Dexter Kozen's book, which is incredibly elegant, but had some resistance from the students. Thinking it over I decided that Kozen's text, although beautiful, may be better suited to students pursuing a degree in pure math. Sipser's book, on the other hand, is more gentle. I find that Sipser demands far less mathematical maturity from his readers, and thus allows the difficulty to be shifted from excessive formalism to the inherent challenges present in the material. In addition, following Sipser's treatment, I was able to cover finite state machines and pushdown automata in far less time, thus allowing me to concentrate on computability and beyond. The book really shines in its treatment of computability theory, eloquently directing attention to some of the most beautiful aspects. Another benefit of Sipser's book is the exercises, of which there are many more in this edition. Someone studying on their own should find the initial group of exercises in each section quite approachable. Even the more challenging problems are not incredibly hard, and typically draw their difficulty from the deeper themes of the chapter instead of obscure details. If you are looking for an enjoyable, well-paced book with an introduction to computability and complexity that is truly inspiring, this is the one for you. A mathematician looking for a bit more rigor may do better with Kozen.

The theory of computation represents a fascinating landscape that intersects computer science and mathematics and can be roughly divided into three overlapping areas: automata and formal languages, computability theory, and computational complexity. And there is enough interesting knowledge about each area to fill three books, each twice the size of this one. And because of this I find it remarkable that the author has succeeded in filling a slim volume with the essential theory and results from each area, in a style that not only seems very accessible and intuitive, but also demonstrates important relationships between the three areas. For example, most books on computability theory do not discuss automata outside of Turing machines, but in his book Sipser elegantly proves that the equivalence problem is decidable for deterministic finite automata, but undecidable for pushdown automata. Not only does the author have very good coverage of the three areas, but he also is able to strike a nice balance between mathematical rigor and intuitive understanding. His "proof idea" proof preambles greatly helped my students better understand the main ideas behind each result. In terms of coverage I found only a handful of introductory topics that were neglected: Greibach Normal Form, Rice and Rice-Shapiro Theorems, algebraic aspects of formal languages, Turing degrees, and perhaps context sensitive languages. With that said, remember that this book is just a semester-long introduction to a vast landscape. I recommend the following books for more depth: Peter Linz, "Introduction to Formal Languages and Automata"; Nigel Cutland, "Introduction to Computability Theory"; Christos Papadimitriou, "Computational Complexity". Another strength of the book is how the author distinguishes exercises and problems: "exercises" are similar to the worked out examples, and can be solved by following one of the presented examples, algorithms or theorems, while "problems" require significant expository writing and deeper insight. Most undergraduates should be able to handle the exercises, but will find the problems very challenging if not impossible, due to the fact that students at this level are mostly familiar with problems that can be solved in a few steps by following some algorithm. So these problems have the capability of developing student intellect, but if assigned in too large a quantity can break the spirit of the developing student. Have care! I congratulate Dr. Sipser on this fine book. May it inspire millions of readers to question the meaning of computation and explore its possibilities and limitations.

Michael Sipser has an undoubted gift for writing on this subject. The book is a coincise and easy read. But be cautious, this doesn't mean superficial and poor. The book contains all the material needed for a good course on Theory of Computation and Complexity. Perhaps it has not plenty of details like other books as Hopcroft & Ullman or Kozen or Papadimitrou, but don't underestimate the vastity of the treated topics, what is important is that every time you finish a chapter, you have the sensation that you've learned what you should have to. And probably you did due to Sipser's writing style, provided that you can afford to skip "some" more detailed/advanced topics. Or you might just be looking for some further stuff like Myhill-Nerode or Rabin-Shepherdson theorems or Chomsky Hierarchy for example, and you would have to look elsewhere for them. However, I've never been told that the best book is the most complete one. As long as I've learned, the best book is the one that best fits your needs, and that fitting these needs it suceeds to transmit the knowledge you're looking for in an effective way. That's why if this stuff is not required by your course, you would be perfectly fine with this book in your hands.Proofs on theorems are given virtually always in two steps: first you're presented with the idea that lies behind the proof, and then you get the proof itself in a more rigorous fashion. Again, Sipser strikes here because it's harder NOT to understand one of his proofs than the contrary simply because the presentation is always clear and understandable.As a matter of fact, Sipser (as he point out in the preface) almost always avoid to overload proofs given by construction with more rigorous following proofs (e.g. induction on the constructed machine to prove its equivalence with ...). This has a strong impact on the attention you can keep when studying throghout a chapter: avoiding to dive into tedious details when the proof (by construction) has been clear enough help to keep you attention high and boredom away. This is a way of learning, an effective way.Sipser uses sometime a notation that's different from the somewhat standard one (e.g. the description of delta or transition function on various machines), but it is coherent throughout the whole book, and that's what does count, together with the note that this notation is noway more complex or hard to understand than the "standard" one.Should I name two books on Theory of Computation (not Complexity), one just a little less rigorous and one just a little more rigorous than this, I would suggest Coehn's "Introduction to computer Theory" and Kozen's "Automata and Computability" respectively.My conclusion is that this is a great book, worth the price (especially if confronted with others ...) and a stable place in my bookshelf.

Reading this book changed my entire set of beliefs regarding the importance and usefulness of computational theory (and math) in computer science. I have been programming since grade 7, yet only after reading this book do I feel like I really have a grasp of it on a fundamental level. Its like there was this whole other world under my nose that I caught passing glimpses of yet was never able to put together. Like in DOS: c:>dir *, why use a star character? Why is XML the way it is? The list goes on and on. This book tied *alot* of 'loose ends' for me.<p>I always felt that being a cs-tist was about programming, object oriented design/analysis, design patterns, UML, etc.. And there is no doubt that mastery of these technologies are required of any good cs-tist. However, if you want to understand where all these technologies you use come from, how they connect, and to get a glimpse of where its all going, you must combine your current programming and trend following expertise with knowledge of the underlying theories of computation.<p>This book should be required reading for all first year CS students so that they may get the 'big picture' right from the start and be able to see CS as a whole rather than a bunch of 'kinda related' courses. I see this book inspiring a whole generation of cs-tists - many of whom may have gone into other professions after reading books like 'Introduction to Automata Theory, Languages, and Computation' by Ullman, Hopcroft (a great, rigorous treatment of cs, but *not* a good book to learn from or be inspired by).<p>Again, great book!

I bought this book in a desperate attempt to pass a Theory of Computation course in which I was enrolled. I was stuck in the sad situation of having a non-English speaking, difficult to understand professor. In addition, the required text for the course was awful. Thanks to Sipser's book, I not only avoided dropping the course, but managed to get an A. (I'm not exagerating). Sipser's book is fantastic compared to others on the subject. It is written in easy to understand, plain, no-nonsense language. (Even the section on pumping lemma is understandable) I became aware of Sipser's book as a result of reading a customer's negative review of another (more expensive) book (Intro to Languages & theory of Computation by J. Martin) on the same subject. The reviewer suggested buying this book by Sipser instead, and that advice was excellent. (Many thanks to that reader, whoever you are!) If you are considering heading for the drop course line at the registrar's office, try this book before you give up and quit!