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Theory of computation

When I started Theory of computation by Dexter C. Kozen I had the feeling of being thrown in at the deep end. This is not the sort of book with a gentle introduction to the subject of computational complexity. Rather it is aimed at the postgraduate level, and so assumes that the student will have previous experience of the subject. That said, it seems remarkably self contained, with at least a sketch of the important proofs of the subject. It also has an extensive set of exercises for each chapter with solutions, and so would be an excellent choice for independent students, provided they have sufficient background knowledge of the subject.

The book consists of short chapters, each based on a lecture the author has given. Kozen is thus able to pack a lot into the 270 pages of the main book. The book deals well with notions such as Alternating Turing Machines and Oracles, which are only sketched upon elsewhere, and so gives the reader a good background on how to prove time and space lower bounds for computational problems. There are also supplementary lectures on subjects such as transfinite ordinals and how they fit into the theory of computational complexity. In conclusion I would say that if you're hoping to prove that P≠NP then this book will help to provide the level of knowledge of the subject that you will need.

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Hardcover 426 pages
ISBN: 1846282977
Salesrank: 723465
Weight:1.98 lbs

Published: 2006 Springer

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Hardcover 426 pages
ISBN: 1846282977
Salesrank: 602078
Weight:1.98 lbs

Published: 2006 Springer-Verlag London Ltd

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Hardcover 426 pages
ISBN: 1846282977
Salesrank: 233661
Weight:1.98 lbs

Published: 2006 Springer

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Product Description
This textbook has been written with the dual purpose to cover core material in the foundations of computing for graduate students in computer science, as well as to provide an introduction to some more advanced topics for those intending further study in the area. This book contains an invaluable collection of lectures for first-year graduates on the theory of computation, focusing primarily on computational complexity theory. Topics and features include: Organization into self-contained lectures of 3-7 pages; 41 primary lectures and a handful of supplementary lectures covering more specialized or advanced topics; 12 homework sets and several miscellaneous homework exercises of varying levels of difficulty, many with hints and complete solutions. Aimed at advanced undergraduates and first-year graduates in Computer Science or Mathematics with an interest in the theory of computation and computational complexity, this book provides a thorough grounding the foundations of computational complexity theory.

Product Description

This textbook has been written with the dual purpose to cover core material in the foundations of computing for graduate students in computer science, as well as to provide an introduction to some more advanced topics for those intending further study in the area.

This book contains an invaluable collection of lectures for first-year graduates on the theory of computation, focusing primarily on computational complexity theory. Topics and features include:

Organization into self-contained lectures of 3-7 pages;
41 primary lectures and a handful of supplementary lectures covering more specialized or advanced topics;
12 homework sets and several miscellaneous homework exercises of varying levels of difficulty, many with hints and complete solutions.

Aimed at advanced undergraduates and first-year graduates in Computer Science or Mathematics with an interest in the theory of computation and computational complexity, this book provides a thorough grounding the foundations of computational complexity theory.

I can immediately apply this book to my research *****
In 1991 I took a class at Cornell called CS681 The Design and Analysis of Algorithms ([Koz92]). At that time, Professor Kozen had finalized his manuscript for a book by the same name based on the class. I wanted to follow this class up with its sequel, CS682 Theory of Computation, but instead I went out and started a career in software engineering. Now that I am back in graduate school (at a different institution), I was pleased when i learned that the lectures for CS682 were available in the book Theory of Computation by Dexter Kozen ([Koz06]). Although the class which the book is based on has CS681 as a prerequisite, I would say that it would be a mistake to say that one needs to read [Koz92] in order to understand [Koz06]. I am only halfway through [Koz06], but it seems to me that the only prereqs required for this book are an ordinary graduate-level class in algorithms (such as CS482 at Cornell or CS600 at Stevens), a class on automata and some exposure to the NP-hierarchy and reductions. The latter is covered in CS681 at Cornell but can be learned in a wide variety of other forums including CS601 Algorithmic Complexity at Stevens. All the material required to understand this book can be found in the qualifying exams or courses for most computer science programs. Although I have only read through lecture 20 (of 41), I have found immediate applications of the material in this book to my research. In fact, last night after reading lecture 18 I was able to add a footnote to a journal submission directing the reader to this lecture for a 7/8-approximation algorithm and a proof that MaxSAT is polynomially solvable iff P=NP. These are both results that my paper cites from separate research papers and it pleased me that I was now able to point the reader to a text for further study. I also have learned about many exotic complexity classes and problems in this book, some of which I had encountered in research-level seminars in the past few years. Having a single text that I can read to learn about all of these results is a godsend. I strongly recommend this book to anyone who is pursuing study or research in computer science at the doctoral level, particularly if they have an interest in theory, complexity or cryptography. This book has already been enormously useful to me. I would like to teach a class someday based on this book.

I can immediately apply this book to my research *****

In 1991 I took a class at Cornell called CS681 The Design and Analysis of Algorithms ([Koz92]). At that time, Professor Kozen had finalized his manuscript for a book by the same name based on the class. I wanted to follow this class up with its sequel, CS682 Theory of Computation, but instead I went out and started a career in software engineering. Now that I am back in graduate school (at a different institution), I was pleased when i learned that the lectures for CS682 were available in the book Theory of Computation by Dexter Kozen ([Koz06]). Although the class which the book is based on has CS681 as a prerequisite, I would say that it would be a mistake to say that one needs to read [Koz92] in order to understand [Koz06]. I am only halfway through [Koz06], but it seems to me that the only prereqs required for this book are an ordinary graduate-level class in algorithms (such as CS482 at Cornell or CS600 at Stevens), a class on automata and some exposure to the NP-hierarchy and reductions. The latter is covered in CS681 at Cornell but can be learned in a wide variety of other forums including CS601 Algorithmic Complexity at Stevens. All the material required to understand this book can be found in the qualifying exams or courses for most computer science programs.

Although I have only read through lecture 20 (of 41), I have found immediate applications of the material in this book to my research. In fact, last night after reading lecture 18 I was able to add a footnote to a journal submission directing the reader to this lecture for a 7/8-approximation algorithm and a proof that MaxSAT is polynomially solvable iff P=NP. These are both results that my paper cites from separate research papers and it pleased me that I was now able to point the reader to a text for further study. I also have learned about many exotic complexity classes and problems in this book, some of which I had encountered in research-level seminars in the past few years. Having a single text that I can read to learn about all of these results is a godsend.

I strongly recommend this book to anyone who is pursuing study or research in computer science at the doctoral level, particularly if they have an interest in theory, complexity or cryptography. This book has already been enormously useful to me. I would like to teach a class someday based on this book.

Extremely comprehensive *****
I came across this book almost by accident, but I'm glad I did. It's among the most comprehensive coverage of theory of computation that I've seen. Understand this book, and you are basically ready to delve into active research areas within the field. This is NOT a book on automata or an introduction to theory of computation. You should already understand what theory of computation is all about before you read this book. A good introduction to the field is Sipser, although Dexter Kozen also has an introductory level book that will probably flow well into this one. This is also NOT a good place to work on basic mathematical tools. You will be expected to have them already; if you aren't good at reading mathematical proofs, you will need either extreme patience and diligence or previous work on the skill before you read this book. Topics include advanced results about basic time/space complexity classes, alternation, probablistic and parallel complexity classes, properties (complexity and decidability) of logical theories, partial recursive function theory, and other topics too numerous to mention. The text covers all major areas of the field, but the emphasis is definitely in favor of complexity results.

Extremely comprehensive *****

I came across this book almost by accident, but I'm glad I did. It's among the most comprehensive coverage of theory of computation that I've seen. Understand this book, and you are basically ready to delve into active research areas within the field.

This is NOT a book on automata or an introduction to theory of computation. You should already understand what theory of computation is all about before you read this book. A good introduction to the field is Sipser, although Dexter Kozen also has an introductory level book that will probably flow well into this one. This is also NOT a good place to work on basic mathematical tools. You will be expected to have them already; if you aren't good at reading mathematical proofs, you will need either extreme patience and diligence or previous work on the skill before you read this book.

Topics include advanced results about basic time/space complexity classes, alternation, probablistic and parallel complexity classes, properties (complexity and decidability) of logical theories, partial recursive function theory, and other topics too numerous to mention. The text covers all major areas of the field, but the emphasis is definitely in favor of complexity results.

Dexter C Kozen

Theory of computation