Theory of Computation (Texts in Computer Science) [Hardcover]

Dexter C. Kozen (Author)

Book Description

Publication Date: March 23, 2006 | ISBN-10: 1846282977 | ISBN-13: 978-1846282973 | Edition: 1st Edition.

This textbook is uniquely written with dual purpose. It cover cores material in the foundations of computing for graduate students in computer science and also provides an introduction to some more advanced topics for those intending further study in the area. This innovative text focuses primarily on computational complexity theory: the classification of computational problems in terms of their inherent complexity. The book contains an invaluable collection of lectures for first-year graduates on the theory of computation. Topics and features include more than 40 lectures for first year graduate students, and a dozen homework sets and exercises.

Editorial Reviews

Review

From the reviews: "This book represents the lecture notes of Dexter Kozen for the first-year graduate students in computer science at Cornell University. The book contains 41 primary lectures and 10 supplementary lectures covering more specialized and advanced topics. There are also 12 homework sets and several miscellaneous homework exercises … many with hints and complete solutions. … there is a bibliography of 127 titles. The book contains a very useful list of notations and abbreviations and an index." (Daniela Marinescu, Zentralblatt MATH, Vol. 1102 (4), 2007) "The book is a collection of lecture notes based on a one-semester course for first-year graduate students in computer science at Cornell … . The course serves a dual purpose: to cover material in the foundations of computing for graduate students in computer science preparing for their Ph.D. qualifying exams, and to provide an introduction to some more advanced topics in the theory of computational complexity for those intending to pursue further study in the area." (Ulrich Tamm, Mathematical Reviews, Issue 2007 f) "This textbook covers topics essential to the theory of computation. … In short, this is an interesting and enjoyable book that is strongly recommended to people who appreciate accuracy and concision. It will surely be an important textbook on the theory of computation for years to come. The intended audience is advanced undergraduate and first-year graduate students in computer science. It could also be useful to computer scientists with an interest in the foundation of computing and computational complexity." (G. Ciobanu, Computing Reviews, Vol. 49 (5), May, 2008) "Kozen does a great job of explaining the material… The book is a continuation of the author’s excellent work in the field… The 12 homework sets, along with several miscellaneous problem sets, make this book an excellent pedagogical option for the classroom." (Hector Zenil, ACM Computing Reviews, Vol. 49 (9), September 2008)

From the Back Cover

In these early years of the 21st Century, researchers in the field of computing are delving ever further into the new possibilities of the science and to the primary tools that form its foundations. The theory behind computation has never been more important. Theory of Computation is a unique textbook that serves the dual purposes of covering core material in the foundations of computing, as well as providing an introduction to some more advanced contemporary topics. This innovative text focuses primarily, although by no means exclusively, on computational complexity theory: the classification of computational problems in terms of their inherent complexity. It incorporates rigorous treatment of computational models, such as deterministic, nondeterministic, and alternating Turing machines; circuits; probabilistic machines; interactive proof systems; automata on infinite objects; and logical formalisms. Although the complexity universe stops at polynomial space in most treatments, this work also examines higher complexity levels all the way up through primitive and partial recursive functions and the arithmetic and analytic hierarchies. Topics and features: • Provides in-depth coverage of both classical and contemporary approaches in one useful, concise volume • Organized into readily applicable, self-contained primary and secondary lectures • Contains more than 180 homework exercises of varying difficulty levels, many with hints and solutions • Includes approximation and inapproximation results, and some lower bounds • Treats complexity theory and classical recursion theory in a unified framework Advanced undergraduates and first-year graduates in Computer Science or Mathematics will receive a thorough grounding in the core theory of computation and computational complexity, as well as an introduction to advanced contemporary topics for further study. Computing professionals and other scientists interested in learning more about these topics will also find this text extremely useful.  Prof. Dexter Kozen teaches at Cornell University, Ithaca, New York, and has comprehensively class-tested this book’s content. He authored the highly successful Automata and Computability, which offers an introduction to the basic theoretical models of computability, and The Design and Analysis of Algorithms.

Product Details

• Hardcover: 440 pages
• Publisher: Springer; 1st Edition. edition (March 23, 2006)
• Language: English
• ISBN-10: 1846282977
• ISBN-13: 978-1846282973
• Product Dimensions: 9.3 x 7.3 x 1 inches
• Shipping Weight: 2 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,418,270 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

10 of 10 people found the following review helpful:

5.0 out of 5 stars Extremely comprehensive, November 26, 2006

By 

Christopher D. Smith (Colorado Springs, CO) - See all my reviews
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This review is from: Theory of Computation (Texts in Computer Science) (Hardcover)

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.

7 of 7 people found the following review helpful:

5.0 out of 5 stars I can immediately apply this book to my research, June 11, 2007

By 

Michael de Mare (Hoboken, NJ United States) - See all my reviews
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This review is from: Theory of Computation (Texts in Computer Science) (Hardcover)

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.