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 About this Textbook

In these early years of the 21^{st} 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 indepth coverage of both classical and contemporary approaches in one useful, concise volume
• Organized into readily applicable, selfcontained 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 firstyear 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 classtested 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.
 Reviews

From the reviews:
"This book represents the lecture notes of Dexter Kozen for the firstyear 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 onesemester course for firstyear 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 firstyear 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)
 Table of contents (78 chapters)


The Complexity of Computations
Pages 310

Time and Space Complexity Classes and Savitch’s Theorem
Pages 1116

Separation Results
Pages 1721

The ImmermanSzelepcsényi Theorem
Pages 2224

Logspace Computability
Pages 2529

Table of contents (78 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Theory of Computation
 Authors

 Dexter C. Kozen
 Series Title
 Texts in Computer Science
 Copyright
 2006
 Publisher
 SpringerVerlag London
 Copyright Holder
 SpringerVerlag London
 eBook ISBN
 9781846284779
 DOI
 10.1007/1846284775
 Hardcover ISBN
 9781846282973
 Softcover ISBN
 9781849965712
 Series ISSN
 18680941
 Edition Number
 1
 Number of Pages
 XIV, 418
 Number of Illustrations
 1 b/w illustrations
 Topics