Theory of Computation: Classical & Contemporary Approaches

From the reviews: <p>"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 a ] many with hints and complete solutions. a ] 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) <p>"The book is a collection of lecture notes based on a one-semester course for first-year graduate students in computer science at Cornell a ] . 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) <p>"This textbook covers topics essential to the theory of computation. a ] 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)

The Complexity of Computations.- Time and Space Complexity Classes and Savitchs Theorem.- Separation Results.- Logspace Computability.- The Circuit Value Problem.- The Knaster-Tarski Theorem.- Alternation.- The Polynomial-Time Hierarchy.- Parallel Complexity.- Probabilistic Complexity.- Chinese Remaindering.- Berlekamps Algorithm.- Interactive Proofs.- Probabilistically Checkable Proofs.- Complexity of Decidable Theories.- Complexity of the Theory of Real Addition.- Lower Bound for the Theory of Real Addition.- Safras Construction.- Relativized Complexity.- Nonexistence of Sparse Complete Sets.- Unique Satisfiability.- Todas Theorem.- Lower Bounds for Constant Depth Circuits.- The Switching Lemma.- Tail Bounds.- Applications of the Recursion Theorem.- The Arithmetic Hierarchy.- Complete Problems in the Arithmetic Hierarchy.- Posts Problem.- The FriedbergMuchnik Theorem.- The Analytic Hierarchy.- Kleenes Theorem.- Fair Termination and Harels Theorem.- Exercises.- Hints and Solutions