Theory of Computation (Hardcover)

Dexter C. Kozen




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.


Table of Contents

The Complexity of Computations.- Time and Space Complexity Classes and Savitch’s Theorem.- Separation Results.- Logspace Computability.- The Circuit Value Problem.- The Knaster-Tarski Theorem.- Alternation.- The Polynomial-Time Hierarchy.- Parallel Complexity.- Probabilistic Complexity.- Chinese Remaindering.- Berlekamp’s 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.- Safra’s Construction.- Relativized Complexity.- Nonexistence of Sparse Complete Sets.- Unique Satisfiability.- Toda’s 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.- Post’s Problem.- The Friedberg–Muchnik Theorem.- The Analytic Hierarchy.- Kleene’s Theorem.- Fair Termination and Harel’s Theorem.- Exercises.- Hints and Solutions.