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Theory of Computation: Classical & Contemporary Approaches
Covers core material in the foundations of computing for graduate students in computer science. This book also provides an introduction to some more advanced topics for those intending further study in the area. It contains a collection of lectures on the theory of computation, focusing primarily on computational complexity theory.
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
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