Kozen Theory of Computation

1. Auflage 2006
ISBN: 978-1-84628-477-9
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 440 Seiten, eBook

Reihe: Texts in Computer Science

This textbook has been written with the dual purpose to cover core material in the foundations of computing for graduate students in computer science, as well as to provide an introduction to some more advanced topics for those intending further study in the area. This book contains an invaluable collection of lectures for first-year graduates on the theory of computation, focusing primarily on computational complexity theory.

Topics and features include:
Organization into self-contained lectures of 3-7 pages;
41 primary lectures and a handful of supplementary lectures covering more specialized or advanced topics;
12 homework sets and several miscellaneous homework exercises of varying levels of difficulty, many with hints and complete solutions.

Aimed at advanced undergraduates and first-year graduates in Computer Science or Mathematics with an interest in the theory of computation and computational complexity, this book provides a thorough grounding the foundations of computational complexity theory.

Zielgruppe

Graduate

Autoren/Hrsg.

Kozen, Dexter C.

Inhaltsverzeichnis

Lectures.- The Complexity of Computations.- Time and Space Complexity Classes and Savitch’s Theorem.- Separation Results.- The Immerman-Szelepcsényi Theorem.- Logspace Computability.- The Circuit Value Problem.- The Knaster-Tarski Theorem.- Alternation.- Problems Complete for PSPACE.- The Polynomial-Time Hierarchy.- More on the Polynomial-Time Hierarchy.- Parallel Complexity.- Relation of NC to Time-Space Classes.- Probabilistic Complexity.- BPP ?2P ? ?2P.- Chinese Remaindering.- Complexity of Primality Testing.- Berlekamp’s Algorithm.- Interactive Proofs.- PSPACE IP.- IP PSPACE.- Probabilistically Checkable Proofs.- NP PCP(n3, 1).- More on PCP.- A Crash Course in Logic.- Complexity of Decidable Theories.- Complexity of the Theory of Real Addition.- Lower Bound for the Theory of Real Addition.- Lower Bound for Integer Addition.- Automata on Infinite Strings and S1S.- Determinization of ?-Automata.- Safra’s Construction.- Relativized Complexity.- Nonexistence of Sparse Complete Sets.- Unique Satisfiability.- Toda’s Theorem.- Circuit Lower Bounds and Relativized PSPACE = PH.- Lower Bounds for Constant Depth Circuits.- The Switching Lemma.- Tail Bounds.- The Gap Theorem and Other Pathology.- Partial Recursive Functions and Gödel Numberings.- Applications of the Recursion Theorem.- Abstract Complexity.- 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.- Homework 1.- Homework 2.- Homework 3.- Homework 4.- Homework 5.- Homework 6.- Homework 7.- Homework 8.- Homework 9.- Homework 10.- Homework 11.- Homework 12.- Miscellaneous Exercises.- Hints and Solutions.- Homework 1Solutions.- Homework 2 Solutions.- Homework 3 Solutions.- Homework 4 Solutions.- Homework 5 Solutions.- Homework 6 Solutions.- Homework 7 Solutions.- Homework 8 Solutions.- Homework 9 Solutions.- Homework 10 Solutions.- Homework 11 Solutions.- Homework 12 Solutions.- Hints for Selected Miscellaneous Exercises.- Solutions to Selected Miscellaneous Exercises.