Computational Complexity Theory ( IAS/Park City Mathematics Series )

Publication series :IAS/Park City Mathematics Series

Author: Steven Rudich;Avi Wigderson  

Publisher: American Mathematical Society‎

Publication year: 2017

E-ISBN: 9781470439095

P-ISBN(Paperback): 9780821828724

Subject: O141.3 recursive function (recursion theory, the effectiveness theory)

Keyword: 暂无分类

Language: ENG

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Computational Complexity Theory

Description

Computational Complexity Theory is the study of how much of a given resource is required to perform the computations that interest us the most. Four decades of fruitful research have produced a rich and subtle theory of the relationship between different resource measures and problems. At the core of the theory are some of the most alluring open problems in mathematics. This book presents three weeks of lectures from the IAS/Park City Mathematics Institute Summer School on computational complexity. The first week gives a general introduction to the field, including descriptions of the basic models, techniques, results and open problems. The second week focuses on lower bounds in concrete models. The final week looks at randomness in computation, with discussions of different notions of pseudorandomness, interactive proof systems and zero knowledge, and probabilistically checkable proofs (PCPs). It is recommended for independent study by graduate students or researchers interested in computational complexity. The volume is recommended for independent study and is suitable for graduate students and researchers interested in computational complexity.

Chapter

Title page

Contents

Preface

Introduction

Week One: Complexity theory: From Gödel to Feynman

Complexity theory: From Gödel to Feynman

Average case complexity

Exploring complexity through reductions

Quantum computation

Week Two: Lower Bounds

Circuit and Communication Complexity

Proof complexity

Week Three: Randomness in computation

Preface to “Week Three: Randomness in Computation”

Pseudorandomness—Part I

Pseudorandomness—Part II

Probabilistic proof systems—Part I

Probabilistically checkable proofs

Back Cover

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