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Introduction To The Theory Of Computation

by: Sipser,Michael

Introduction To The Theory Of Computation

by: Sipser,Michael

ISBN 13:
9780534950972
ISBN 10:
0534950973
Edition: 2nd
Format: Hardcover
Copyright: 02/15/2005
Publisher: Cengage Learning
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Summary

This highly anticipated revision builds upon the strengths of the previous edition. Sipser's candid, crystal-clear style allows students at every level to understand and enjoy this field. His innovative "proof idea" sections explain profound concepts in plain English. The new edition incorporates many improvements students and professors have suggested over the years, and offers updated, classroom-tested problem sets at the end of each chapter.

Preface to the First Edition

To the student

To the educator

xii

The first edition

xiii

Feedback to the author

xiii

Acknowledgments

xiv

Preface to the Second Edition

xvii

Introduction

(28)

Automata, Computability, and Complexity

(2)

Complexity theory

(1)

Computability theory

(1)

Automata theory

(1)

Mathematical Notions and Terminology

(14)

Sets

(3)

Sequences and tuples

(1)

Functions and relations

(3)

Graphs

(3)

Strings and languages

(1)

Boolean logic

(2)

Summary of mathematical terms

(1)

Definitions, Theorems, and Proofs

(4)

Finding proofs

(4)

Types of Proof

(8)

Proof by construction

(1)

Proof by contradiction

(1)

Proof by induction

(3)

Exercises, Problems, and Solutions

(4)

Part One: Automata and Languages

(106)

Regular Languages

(68)

Finite Automata

(16)

Formal definition of a finite automaton

(2)

Examples of finite automata

(3)

Formal definition of computation

(1)

Designing finite automata

(3)

The regular operations

(3)

Nondeterminism

(16)

Formal definition of a nondeterministic finite automaton

(1)

Equivalence of NFAs and DFAs

(4)

Closure under the regular operations

(5)

Regular Expressions

(14)

Formal definition of a regular expression

(2)

Equivalence with finite automata

(11)

Nonregular Languages

(22)

The pumping lemma for regular languages

(5)

Exercises, Problems, and Solutions

(17)

Context-Free Languages

(36)

Context-free Grammars

100

(9)

Formal definition of a context-free grammar

102

(1)

Examples of context-free grammars

103

(1)

Designing context-free grammars

104

(1)

Ambiguity

105

(1)

Chomsky normal form

106

(3)

Pushdown Automata

109

(14)

Formal definition of a pushdown automaton

111

(1)

Examples of pushdown automata

112

(3)

Equivalence with context-free grammars

115

(8)

Non-context-free Languages

123

(12)

The pumping lemma for context-free languages

123

(5)

Exercises, Problems, and Solutions

128

(7)

Part Two: Computability Theory

135

(110)

The Church-Turing Thesis

137

(28)

Turing Machines

137

(11)

Formal definition of a Turing machine

139

(3)

Examples of Turing machines

142

(6)

Variants of Turing Machines

148

(6)

Multitape Turing machines

148

(2)

Nondeterministic Turing machines

150

(2)

Enumerators

152

(1)

Equivalence with other models

153

(1)

The Definition of Algorithm

154

(11)

Hilbert's problems

154

(2)

Terminology for describing Turing machines

156

(3)

Exercises, Problems, and Solutions

159

(6)

Decidability

165

(22)

Decidable Languages

166

(7)

Decidable problems concerning regular languages

166

(4)

Decidable problems concerning context-free languages

170

(3)

The Halting Problem

173

(14)

The diagonalization method

174

(5)

The halting problem is undecidable

179

(2)

A Turing-unrecognizable language

181

(1)

Exercises, Problems, and Solutions

182

(5)

Reducibility

187

(30)

Undecidable Problems from Language Theory

188

(11)

Reductions via computation histories

192

(7)

A Simple Undecidable Problem

199

(7)

Mapping Reducibility

206

(11)

Computable functions

206

(1)

Formal definition of mapping reducibility

207

(4)

Exercises, Problems, and Solutions

211

(6)

Advanced Topics in Computability Theory

217

(28)

The Recursion Theorem

217

(7)

Self-reference

218

(3)

Terminology for the recursion theorem

221

(1)

Applications

222

(2)

Decidability of logical theories

224

(8)

A decidable theory

227

(2)

An undecidable theory

229

(3)

Turing Reducibility

232

(1)

A Definition of Information

233

(12)

Minimal length descriptions

234

(4)

Optimality of the definition

238

(1)

Incompressible strings and randomness

239

(3)

Exercises, Problems, and Solutions

242

(3)

Part Three: Complexity Theory

245

(170)

Time Complexity

247

(56)

Measuring Complexity

247

(9)

Big-O and small-o notation

248

(3)

Analyzing algorithms

251

(3)

Complexity relationships among models

254

(2)

The Class P

256

(8)

Polynomial time

256

(2)

Examples of problems in P

258

(6)

The Class NP

264

(7)

Examples of problems in NP

267

(2)

The P versus NP question

269

(2)

NP-completeness

271

(12)

Polynomial time reducibility

272

(4)

Definition of NP-completeness

276

(1)

The Cook-Levin Theorem

276

(7)

Additional NP-complete Problems

283

(20)

The vertex cover problem

284

(2)

The Hamiltonian path problem

286

(5)

The subset sum problem

291

(3)

Exercises, Problems, and Solutions

294

(9)

Space Complexity

303

(32)

Savitch's Theorem

305

(3)

The Class PSPACE

308

(1)

PSPACE-completeness

309

(11)

The TQBF problem

310

(3)

Winning strategies for games

313

(2)

Generalized geography

315

(5)

The Classes L and NL

320

(3)

NL-completeness

323

(3)

Searching in graphs

325

(1)

NL equals coNL

326

(9)

Exercises, Problems, and Solutions

328

(7)

Intractability

335

(30)

Hierarchy Theorems

336

(12)

Exponential space completeness

343

(5)

Relativization

348

(3)

Limits of the diagonalization method

349

(2)

Circuit Complexity

351

(14)

Exercises, Problems, and Solutions

360

(5)

Advanced topics in complexity theory

365

(50)

Approximation Algorithms

365

(3)

Probabilistic Algorithms

368

(12)

The class BPP

368

(3)

Primality

371

(5)

Read-once branching programs

376

(4)

Alternation

380

(7)

Alternative time and space

381

(5)

The Polynomial time hierarchy

386

(1)

Interactive Proof Systems

387

(12)

Graph nonisomorphism

387

(1)

Definition of the model

388

(2)

IP = PSPACE

390

(9)

Parallel Computation

399

(6)

Uniform Boolean circuits

400

(2)

The class NC

402

(2)

P-completeness

404

(1)

Cryptography

405

(10)

Secret keys

405

(2)

Public-key cryptosystems

407

(1)

One-way functions

407

(2)

Trapdoor functions

409

(2)

Exercises, Problems, and Solutions

411

(4)

Selected Bibliography

415

(6)

Index

421

Amazon no longer offers textbook rentals. We do!

Introduction To The Theory Of Computation

Introduction To The Theory Of Computation

9780534950972

0534950973

Summary

Author Biography

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

Introduction To The Theory Of Computation

Introduction To The Theory Of Computation

9780534950972

0534950973

Summary

Author Biography

Table of Contents

Supplemental Materials

Write a Review

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