Elements of the Theory of Computation: Lewis, Harry; Papadimitriou, Christos H.: 9780132624787: Book: Computers: eCampus.com

Lewis and Papadimitriou present this long awaited Second Edition of their best-selling theory of computation. The authors are well-known for their clear presentation that makes the material accessible to a a broad audience and requires no special previous mathematical experience. In this new edition, the authors incorporate a somewhat more informal, friendly writing style to present both classical and contemporary theories of computation. Algorithms, complexity analysis, and algorithmic ideas are introduced informally in Chapter 1, and are pursued throughout the book. Each section is followed by problems.

Preface to the First Edition

vii

(2)

Preface to the Second Edition

Introduction

(4)

1 Sets, Relations, and Languages

(50)

1.1 Sets

(4)

1.2 Relations and functions

(4)

1.3 Special types of binary relations

(7)

1.4 Finite and infinite sets

(3)

1.5 Three fundamental proof techniques

(7)

1.6 Closures and algorithms

(12)

1.7 Alphabets and languages

(5)

1.8 Finite representations of languages

(5)

References

(3)

2 Finite Automata

(58)

2.1 Deterministic finite automata

(8)

2.2 Nondeterministic finite automata

(12)

2.3 Finite automata and regular expressions

(11)

2.4 Languages that are and are not regular

(6)

2.5 State minimization

(10)

2.6 Algorithmic aspects of finite automata

102

(8)

References

110

(3)

3 Context-free Languages

113

(66)

3.1 Context-free grammars

113

(9)

3.2 Parse trees

122

(8)

3.3 Pushdown automata

130

(6)

3.4 Pushdown automata and context-free grammars

136

(7)

3.5 Languages that are and are not context-free

143

(7)

3.6 Algorithms for context-free grammars

150

(8)

3.7 Determinism and parsing

158

(17)

References

175

(4)

4 Turing machines

179

(66)

4.1 The definition of a Turing machine

179

(15)

4.2 Computing with Turing machines

194

(6)

4.3 Extensions of Turing machines

200

(10)

4.4 Random access Turing machines

210

(11)

4.5 Nondeterministic Turing machines

221

(6)

4.6 Grammars

227

(6)

4.7 Numerical functions

233

(10)

References

243

(2)

5 Undecidability

245

(30)

5.1 The Church-Turing thesis

245

(2)

5.2 Universal Turing machines

247

(4)

5.3 The halting problem

251

(3)

5.4 Unsolvable problems about Turing machines

254

(4)

5.5 Unsolvable problems about grammars

258

(4)

5.6 An unsolvable tiling problem

262

(5)

5.7 Properties of recursive languages

267

(5)

References

272

(3)

6 Computational Complexity

275

(26)

6.1 The class P

275

(3)

6.2 Problems, problems

278

(10)

6.3 Boolean satisfiability

288

(4)

6.4 The class (NP)

292

(7)

References

299

(2)

7 NP-completeness

301

(52)

7.1 Polynomial-time reductions

301

(8)

7.2 Cook's Theorem

309

(8)

7.3 More (NP)-complete problems

317

(16)

7.4 Coping with (NP)-completeness

333

(17)

References

350

(3)

Index

353


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