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Languages and Machines An Introduction to the Theory of Computer Science

by: Sudkamp, Thomas A.

Languages and Machines An Introduction to the Theory of Computer Science

by: Sudkamp, Thomas A.

ISBN 13:
9780321322210
ISBN 10:
0321322215
Edition: 3rd
Format: Paperback
Copyright: 02/14/2005
Publisher: Pearson

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Summary

The third edition ofLanguages and Machines: An Introduction to the Theory of Computer Scienceprovides readers with a mathematically sound presentation of the theory of computer science. The theoretical concepts and associated mathematics are made accessible by a "learn as you go" approach that develops an intuitive understanding of the concepts through numerous examples and illustrations.

Preface

xiii

Introduction

(6)

PART I Foundations

Chapter 1 Mathematical Preliminaries

(34)

1.1 Set Theory

(3)

1.2 Cartesian Product, Relations, and Functions

(3)

1.3 Equivalence Relations

(2)

1.4 Countable and Uncountable Sets

(5)

1.5 Diagonalization and Self-Reference

(2)

1.6 Recursive Definitions

(4)

1.7 Mathematical Induction

(5)

1.8 Directed Graphs

(4)

Exercises

(4)

Bibliographic Notes

(1)

Chapter 2 Languages

(24)

2.1 Strings and Languages

(3)

2.2 Finite Specification of Languages

(4)

2.3 Regular Sets and Expressions

(5)

2.4 Regular Expressions and Text Searching

(4)

Exercises

(3)

Bibliographic Notes

(4)

PART II Grammars, Automata, and Languages

Chapter 3 Context-Free Grammars

(38)

3.1 Context-Free Grammars and Languages

(8)

3.2 Examples of Grammars and Languages

(5)

3.3 Regular Grammars

(2)

3.4 Verifying Grammars

(6)

3.5 Leftmost Derivations and Ambiguity

(4)

3.6 Context-Free Grammars and Programming Language Definition

(4)

Exercises

(5)

Bibliographic Notes

102

(1)

Chapter 4 Normal Forms for Context-Free Grammars

103

(42)

4.1 Grammar Transformations

104

(2)

4.2 Elimination of A-Rules

106

(7)

4.3 Elimination of Chain Rules

113

(3)

4.4 Useless Symbols

116

(5)

4.5 Chomsky Normal Form

121

(3)

4.6 The CYK Algorithm

124

(5)

4.7 Removal of Direct Left Recursion

129

(2)

4.8 Greibach Normal Form

131

(7)

Exercises

138

(5)

Bibliographic Notes

143

(2)

Chapter 5 Finite Automata

145

(46)

5.1 A Finite-State Machine

145

(2)

5.2 Deterministic Finite Automata

147

(4)

5.3 State Diagrams and Examples

151

(8)

5.4 Nondeterministic Finite Automata

159

(6)

5.5 λ-Transitions

165

(5)

5.6 Removing Nondeterminism

170

(8)

5.7 DFA Minimization

178

(6)

Exercises

184

(6)

Bibliographic Notes

190

(1)

Chapter 6 Properties of Regular Languages

191

(30)

6.1 Finite-State Acceptance of Regular Languages

191

(2)

6.2 Expression Graphs

193

(3)

6.3 Regular Grammars and Finite Automata

196

(4)

6.4 Closure Properties of Regular Languages

200

(3)

6.5 A Nonregular Language

203

(2)

6.6 The Pumping Lemma for Regular Languages

205

(6)

6.7 The Myhill-Nerode Theorem

211

(6)

Exercises

217

(3)

Bibliographic Notes

220

(1)

Chapter 7 Pushdown Automata and Context-Free Languages

221

(34)

7.1 Pushdown Automata

221

(6)

7.2 Variations on the PDA Theme

227

(5)

7.3 Acceptance of Context-Free Languages

232

(7)

7.4 The Pumping Lemma for Context-Free Languages

239

(4)

7.5 Closure Properties of Context-Free Languages

243

(4)

Exercises

247

(4)

Bibliographic Notes

251

(4)

PART III Computability

Chapter 8 Turing Machines

255

(40)

8.1 The Standard Turing Machine

255

(4)

8.2 Turing Machines as Language Acceptors

259

(3)

8.3 Alternative Acceptance Criteria

262

(1)

8.4 Multitrack Machines

263

(2)

8.5 Two-Way Tape Machines

265

(3)

8.6 Multitape Machines

268

(6)

8.7 Nondeterministic Turing Machines

274

(8)

8.8 Turing Machines as Language Enumerators

282

(6)

Exercises

288

(5)

Bibliographic Notes

293

(2)

Chapter 9 Turing Computable Functions

295

(30)

9.1 Computation of Functions

295

(4)

9.2 Numeric Computation

299

(2)

9.3 Sequential Operation of Turing Machines

301

(7)

9.4 Composition of Functions

308

(4)

9.5 Uncomputable Functions

312

(1)

9.6 Toward a Programming Language

313

(7)

Exercises

320

(3)

Bibliographic Notes

323

(2)

Chapter 10 The Chomsky Hierarchy

325

(18)

10.1 Unrestricted Grammars

325

(7)

10.2 Context-Sensitive Grammars

332

(2)

10.3 Linear-Bounded Automata

334

(4)

10.4 The Chomsky Hierarchy

338

(1)

Exercises

339

(2)

Bibliographic Notes

341

(2)

Chapter 11 Decision Problems and the Church-Turing Thesis

343

(18)

11.1 Representation of Decision Problems

344

(2)

11.2 Decision Problems and Recursive Languages

346

(2)

11.3 Problem Reduction

348

(4)

11.4 The Church-Turing Thesis

352

(2)

11.5 A Universal Machine

354

(4)

Exercises

358

(2)

Bibliographic Notes

360

(1)

Chapter 12 Undecidability

361

(28)

12.1 The Halting Problem for Turing Machines

362

(3)

12.2 Problem Reduction and Undecidability

365

(3)

12.3 Additional Halting Problem Reductions

368

(3)

12.4 Rice's Theorem

371

(2)

12.5 An Unsolvable Word Problem

373

(4)

12.6 The Post Correspondence Problem

377

(5)

12.7 Undecidable Problems in Context-Free Grammars

382

(4)

Exercises

386

(2)

Bibliographic Notes

388

(1)

Chapter 13 Mu-Recursive Functions

389

(44)

13.1 Primitive Recursive Functions

389

(5)

13.2 Some Primitive Recursive Functions

394

(4)

13.3 Bounded Operators

398

(6)

13.4 Division Functions

404

(2)

13.5 Gödel Numbering and Course-of-Values Recursion

406

(4)

13.6 Computable Partial Functions

410

(5)

13.7 Turing Computability and Mu-Recursive Functions

415

(6)

13.8 The Church-Turing Thesis Revisited

421

(3)

Exercises

424

(6)

Bibliographic Notes

430

(3)

PART IV Computational Complexity

Chapter 14 Time Complexity

433

(32)

14.1 Measurement of Complexity

434

(2)

14.2 Rates of Growth

436

(6)

14.3 Time Complexity of a Turing Machine

442

(4)

14.4 Complexity and Turing Machine Variations

446

(2)

14.5 Linear Speedup

448

(3)

14.6 Properties of Time Complexity of Languages

451

(7)

14.7 Simulation of Computer Computations

458

(4)

Exercises

462

(2)

Bibliographic Notes

464

(1)

Chapter 15 P, NP, and Cook's Theorem

465

(32)

15.1 Time Complexity of Nondeterministic Turing Machines

466

(2)

15.2 The Classes P and NP

468

(1)

15.3 Problem Representation and Complexity

469

(3)

15.4 Decision Problems and Complexity Classes

472

(2)

15.5 The Hamiltonian Circuit Problem

474

(3)

15.6 Polynomial-Time Reduction

477

(2)

15.7 P=NP?

479

(2)

15.8 The Satisfiability Problem

481

(11)

15.9 Complexity Class Relations

492

(1)

Exercises

493

(3)

Bibliographic Notes

496

(1)

Chapter 16 NP-Complete Problems

497

(32)

16.1 Reduction and NP-Complete Problems

497

(1)

16.2 The 3-Satisfiability Problem

498

(2)

16.3 Reductions from 3-Satisfiability

500

(13)

16.4 Reduction and Subproblems

513

(4)

16.5 Optimization Problems

517

(2)

16.6 Approximation Algorithms

519

(4)

16.7 Approximation Schemes

523

(3)

Exercises

526

(2)

Bibliographic Notes

528

(1)

Chapter 17 Additional Complexity Classes

529

(26)

17.1 Derivative Complexity Classes

529

(3)

17.2 Space Complexity

532

(3)

17.3 Relations between Space and Time Complexity

535

(5)

17.4 P-Space, NP-Space, and Savitch's Theorem

540

(4)

17.5 P-Space Completeness

544

(4)

17.6 An Intractable Problem

548

(2)

Exercises

550

(1)

Bibliographic Notes

551

(4)

PART V Deterministic Parsing

Chapter 18 Parsing: An Introduction

555

(16)

18.1 The Graph of a Grammar

555

(2)

18.2 A Top-Down Parser

557

(4)

18.3 Reductions and Bottom-Up Parsing

561

(2)

18.4 A Bottom-Up Parser

563

(4)

18.5 Parsing and Compiling

567

(1)

Exercises

568

(1)

Bibliographic Notes

569

(2)

Chapter 19 LL(k) Grammars

571

(24)

19.1 Lookahead in Context-Free Grammars

571

(5)

19.2 FIRST, FOLLOW, and Lookahead Sets

576

(3)

19.3 Strong LL(k) Grammars

579

(1)

19.4 Construction of FIRSTk Sets

580

(3)

19.5 Construction of FOLLOWk Sets

583

(2)

19.6 A Strong LL(1) Grammar

585

(2)

19.7 A Strong LL(k) Parser

587

(2)

19.8 LL(k) Grammars

589

(2)

Exercises

591

(2)

Bibliographic Notes

593

(2)

Chapter 20 LR(k) Grammars

595

(28)

20.1 LR(0) Contexts

595

(4)

20.2 An LR(O) Parser

599

(2)

20.3 The LR(0) Machine

601

(5)

20.4 Acceptance by the LR(0) Machine

606

(6)

20.5 LR(1) Grammars

612

(8)

Exercises

620

(1)

Bibliographic Notes

621

(2)

Appendix I Index of Notation

623

(4)

Appendix II The Greek Alphabet

627

(2)

Appendix III The ASCII Character Set

629

(2)

Appendix IV Backus-Naur Form Definition of Java

631

(10)

Bibliography

641

(8)

Subject Index

649

Amazon no longer offers textbook rentals. We do!

Languages and Machines An Introduction to the Theory of Computer Science

Languages and Machines An Introduction to the Theory of Computer Science

9780321322210

0321322215

Summary

Table of Contents

Supplemental Materials

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