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5 TURING MACHINES: THE SIMPLEST COMPUTERS
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Chapters in this book
- Frontmatter i
- CONTENTS v
- ACKNOWLEDGMENTS xiii
- PREFACE FOR INSTRUCTORS xv
-
OVERVIEW
- 1 INTRODUCTION: WHAT CAN AND CANNOT BE COMPUTED? 3
-
Part I COMPUTABILITY THEORY
- 2 WHAT IS A COMPUTER PROGRAM? 15
- 3 SOME IMPOSSIBLE PYTHON PROGRAMS 30
- 4 WHAT IS A COMPUTATIONAL PROBLEM? 45
- 5 TURING MACHINES: THE SIMPLEST COMPUTERS 71
- 6 UNIVERSAL COMPUTER PROGRAMS: PROGRAMS THAT CAN DO ANYTHING 103
- 7 REDUCTIONS: HOW TO PROVE A PROBLEM IS HARD 116
- 8 NONDETERMINISM: MAGIC OR REALITY? 143
- 9 FINITE AUTOMATA: COMPUTING WITH LIMITED RESOURCES 164
-
Part II COMPUTATIONAL COMPLEXITY THEORY
- 10 COMPLEXITY THEORY: WHEN EFFICIENCY DOES MATTER 195
- 11 Poly AND Expo: THE TWO MOST FUNDAMENTAL COMPLEXITY CLASSES 228
- 12 PolyCheck AND NPoly: HARD PROBLEMS THAT ARE EASY TO VERIFY 250
- 13 POLYNOMIAL-TIME MAPPING REDUCTIONS: PROVING X IS AS EASY AS Y 272
- 14 NP-COMPLETENESS: MOST HARD PROBLEMS ARE EQUALLY HARD 294
-
Part III ORIGINS AND APPLICATIONS
- 15 THE ORIGINAL TURING MACHINE 317
- 16 YOU CAN’T PROVE EVERYTHING THAT’S TRUE 332
- 17 KARP’S 21 PROBLEMS 353
- 18 CONCLUSION: WHAT WILL BE COMPUTED? 370
- BIBLIOGRAPHY 373
- INDEX 375
Chapters in this book
- Frontmatter i
- CONTENTS v
- ACKNOWLEDGMENTS xiii
- PREFACE FOR INSTRUCTORS xv
-
OVERVIEW
- 1 INTRODUCTION: WHAT CAN AND CANNOT BE COMPUTED? 3
-
Part I COMPUTABILITY THEORY
- 2 WHAT IS A COMPUTER PROGRAM? 15
- 3 SOME IMPOSSIBLE PYTHON PROGRAMS 30
- 4 WHAT IS A COMPUTATIONAL PROBLEM? 45
- 5 TURING MACHINES: THE SIMPLEST COMPUTERS 71
- 6 UNIVERSAL COMPUTER PROGRAMS: PROGRAMS THAT CAN DO ANYTHING 103
- 7 REDUCTIONS: HOW TO PROVE A PROBLEM IS HARD 116
- 8 NONDETERMINISM: MAGIC OR REALITY? 143
- 9 FINITE AUTOMATA: COMPUTING WITH LIMITED RESOURCES 164
-
Part II COMPUTATIONAL COMPLEXITY THEORY
- 10 COMPLEXITY THEORY: WHEN EFFICIENCY DOES MATTER 195
- 11 Poly AND Expo: THE TWO MOST FUNDAMENTAL COMPLEXITY CLASSES 228
- 12 PolyCheck AND NPoly: HARD PROBLEMS THAT ARE EASY TO VERIFY 250
- 13 POLYNOMIAL-TIME MAPPING REDUCTIONS: PROVING X IS AS EASY AS Y 272
- 14 NP-COMPLETENESS: MOST HARD PROBLEMS ARE EQUALLY HARD 294
-
Part III ORIGINS AND APPLICATIONS
- 15 THE ORIGINAL TURING MACHINE 317
- 16 YOU CAN’T PROVE EVERYTHING THAT’S TRUE 332
- 17 KARP’S 21 PROBLEMS 353
- 18 CONCLUSION: WHAT WILL BE COMPUTED? 370
- BIBLIOGRAPHY 373
- INDEX 375