Chapters in this book

1. Frontmatter i
2. CONTENTS v
3. ACKNOWLEDGMENTS xiii
4. PREFACE FOR INSTRUCTORS xv
5. OVERVIEW
6. 1 INTRODUCTION: WHAT CAN AND CANNOT BE COMPUTED? 3
7. Part I COMPUTABILITY THEORY
8. 2 WHAT IS A COMPUTER PROGRAM? 15
9. 3 SOME IMPOSSIBLE PYTHON PROGRAMS 30
10. 4 WHAT IS A COMPUTATIONAL PROBLEM? 45
11. 5 TURING MACHINES: THE SIMPLEST COMPUTERS 71
12. 6 UNIVERSAL COMPUTER PROGRAMS: PROGRAMS THAT CAN DO ANYTHING 103
13. 7 REDUCTIONS: HOW TO PROVE A PROBLEM IS HARD 116
14. 8 NONDETERMINISM: MAGIC OR REALITY? 143
15. 9 FINITE AUTOMATA: COMPUTING WITH LIMITED RESOURCES 164
16. Part II COMPUTATIONAL COMPLEXITY THEORY
17. 10 COMPLEXITY THEORY: WHEN EFFICIENCY DOES MATTER 195
18. 11 Poly AND Expo: THE TWO MOST FUNDAMENTAL COMPLEXITY CLASSES 228
19. 12 PolyCheck AND NPoly: HARD PROBLEMS THAT ARE EASY TO VERIFY 250
20. 13 POLYNOMIAL-TIME MAPPING REDUCTIONS: PROVING X IS AS EASY AS Y 272
21. 14 NP-COMPLETENESS: MOST HARD PROBLEMS ARE EQUALLY HARD 294
22. Part III ORIGINS AND APPLICATIONS
23. 15 THE ORIGINAL TURING MACHINE 317
24. 16 YOU CAN’T PROVE EVERYTHING THAT’S TRUE 332
25. 17 KARP’S 21 PROBLEMS 353
26. 18 CONCLUSION: WHAT WILL BE COMPUTED? 370
27. BIBLIOGRAPHY 373
28. INDEX 375