Book contents
- Frontmatter
- Contents
- List of Figures
- Preface
- Organization and Chapter Summaries
- Acknowledgments
- 1 Introduction and Preliminaries
- 2 P, NP, and NP-Completeness
- 3 Variations on P and NP
- 4 More Resources, More Power?
- 5 Space Complexity
- 6 Randomness and Counting
- 7 The Bright Side of Hardness
- 8 Pseudorandom Generators
- 9 Probabilistic Proof Systems
- 10 Relaxing the Requirements
- Epilogue
- Appendix A Glossary of Complexity Classes
- Appendix B On the Quest for Lower Bounds
- Appendix C On the Foundations of Modern Cryptography
- Appendix D Probabilistic Preliminaries and Advanced Topics in Randomization
- Appendix E Explicit Constructions
- Appendix F Some Omitted Proofs
- Appendix G Some Computational Problems
- Bibliography
- Index
Epilogue
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- List of Figures
- Preface
- Organization and Chapter Summaries
- Acknowledgments
- 1 Introduction and Preliminaries
- 2 P, NP, and NP-Completeness
- 3 Variations on P and NP
- 4 More Resources, More Power?
- 5 Space Complexity
- 6 Randomness and Counting
- 7 The Bright Side of Hardness
- 8 Pseudorandom Generators
- 9 Probabilistic Proof Systems
- 10 Relaxing the Requirements
- Epilogue
- Appendix A Glossary of Complexity Classes
- Appendix B On the Quest for Lower Bounds
- Appendix C On the Foundations of Modern Cryptography
- Appendix D Probabilistic Preliminaries and Advanced Topics in Randomization
- Appendix E Explicit Constructions
- Appendix F Some Omitted Proofs
- Appendix G Some Computational Problems
- Bibliography
- Index
Summary
Farewell, Hans – whether you live or end where you are! Your chances are not good. The wicked dance in which you are caught up will last a few more sinful years, and we would not wager much that you will come out whole. To be honest, we are not really bothered about leaving the question open. Adventures in the flesh and spirit, which enhanced and heightened your ordinariness, allowed you to survive in the spirit what you probably will not survive in the flesh. There were majestic moments when you saw the intimation of a dream of love rising up out of death and the carnal body. Will love someday rise up out of this worldwide festival of death, this ugly rutting fever that inflames the rainy evening sky all round?
Thomas Mann, The Magic Mountain, “The Thunderbolt.”We hope that this work has succeeded in conveying the fascinating flavor of the concepts, results, and open problems that dominate the field of Computational Complexity. We believe that the new century will witness even more exciting developments in this field, and urge the reader to try to contribute to them. But before bidding good-bye, we wish to express a few more thoughts.
As noted in Section 1.1.1, so far Complexity Theory has been far more successful in relating fundamental computational phenomena than in providing definite answers regarding fundamental questions. Consider, for example, the theory of NP-completeness versus the P-vs-NP Question, or the theory of pseudorandomness versus establishing the existence of one-way functions (even under P ≠ NP).
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- Information
- Computational ComplexityA Conceptual Perspective, pp. 461 - 462Publisher: Cambridge University PressPrint publication year: 2008