A conceptual introduction to the study of the intrinsic complexity of computational tasks. It will serve advanced undergraduate and graduate students, either as a textbook or for self-study. It provides explanations of the various sub-areas of complexity theory such as hardness amplification, pseudorandomness, and probabilistic proof systems.
A conceptual introduction to the study of the intrinsic complexity of computational tasks. It will serve advanced undergraduate and graduate students, either as a textbook or for self-study. It provides explanations of the various sub-areas of complexity theory such as hardness amplification, pseudorandomness, and probabilistic proof systems.
Oded Goldreich is a Professor of Computer Science at the Weizmann Institute of Science and an Incumbent of the Meyer W. Weisgal Professorial Chair. He is an editor for the SIAM Journal on Computing, the Journal of Cryptology, and Computational Complexity and previously authored the books Modern Cryptography, Probabalistic Proofs and Pseudorandomness and the two-volume work Foundations of Cryptography.
Inhaltsangabe
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.
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.
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