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21cs422 [2021-11-23] – [Synopsis/Syllabus:] Martin Ziegler | 21cs422 [2021-11-29] – [Synopsis/Syllabus:] Martin Ziegler | ||
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* Boolean formulas and Satisfiability | * Boolean formulas and Satisfiability | ||
* nondeterministic WHILE+ programs | * nondeterministic WHILE+ programs | ||
- | * (Time) Hierarchy Theorem: P≠EXP | + | * Time Hierarchy Theorem: P≠EXP |
IV. Structural Complexity / NPc ({{cs422d.ppt|ppt}}, | IV. Structural Complexity / NPc ({{cs422d.ppt|ppt}}, | ||
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* equivalent problems Clique, Independent Set, Boolean Satisfiability, | * equivalent problems Clique, Independent Set, Boolean Satisfiability, | ||
* Cook-Levin Theorem, Master Reduction | * Cook-Levin Theorem, Master Reduction | ||
- | * Ladner' | + | * Bin Packing is NP-complete |
+ | * Scenarios for P/NP, Ladner' | ||
V. PSPACE and Polynomial Hierarchy ({{cs422e.ppt|ppt}}, | V. PSPACE and Polynomial Hierarchy ({{cs422e.ppt|ppt}}, | ||
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* Limitations of Relativizing Proofs: Baker, Gill & Solovay; | * Limitations of Relativizing Proofs: Baker, Gill & Solovay; | ||
- | VI. Advanced Complexity | + | VI. Perspectives |
- | * (Time Hierarchy) | + | |
* complexity of cryptography: | * complexity of cryptography: | ||
- | * (counting problems, Toda's Theorem) | + | * counting problems: #P and Toda's Theorem |
- | * (LOGSPACE, Immerman-Szelepcsenyi Theorem) | + | * Approximation algorithms and hardness |
- | * (Approximation algorithms and hardness) | + | * randomized algorithms, probability amplification, |
- | * (randomized algorithms, probability amplification, | + | * fixed-parameter tractability and hardness |
===== Homework/ | ===== Homework/ |