| 1 |
Course Overview
Review
P-Completeness and the Circuit Value Problem (CVP) |
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| 2 |
Alternation
Relations to Deterministic Classes |
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| 3 |
Polynomial Hierarchy |
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| 4 |
Polynomial Hierarchy (cont.)
The Polynomial Time Hierarchy Collapses
Non-Uniform Complexity |
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| 5 |
NP and P/poly
Circuit Complexity |
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| 6 |
Relativization, The Baker-Gill-Solovay Theorem
Randomized Computation |
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| 7 |
BPP Error Amplification
Verifying Polynomial Identities |
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| 8 |
The Valiant-Vazirani Theorem
Universal Hash Functions |
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| 9 |
Counting Classes
Toda's Theorem |
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| 10 |
Quantum Computation |
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| 11 |
Quantum Complexity |
Problem set 1 due |
| 12 |
Fourier Transform
Discrete Log Problem
Calculable Quantum Fourier Transforms
Sufficiency of these Transforms |
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| 13 |
Oracle Quantum Turing Machines |
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| 14 |
Reusing Random Bits for BPP Algorithms: Definitions, Analysis |
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| 15 |
Interactive Proofs
Zero-Knowledge Proofs
Arthur-Merlin Games |
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| 16 |
Interactive proofs of graph non-isomorphism |
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| 17 |
Recap of Arthur-Merlin Games
Graph Isomorphism
Probabilistically Checkable Proofs
3SAT Approximation is NP-hard |
Problem set 2 due |
| 18 |
#P ⊆ IP
PSPACE ⊆ IP |
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| 19 |
Recall Proof Strategy of PSPACE ⊆ IP
Implicit Circuit Sat and the Proof Outline
Multilinear Polynomials
The Multilinearity Test |
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| 20 |
The Multilinearity Test (cont.) |
Problem set 3 due before next lecture |
| 21 |
Approximating Max-Clique
Reducing Satisfiable Clauses in 3CNF |
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| 22 |
Derandomizing Logspace Computations |
Problem set 4 due (a week after this lecture) |