| LEC # | TOPICS | KEY DATES |
|---|---|---|
| 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 | |
| 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 | |
| 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 | |
| 14 | Reusing Random Bits for BPP Algorithms: Definitions, Analysis | |
| 15 | Interactive Proofs Zero-Knowledge Proofs Arthur-Merlin Games |
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| 16 | Interactive proofs of graph non-isomorphism | |
| 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) |
