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