1 Course Overview


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

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)