Lecture 41

Introduction to Quantum Computing: Basic quantum transformations and definition of BQP.

One Complexity Theorist's View of Quantum Computing

Lectures 1 and 2 of John Watrous' lecture notes

Lecture 40

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Laszlo Babai's first talk on his new graph isomorphism algorithm is now on video. Babai is an excellent lecturer and I highly recommend finding 100 minutes to watch the talk.

Today we covered time-space tradeoffs for SAT from the papers:
Time-space tradeoffs for satisfiability by L. Fortnow. .
Time-space lower bounds for satisfiability by L. Fortnow, R. Lipton, D. van Melkebeek, and A. Viglas.

Lecture 39

Assignment 4, our last assignment, has been posted to T-Square and is due on Wednesday, December 2 at 8 PM. There will be no final exam.

Arefin Huq covered zero-knowledge for Sudoku from the paper Cryptographic and Physical Zero-Knowledge Proof Systems for Solutions of Sudoku Puzzles by Ronen Gradwohl, Moni Naor, Benny Pinkas and Guy N. Rothblum.

He also discussed bit commitment and presented the zero-knowledge proof for graph isomorphism, comparing and contrasting with the Arthur-Merlin protocol for graph non-isomorphism.

Lecture 38

Conclude lecture series on PCP theorem with Proof of BLR test and PCP systems for quadratic-SAT.

Lecture 37

The Blum-Luby-Rubinfeld test and an introduction to Fourier analysis.

Lecture 36

The Long Code Test (Appendix B in Dinur)

Lecture 35

A sketch of the proof of the amplification lemma (Lemma 6.1 in Dinur). Introduction to the assignment tester.

Lecture 34

Second part of prep that converts bounded degree regular graph to an expander with self-loops (Definition 4.3 and Lemma 4.4 of Dinur).

Construction of Graph Powering for Amplification step (follows after Theorem 1.7 in Dinur).

Lecture 33

Proof of the first step of the preprocessing lemma (Lemma 4.2 in Dinur).

Lecture 32

Continuation of PCP proof. Laid out the three lemmas: Preprocessing (Lemma 1.9 in Dinur's paper), Amplification and Composition. Gave construction of the first phase of the preprocessing lemma (Def 4.1).

Lecture 31

We have begun working through Irit Dinur's proof of the PCP theorem by gap amplification. Today we defined constraint graphs, stated the main theorem (Theorem 1.7) and defined expander graphs (Section 2.1).