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手机扫码下载CS G399: Gems of Theoretical Computer S Spring 2009
Instructor:&
Meetings: Tuesday 10:30 - 12:10 in Room 166 WVH
and Friday 1:35 PM - 3:15 PM Room
Hall (RY), 11 Leon St.,
campus map,
Office Hours: by appointment.
Course Description
This course covers some of the most exciting and recent
progress in theoretical computer science. It presents state-of-the-art results on active research areas, and teaches related proof techniques. A tentative list of topics includes:
Lower bounds for constant-depth circuits.
The Nisan-Wigderson pseudorandom generator.
Cryptography in constant parallel time.
The complexity of Nash equilibria.
Undirected connectivity in logarithmic space (SL = L).
Communication complexity.
Primes is in P.
Fast matrix multiplication.
No background is required for this class. However, this is a theoretical course with emphasis on theorems and proofs, so ``mathematical maturity'' is expected.
Each student is required to scribe (#lectures/#students) lectures.
Class schedule
Content of future lectures is tentative.
Lecture notes
Overview of the course.
for scribes.
Sanjeev Arora and Boaz Barak's
on complexity.
Oded Goldreich's
on complexity, including his .
Preliminaries: Probability, correlation, circuits, and pseudorandom generators.
Problem 1. (*)
The Nisan-Wigderson pseudorandom generator: I
Yao's next-bit predictor.
The Nisan-Wigderson pseudorandom generator: II
Problems 2,3. (*)
Parity requires large constant-depth circuits:
Aspnes, Beigel, Furst, and Rudich's proof. I
Parity requires large constant-depth circuits:
Aspnes, Beigel, Furst, and Rudich's proof. II
Parity requires large constant-depth circuits:
Aspnes, Beigel, Furst, and Rudich's proof. III
Parity has exponentially small correlation with small
constant-depth circuits: Klivans and Vadhan's proof.
Problem 4. (*)
Arithmetic in log-depth circuits: addition, iterated addition,
multiplication.
Beame, Cook, and Hoover's log-depth circuits for division. I
Beame, Cook, and Hoover's log-depth circuits for division. II
Proof of the weak prime number theorem.
Valiant's result that log-depth linear-size is in depth-3
subexponential-size.
Barrington's theorem.
Applebaum, Ishai, and Kushilevitz's cryptograhy in constant depth: I
Applebaum, Ishai, and Kushilevitz's cryptograhy in constant depth: II
Applebaum, Ishai, and Kushilevitz's cryptograhy in constant depth: III
Spectral graph theory.
Undirected reachability in randomized log space.
Spring break.
Problems 5,6. (*)
Undirected reachability in log space, Rozenman and Vadhan's proof: I
by Linial and Wigderson.
Undirected reachability in log space, Rozenman and Vadhan's proof: II
Undirected reachability in log space, Rozenman and Vadhan's proof: III
Primes in P: I
on undirected reachability in log space.
Primes in P: II
Andrew Granville's ,
Victor Shoup's .
Primes in P: III
on Primes in P.
Group-theoretic algorithms for fast matrix multiplication: I
Group-theoretic algorithms for fast matrix multiplication: II
Group-theoretic algorithms for fast matrix multiplication: III
Succinct data structures: I
on matrix multiplication.
Succinct data structures: II
on succinct data structures.
Communication complexity
Multiparty communication complexity: I
Multiparty communication complexity: II
on communication complexity.
Natural Proofs
on natural proofs.
Problems (*)
Problems are optional and stated in the following continuously
The above class schedule signals when a new problem is inserted in&&|||&|& ||
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