Comments on: Lecture 1: Cheating with foams http://tcsmath.wordpress.com/2008/09/21/lecture-1-cheating-with-foams/ some mathematics of theoretical computer science Fri, 16 Oct 2009 11:37:51 +0000 http://wordpress.com/ hourly 1 By: James Lee http://tcsmath.wordpress.com/2008/09/21/lecture-1-cheating-with-foams/#comment-79 James Lee Fri, 03 Oct 2008 00:51:12 +0000 http://tcsmath.wordpress.com/?p=71#comment-79 You might want to check out <a href="http://tcsmath.wordpress.com/2008/09/26/lecture-2-spectral-partitioning-and-near-optimal-foams/" rel="nofollow">Lecture 2</a>. You might want to check out Lecture 2.

]]> By: sachdevasushant http://tcsmath.wordpress.com/2008/09/21/lecture-1-cheating-with-foams/#comment-78 sachdevasushant Fri, 03 Oct 2008 00:47:53 +0000 http://tcsmath.wordpress.com/?p=71#comment-78 Hi James, I liked your lecture and it was very well scribed. I had a comment. You mention about the implication of a strong parallel repetition theorem (One with an exponent of < 2 for $latex \epsilon$. You don't mention a recent paper by Ran Raz, <i>A counter example to strong parallel repetition theorem</i> where he rules out the existence of such a theorem even for projection/unique/XOR games. In essence he shows a protocol for the n-repeated odd cycle game that achieves $latex (1-(\frac{1}{m})O(\sqrt{n}))$ Hi James,

I liked your lecture and it was very well scribed.
I had a comment. You mention about the implication of a strong parallel repetition theorem (One with an exponent of < 2 for \epsilon.

You don’t mention a recent paper by Ran Raz,

A counter example to strong parallel repetition theorem

where he rules out the existence of such a theorem even for projection/unique/XOR games.

In essence he shows a protocol for the n-repeated odd cycle game that achieves (1-(\frac{1}{m})O(\sqrt{n}))

]]> By: James Lee http://tcsmath.wordpress.com/2008/09/21/lecture-1-cheating-with-foams/#comment-77 James Lee Tue, 30 Sep 2008 06:19:46 +0000 http://tcsmath.wordpress.com/?p=71#comment-77 thanks dave! at least I got this right in the actual lecture :) thanks dave! at least I got this right in the actual lecture :)

]]> By: Dave Bacon http://tcsmath.wordpress.com/2008/09/21/lecture-1-cheating-with-foams/#comment-76 Dave Bacon Tue, 30 Sep 2008 00:46:09 +0000 http://tcsmath.wordpress.com/?p=71#comment-76 Some typos: In the proof of Claim 1.4, the equation for the value of the game played multiple times is missing a factor of m^k in the denominator (and in the description of the number of edges in the double cover graph listed below the equation.) Also you say at the end of the proof "Note that topologically trivial odd cycles..." Do you really mean to add "odd" there? Some typos:

In the proof of Claim 1.4, the equation for the value of the game played multiple times is missing a factor of m^k in the denominator (and in the description of the number of edges in the double cover graph listed below the equation.)

Also you say at the end of the proof “Note that topologically trivial odd cycles…” Do you really mean to add “odd” there?

]]> By: Lecture 2: Spectral partitioning and near-optimal foams « tcs math - some mathematics of theoretical computer science http://tcsmath.wordpress.com/2008/09/21/lecture-1-cheating-with-foams/#comment-71 Lecture 2: Spectral partitioning and near-optimal foams « tcs math - some mathematics of theoretical computer science Fri, 26 Sep 2008 09:09:54 +0000 http://tcsmath.wordpress.com/?p=71#comment-71 [...] and near-optimal foams Filed under: Uncategorized — jrluw @ 2:09 am In the last lecture, we reduced the problem of cheating in (the k-times repeated m-cycle game) to finding a small set [...] [...] and near-optimal foams Filed under: Uncategorized — jrluw @ 2:09 am In the last lecture, we reduced the problem of cheating in (the k-times repeated m-cycle game) to finding a small set [...]

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