Analytical Approach to Parallel Repetition

Analytical Approach to Parallel Repetition - Irit Dinur

Irit Dinur
Weizmann Institute; Radcliffe institute
April 15, 2013

We propose an “analytical” framework for studying parallel repetitions of one-round two-prover games. We define a new relaxation of the value of a game, val+, and prove that it is both multiplicative and a good approximation for the true value of the game. These two properties imply Raz's parallel repetition theorem as
$val(G^k) ~ val+(G^k) = val+(G)^k ~ val(G)^k$
Using this approach, we will describe a reasonably simple proof for the NP-hardness for $label-cover(1,delta)$, the starting point of many inapproximability results.
We also discuss some new results, including
* parallel repetition for small-soundness games
* a new reduction from general to projection games
* a tight bound for few repetitions matching Raz's counterexample.