Derandomized Parallel Repetition Theorems for Free Games

A No - Go Theorem for Derandomized Parallel Repetition

In this work we show a barrier towards proving a randomness-efficient parallel repetition, a promising avenue for achieving many tight inapproximability results. Feige and Kilian (STOC'95) proved an impossibility result for randomnessefficient parallel repetition for two prover games with small degree, i.e., when each prover has only few possibilities for the question of the other prover. In re...

Strong Parallel Repetition Theorem for Free Projection Games

The parallel repetition theorem states that for any two provers one round game with value at most 1 − 2 (for 2 < 1/2), the value of the game repeated n times in parallel is at most (1−23)Ω(n/ log s) where s is the size of the answers set [Raz98],[Hol07]. For Projection Games the bound on the value of the game repeated n times in parallel was improved to (1−22)Ω(n) [Rao08] and was shown to be ti...

Anchoring games for parallel repetition

Raz's celebrated Parallel Repetition Theorem shows that the probability of simultaneously winning n independent instances of a two-player one-round game G is exponentially small in n, when the maximum success probability of G is less than 1. Though the statement is intuitive, the proof is rather nontrivial and has found important application in hardness of approximation, cryptography, and commu...

Parallel Repetition Theorems for Interactive Arguments

We study efficient parallel repetition theorems for several classes of interactive arguments and obtain the following results: 1. We show a tight parallel repetition theorem for public-coin interactive arguments by giving a tight analysis for a reduction algorithm of H̊astad et al. [HPPW08]. That is, n-fold parallel repetition decreases the soundness error from δ to δ. The crux of our improvemen...

Parallel repetition of XOR games