Uriel Feige, Guy Kindler, Ryan O'Donnell

Motivated by the study of Parallel Repetition and also by the Unique

Games Conjecture, we investigate the value of the ``Odd Cycle Games''

under parallel repetition. Using tools from discrete harmonic

analysis, we show that after $d$ rounds on the cycle of length $m$,

the value of the game is ...
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Anup Rao

In a two player game, a referee asks two cooperating players (who are

not allowed to communicate) questions sampled from some distribution

and decides whether they win or not based on some predicate of the

questions and their answers. The parallel repetition of the game is

the game in which ...
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Ran Raz

The parallel repetition theorem states that for any two-prover game,

with value $1- \epsilon$ (for, say, $\epsilon \leq 1/2$), the value of

the game repeated in parallel $n$ times is at most

$(1- \epsilon^c)^{\Omega(n/s)}$, where $s$ is the answers' length

(of the original game) and $c$ is a universal ...
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Iftach Haitner

The question whether or not parallel repetition reduces the soundness error is a fundamental question in the theory of protocols. While parallel repetition reduces (at an exponential rate) the error in interactive proofs and (at a weak exponential rate) in special cases of interactive arguments (e.g., 3-message protocols - Bellare, ... more >>>

Kai-Min Chung, Feng-Hao Liu

Following Hastad, Pass, Pietrzak, and Wikstrom (2008), we study parallel repetition theorems for public-coin interactive arguments and their generalization. We obtain the following results:

1. We show that the reduction of Hastad et al. actually gives a tight direct product theorem for public-coin interactive arguments. That is, $n$-fold parallel repetition ... more >>>

Charanjit Jutla

We consider weakly-verifiable puzzles which are challenge-response puzzles such that the responder may not

be able to verify for itself whether it answered the challenge correctly. We consider $k$-wise direct product of

such puzzles, where now the responder has to solve $k$ puzzles chosen independently in parallel.

Canetti et ...
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Irit Dinur, Or Meir

A PCP is a proof system for NP in which the proof can be checked by a probabilistic verifier. The verifier is only allowed to read a very small portion of the proof, and in return is allowed to err with some bounded probability. The probability that the verifier accepts ... more >>>

Irit Dinur, David Steurer

A direct product is a function of the form $g(x_1,\ldots,x_k)=(g_1(x_1),\ldots,g_k(x_k))$. We show that the direct product property is locally testable with $2$ queries, that is, a canonical two-query test distinguishes between direct products and functions that are from direct products with constant probability.

This local testing question comes up ... more >>>

Mark Braverman, Ankit Garg

We prove a parallel repetition theorem for general games with value tending to 0. Previously Dinur and Steurer proved such a theorem for the special case of projection games. We use information theoretic techniques in our proof. Our proofs also extend to the high value regime (value close to 1) ... more >>>

Dana Moshkovitz

In this work we analyze a direct product test in which each of two provers receives a subset of size n of a ground set U,

and the two subsets intersect in about (1-\delta)n elements.

We show that if each of the provers provides labels to the n ...
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Amey Bhangale, Ramprasad Saptharishi, Girish Varma, Rakesh Venkat

A recent result of Moshkovitz~\cite{Moshkovitz14} presented an ingenious method to provide a completely elementary proof of the Parallel Repetition Theorem for certain projection games via a construction called fortification. However, the construction used in \cite{Moshkovitz14} to fortify arbitrary label cover instances using an arbitrary extractor is insufficient to prove parallel ... more >>>

Mohammad Bavarian, Thomas Vidick, Henry Yuen

In a recent work, Moshkovitz [FOCS '14] presented a transformation on two-player games called "fortification'', and gave an elementary proof of an (exponential decay) parallel repetition theorem for fortified two-player projection games. In this paper, we give an analytic reformulation of Moshkovitz's fortification framework, which was originally cast in combinatorial ... more >>>

Henry Yuen

The behavior of games repeated in parallel, when played with quantumly entangled players, has received much attention in recent years. Quantum analogues of Raz's classical parallel repetition theorem have been proved for many special classes of games. However, for general entangled games no parallel repetition theorem was known.

...
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Irit Dinur, Prahladh Harsha, Rakesh Venkat, Henry Yuen

We investigate the value of parallel repetition of one-round games with any number of players $k\ge 2$. It has been an open question whether an analogue of Raz's Parallel Repetition Theorem holds for games with more than two players, i.e., whether the value of the repeated game decays exponentially ... more >>>