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A Parallel Repetition Theorem
 SIAM Journal on Computing
, 1998
"... We show that a parallel repetition of any twoprover oneround proof system (MIP(2, 1)) decreases the probability of error at an exponential rate. No constructive bound was previously known. The constant in the exponent (in our analysis) depends only on the original probability of error and on the t ..."
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Cited by 378 (9 self)
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We show that a parallel repetition of any twoprover oneround proof system (MIP(2, 1)) decreases the probability of error at an exponential rate. No constructive bound was previously known. The constant in the exponent (in our analysis) depends only on the original probability of error
An efficient parallel repetition theorem
"... We present a general parallelrepetition theorem with an efficient reduction. As a corollary of this theorem we establish that parallel repetition reduces the soundness error at an exponential rate in any publiccoin argument, and more generally, any argument where the verifier’s messages, but not ..."
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Cited by 3 (1 self)
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We present a general parallelrepetition theorem with an efficient reduction. As a corollary of this theorem we establish that parallel repetition reduces the soundness error at an exponential rate in any publiccoin argument, and more generally, any argument where the verifier’s messages
An Efficient Parallel Repetition Theorem . . .
 STOC'07
, 2007
"... We show a parallelrepetition theorem for constantround ArthurMerlin Games, using an efficient reduction. As a consequence, we show that parallel repetition reduces the soundnesserror at an optimal rate (up to a negligible factor) in constantround publiccoin argument systems, and constantround ..."
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Cited by 3 (1 self)
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We show a parallelrepetition theorem for constantround ArthurMerlin Games, using an efficient reduction. As a consequence, we show that parallel repetition reduces the soundnesserror at an optimal rate (up to a negligible factor) in constantround publiccoin argument systems, and constant
Parallel repetition theorems for interactive arguments
 Electronic Colloquium on Computational Complexity (ECCC
"... Abstract. 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 publiccoin interactive arguments by giving a tight analysis for a reduction algorithm of H˚astad et al. [HPPW08 ..."
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Cited by 6 (3 self)
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Abstract. 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 publiccoin interactive arguments by giving a tight analysis for a reduction algorithm of H˚astad et al. [HPPW
Parallel Repetition Theorem and Unique Games
, 2007
"... A twoplayer oneround cooperative refereed game is a protocol in which a referee asks two randomly chosen questions to two uncommunicated players. The players send their answers to the referee, and these are jointly evaluated by a known predicate to decide if the game is won or not. The repetition ..."
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A twoplayer oneround cooperative refereed game is a protocol in which a referee asks two randomly chosen questions to two uncommunicated players. The players send their answers to the referee, and these are jointly evaluated by a known predicate to decide if the game is won or not. The repetition
Strong Parallel Repetition Theorem for Free Projection Games
, 2009
"... The parallel repetition theorem states that for any two provers one round game with value at most 1 − ɛ (for ɛ < 1/2), the value of the game repeated n times in parallel is at most (1−ɛ 3) Ω(n / log s) where s is the size of the answers set [Raz98],[Hol07]. For Projection Games the bound on the v ..."
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Cited by 9 (1 self)
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The parallel repetition theorem states that for any two provers one round game with value at most 1 − ɛ (for ɛ < 1/2), the value of the game repeated n times in parallel is at most (1−ɛ 3) Ω(n / log s) where s is the size of the answers set [Raz98],[Hol07]. For Projection Games the bound
Efficient Parallel Repetition Theorems with Applications to Security Amplification
, 2011
"... This thesis focuses on establishing efficient parallel repetition theorems for computationally sound protocols, which assert that under parallel repetition, the computational soundness error of interactive protocols decreases at an exponential rate, and ideally, behaves as if the repetitions are com ..."
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Cited by 1 (0 self)
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This thesis focuses on establishing efficient parallel repetition theorems for computationally sound protocols, which assert that under parallel repetition, the computational soundness error of interactive protocols decreases at an exponential rate, and ideally, behaves as if the repetitions
Derandomized parallel repetition theorems for free games
, 2010
"... Raz’s parallel repetition theorem [Raz98] together with improvements of Holenstein [Hol07] shows that for any twoprover oneround game with value at most 1−ɛ (for ɛ ≤ 1/2), the value of the game repeated n times in parallel on independent inputs is at most (1 − ɛ) Ω ( ɛ2n ℓ) where ℓ is the answer l ..."
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Cited by 2 (0 self)
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Raz’s parallel repetition theorem [Raz98] together with improvements of Holenstein [Hol07] shows that for any twoprover oneround game with value at most 1−ɛ (for ɛ ≤ 1/2), the value of the game repeated n times in parallel on independent inputs is at most (1 − ɛ) Ω ( ɛ2n ℓ) where ℓ is the answer
Tight Parallel Repetition Theorems for Publiccoin Arguments
 ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY, REPORT NO. 109
, 2009
"... Following Hastad et al. [HPPW08], we study parallel repetition theorems for publiccoin interactive arguments and their generalizations. We obtain the following results: 1. We show that the reduction of Hastad et al. [HPPW08] actually gives a tight direct product theorem for publiccoin interactive ..."
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Cited by 2 (0 self)
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Following Hastad et al. [HPPW08], we study parallel repetition theorems for publiccoin interactive arguments and their generalizations. We obtain the following results: 1. We show that the reduction of Hastad et al. [HPPW08] actually gives a tight direct product theorem for publiccoin interactive
Tight Parallel Repetition Theorems for Publiccoin Arguments
, 2009
"... Following Hastad et al. [HPPW08], we study parallel repetition theorems for publiccoin interactive arguments and their generalizations. We obtain the following results: 1. We show that the reduction of Hastad et al. [HPPW08] actually gives a tight direct product theorem for publiccoin interactive ..."
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Following Hastad et al. [HPPW08], we study parallel repetition theorems for publiccoin interactive arguments and their generalizations. We obtain the following results: 1. We show that the reduction of Hastad et al. [HPPW08] actually gives a tight direct product theorem for publiccoin interactive
Results 1  10
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502,697