Multi-prover interactive proofs: how to remove intractability assumptions
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Randomness in interactive proofs
Computational Complexity
Impossibility results for recycling random bits in two-prover proof systems
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Journal of Computer and System Sciences
P = BPP if E requires exponential circuits: derandomizing the XOR lemma
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Direct product results and the GCD problem, in old and new communication models
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Communication complexity
Randomness-optimal oblivious sampling
Proceedings of the workshop on Randomized algorithms and computation
SIAM Journal on Computing
Products and Help Bits in Decision Trees
SIAM Journal on Computing
Hard-core distributions for somewhat hard problems
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Error reduction by parallel repetition-the state of the art
Error reduction by parallel repetition-the state of the art
Error Reduction by Parallel Repetition—A Negative Result
Combinatorica
Towards proving strong direct product theorems
Computational Complexity
Parallel repetition: simplifications and the no-signaling case
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Parallel repetition in projection games and a concentration bound
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Uniform direct product theorems: simplified, optimized, and derandomized
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Security preserving amplification of hardness
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
A Counterexample to Strong Parallel Repetition
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Rounding Parallel Repetitions of Unique Games
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Unbalanced expanders and randomness extractors from Parvaresh--Vardy codes
Journal of the ACM (JACM)
Strong Parallel Repetition Theorem for Free Projection Games
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
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Raz's parallel repetition theorem (SIAM J Comput 27(3):763---803, 1998) together with improvements of Holenstein (STOC, pp 411---419, 2007) shows that for any two-prover one-round game with value at most $${1- \epsilon}$$ 1 - 驴 (for $${\epsilon \leq 1/2}$$ 驴 驴 1 / 2 ), the value of the game repeated n times in parallel on independent inputs is at most $${(1- \epsilon)^{\Omega(\frac{\epsilon^2 n}{\ell})}}$$ ( 1 - 驴 ) 驴 ( 驴 2 n 驴 ) , where 驴 is the answer length of the game. For free games (which are games in which the inputs to the two players are uniform and independent), the constant 2 can be replaced with 1 by a result of Barak et al. (APPROX-RANDOM, pp 352---365, 2009). Consequently, $${n=O(\frac{t \ell}{\epsilon})}$$ n = O ( t 驴 驴 ) repetitions suffice to reduce the value of a free game from $${1- \epsilon}$$ 1 - 驴 to $${(1- \epsilon)^t}$$ ( 1 - 驴 ) t , and denoting the input length of the game by m, it follows that $${nm=O(\frac{t \ell m}{\epsilon})}$$ n m = O ( t 驴 m 驴 ) random bits can be used to prepare n independent inputs for the parallel repetition game.In this paper, we prove a derandomized version of the parallel repetition theorem for free games and show that O(t(m + 驴)) random bits can be used to generate correlated inputs, such that the value of the parallel repetition game on these inputs has the same behavior. That is, it is possible to reduce the value from $${1- \epsilon}$$ 1 - 驴 to $${(1- \epsilon)^t}$$ ( 1 - 驴 ) t while only multiplying the randomness complexity by O(t) when m = O(驴).Our technique uses strong extractors to "derandomize" a lemma of Raz and can be also used to derandomize a parallel repetition theorem of Parnafes et al. (STOC, pp 363---372, 1997) for communication games in the special case that the game is free.