Two prover protocols: low error at affordable rates
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
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
SIAM Journal on Computing
A Combinatorial Consistency Lemma with Application to Proving the PCP Theorem
SIAM Journal on Computing
A new PCP outer verifier with applications to homogeneous linear equations and max-bisection
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Robust PCPs of Proximity, Shorter PCPs, and Applications to Coding
SIAM Journal on Computing
Assignment Testers: Towards a Combinatorial Proof of the PCP Theorem
SIAM Journal on Computing
Locally Testing Direct Product in the Low Error Range
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
New direct-product testers and 2-query PCPs
Proceedings of the forty-first annual ACM symposium on Theory of computing
Composition of Low-Error 2-Query PCPs Using Decodable PCPs
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Hi-index | 0.00 |
Given a function f: X → Σ, its l-wise direct product is the function F = fl: Xl → Σl defined by F(x1,..., xl) = (f(x1),...,f(xl)). A two prover game G is a game that involves 3 participants: V,A, and B. V picks a random pair (x, y) and sends x to A, and y to B. A responds with f(x), B with g(y). A, B win if V(x, y, f(x), g(y)) = 1. The repeated game Gl is the game where A, B get l questions in a single round and each of them responds with an l symbol string (this is also called the parallel repetition of the game). A, B win if they win each of the questions. In this work we analyze the structure of the provers that win the repeated game with non negligible probability. We would like to deduce that in such a case A, B must have a global structure, and in particular they are close to some direct product encoding. A similar question was studied by the authors and by Impagliazzo et. al. in the context of testing Direct Product. Their result can be be interpreted as follows: For a specific game G, if A, B win Gl with non negligible probability, then A, B must be close to be a direct product encoding. We would like to generalize these results for any 2-prover game. In this work we prove two main results: In the first part of the work we show that for a certain type of games, there exist A, B that win the repeated game with non negligible probability yet are still very far from any Direct Product encoding. In contrast, in the second part of the work we show that for a certain type of games, called "miss match" games, we have the following behavior. Whenever A, B win non negligibly then they are both close to a Direct Product strategy.