# On the power of unique 2-prover 1-round games

@inproceedings{Khot2002OnTP,
title={On the power of unique 2-prover 1-round games},
author={Subhash Khot},
booktitle={STOC '02},
year={2002}
}
• Subhash Khot
• Published in STOC '02 19 May 2002
• Mathematics, Computer Science
A 2-prover game is called unique if the answer of one prover uniquely determines the answer of the second prover and vice versa (we implicitly assume games to be one round games). The value of a 2-prover game is the maximum acceptance probability of the verifier over all the prover strategies. We make the following conjecture regarding the power of unique 2-prover games, which we call the Unique Games Conjecture:(MATH) The Unique Games Conjecture: For arbitrarily small constants $\ \zeta… Expand 489 Citations A note on Unique Games • Mathematics, Computer Science • Inf. Process. Lett. • 2006 A tighter analysis of the algorithm of Khot shows that given a unique 2-prover-1-round game with value 1 - e, one can find in polynomial time an assignment to the game with an expected weight of 1 - O(k6/5e1/5 (log 1/ek)2/5), where k is the size of the answer domain. Expand Parallel Repetition of Two-Prover One-Round Games: An Exposition A two-prover one-round game is a fundamental combinatorial optimization problem arising from such areas as interactive proof systems, hardness of approximation, cryptography and quantum mechanics.Expand Unique Games with Entangled Provers are Easy • Mathematics, Physics • 2008 49th Annual IEEE Symposium on Foundations of Computer Science • 2008 We consider one-round games between a classical verifier and two provers who share entanglement. We show that when the constraints enforced by the verifier are unique' constraints (i.e.,Expand Unique Games with Entangled Provers are Easy • Mathematics, Computer Science • FOCS • 2008 We consider one-round games between a classical verifier and two provers who share entanglement. We show that when the constraints enforced by the verifier are unique' constraints (i.e.,Expand On the complexity of unique games and graph expansion • Mathematics • 2010 Understanding the complexity of approximating basic optimization problems is one of the grand challenges of theoretical computer science. In recent years, a sequence of works established that Khot’sExpand On the power of many one-bit provers • Mathematics, Computer Science • ITCS '13 • 2013 It is demonstrated that for the case that k ≥ 2, 1-bit k-prover games exhibit a significantly richer structure and yield a natural "quantitative" approach to relating complexity classes such as BPP, SZK, AM, EXP, and NEXP. Expand Refuting Unique Game Conjecture and d-to-1 Conjecture In this paper, the author proves a weighted k-CSP with the support of its predicate the ground of a balanced pairwise independent distribution is approximation resistant under weak form of d-to-1Expand NP-Hardness of Approximately Solving Linear Equations over Reals • Computer Science, Mathematics • SIAM J. Comput. • 2010 This paper considers the problem of approximately solving a system of homogeneous linear equations over reals, where each equation contains at most three variables and develops linearity and dictatorship testing procedures for functions$f: \mathbb{R}^n \mapsto Â£R}\$ over a Gaussian space, which could be of independent interest. Expand
The Parallel Repetition Theorem and Related Results
In a 2-Prover 1-Round Game, a verifier draws a pair of questions (X,Y ) from a distribution D and sends one each to two co-operating, non-communicating players who need to respond back with answersExpand
A Counterexample to Strong Parallel Repetition
• R. Raz
• Mathematics, Computer Science
• FOCS
• 2008
A major motivation for the recent interest in the strong parallel repetition problem is that a strong Parallel repetition theorem would have implied that the unique game conjecture is equivalent to the NP hardness of distinguishing between instances of Max-Cut that are at least 1 - isin2 satisfiable from instances that areat most 1 - (2/pi) ldr isin satisfiable. Expand

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