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A Parallel Repetition Theorem
Abstract
We show that a parallel repetition of any two-prover one-round 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 total number of possible answers of the two provers. The dependency on the total number of possible answers is logarithmic, which was recently proved to be almost the best possible [U. Feige and O. Verbitsky, Proc.11th Annual IEEE Conference on Computational Complexity, IEEE Computer Society Press, Los Alamitos, CA, 1996, pp. 70--76].
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Cited by
Brunner, N., Cavalcanti, D., Pironio, S., Scarani, V., & Wehner, S. (2014) · Reviews of Modern Physics · doi:10.1103/revmodphys.86.419 · Cited by 2,688
Some optimal inapproximability results
Håstad, J. (2001) · Journal of the ACM · doi:10.1145/502090.502098 · Cited by 1,902
Analytical approach to parallel repetition
Dinur, I., & Steurer, D. (2014) · Proceedings of the forty-sixth annual ACM symposium on Theory of computing · doi:10.1145/2591796.2591884 · Cited by 406
Quantum Theory: Informational Foundations and Foils
(2016) · Fundamental Theories of Physics · doi:10.1007/978-94-017-7303-4 · Cited by 178
Hardness Results for Agnostically Learning Low-Degree Polynomial Threshold Functions
Diakonikolas, I., O'Donnell, R., Servedio, R. A., & Wu, Y. (2011) · Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms · doi:10.1137/1.9781611973082.123 · Cited by 6
Metadata
- Authors
- Raz, R.
- Venue
- SIAM Journal on Computing
- Published
- 1998-06
- Volume
- 27
- Issue
- 3
- Pages
- 763-803
- ISSN
- 0097-5397 (ISSN-L)
- 1095-7111
- OpenAlex
- W1970259241
- Cited by
- 703
- References
- 0
- FWCI
- 14.06
- Type
- journal article
- Language
- en
- Open access
- closed
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