A two prover one round game with strong soundness

Subhash Khot, Muli Safra

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We show that for any fixed prime q ≥ 5 and constant ζ > 0, it is NP-hard to distinguish whether a two prove one round game with q 6 answers has value at least 1-ζ or at most 4/q. The result is obtained by combining two techniques: (i) An Inner PCP based on the point versus subspace test for linear functions. The testis analyzed Fourier analytically. (ii) The Outer/Inner PCP composition that relies on a certain sub-code covering property for Hadamard codes. This is a new and essentially black-box method to translate a codeword test for Hadamard codes to a consistency test, leading to a full PCP construction. As an application, we show that unless NP has quasi-polynomial time deterministic algorithms, the Quadratic Programming Problem is in approximable within factor (log n) 1/6 - o(1).

Original languageEnglish (US)
Title of host publicationProceedings - 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011
Pages648-657
Number of pages10
DOIs
StatePublished - 2011
Event2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011 - Palm Springs, CA, United States
Duration: Oct 22 2011Oct 25 2011

Other

Other2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011
CountryUnited States
CityPalm Springs, CA
Period10/22/1110/25/11

Fingerprint

Quadratic programming
Polynomials
Chemical analysis

ASJC Scopus subject areas

  • Computer Science(all)

Cite this

Khot, S., & Safra, M. (2011). A two prover one round game with strong soundness. In Proceedings - 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011 (pp. 648-657). [6108226] https://doi.org/10.1109/FOCS.2011.62

A two prover one round game with strong soundness. / Khot, Subhash; Safra, Muli.

Proceedings - 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011. 2011. p. 648-657 6108226.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Khot, S & Safra, M 2011, A two prover one round game with strong soundness. in Proceedings - 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011., 6108226, pp. 648-657, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011, Palm Springs, CA, United States, 10/22/11. https://doi.org/10.1109/FOCS.2011.62
Khot S, Safra M. A two prover one round game with strong soundness. In Proceedings - 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011. 2011. p. 648-657. 6108226 https://doi.org/10.1109/FOCS.2011.62
Khot, Subhash ; Safra, Muli. / A two prover one round game with strong soundness. Proceedings - 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011. 2011. pp. 648-657
@inproceedings{43c1c86f10f74f60a6aaf51b8197428a,
title = "A two prover one round game with strong soundness",
abstract = "We show that for any fixed prime q ≥ 5 and constant ζ > 0, it is NP-hard to distinguish whether a two prove one round game with q 6 answers has value at least 1-ζ or at most 4/q. The result is obtained by combining two techniques: (i) An Inner PCP based on the point versus subspace test for linear functions. The testis analyzed Fourier analytically. (ii) The Outer/Inner PCP composition that relies on a certain sub-code covering property for Hadamard codes. This is a new and essentially black-box method to translate a codeword test for Hadamard codes to a consistency test, leading to a full PCP construction. As an application, we show that unless NP has quasi-polynomial time deterministic algorithms, the Quadratic Programming Problem is in approximable within factor (log n) 1/6 - o(1).",
author = "Subhash Khot and Muli Safra",
year = "2011",
doi = "10.1109/FOCS.2011.62",
language = "English (US)",
isbn = "9780769545714",
pages = "648--657",
booktitle = "Proceedings - 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011",

}

TY - GEN

T1 - A two prover one round game with strong soundness

AU - Khot, Subhash

AU - Safra, Muli

PY - 2011

Y1 - 2011

N2 - We show that for any fixed prime q ≥ 5 and constant ζ > 0, it is NP-hard to distinguish whether a two prove one round game with q 6 answers has value at least 1-ζ or at most 4/q. The result is obtained by combining two techniques: (i) An Inner PCP based on the point versus subspace test for linear functions. The testis analyzed Fourier analytically. (ii) The Outer/Inner PCP composition that relies on a certain sub-code covering property for Hadamard codes. This is a new and essentially black-box method to translate a codeword test for Hadamard codes to a consistency test, leading to a full PCP construction. As an application, we show that unless NP has quasi-polynomial time deterministic algorithms, the Quadratic Programming Problem is in approximable within factor (log n) 1/6 - o(1).

AB - We show that for any fixed prime q ≥ 5 and constant ζ > 0, it is NP-hard to distinguish whether a two prove one round game with q 6 answers has value at least 1-ζ or at most 4/q. The result is obtained by combining two techniques: (i) An Inner PCP based on the point versus subspace test for linear functions. The testis analyzed Fourier analytically. (ii) The Outer/Inner PCP composition that relies on a certain sub-code covering property for Hadamard codes. This is a new and essentially black-box method to translate a codeword test for Hadamard codes to a consistency test, leading to a full PCP construction. As an application, we show that unless NP has quasi-polynomial time deterministic algorithms, the Quadratic Programming Problem is in approximable within factor (log n) 1/6 - o(1).

UR - http://www.scopus.com/inward/record.url?scp=84863318515&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84863318515&partnerID=8YFLogxK

U2 - 10.1109/FOCS.2011.62

DO - 10.1109/FOCS.2011.62

M3 - Conference contribution

AN - SCOPUS:84863318515

SN - 9780769545714

SP - 648

EP - 657

BT - Proceedings - 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011

ER -