### 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 language | English (US) |
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Title of host publication | Proceedings - 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011 |

Pages | 648-657 |

Number of pages | 10 |

DOIs | |

State | Published - 2011 |

Event | 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011 - Palm Springs, CA, United States Duration: Oct 22 2011 → Oct 25 2011 |

### Other

Other | 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011 |
---|---|

Country | United States |

City | Palm Springs, CA |

Period | 10/22/11 → 10/25/11 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

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 -