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).

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U2 - 10.1109/FOCS.2011.62

DO - 10.1109/FOCS.2011.62

M3 - Conference contribution

AN - SCOPUS:84863318515

SN - 9780769545714

T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

SP - 648

EP - 657

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

T2 - 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011

Y2 - 22 October 2011 through 25 October 2011

ER -