Abstract
We show that for any fixed prime q≥5
and constant ζ>0
, it is NP-hard to distinguish whether a two-prover one-round game with q6 possible answers has value at least 1−ζ
or at most 4q
. The result is obtained by combining two techniques: (i) An Inner PCP based on the point versus subspace test for linear functions. The test is 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 inapproximable within factor (logn)1/6−o(1).
and constant ζ>0
, it is NP-hard to distinguish whether a two-prover one-round game with q6 possible answers has value at least 1−ζ
or at most 4q
. The result is obtained by combining two techniques: (i) An Inner PCP based on the point versus subspace test for linear functions. The test is 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 inapproximable within factor (logn)1/6−o(1).
| Original language | English |
|---|---|
| Article number | 28 |
| Pages (from-to) | 863-887 |
| Number of pages | 25 |
| Journal | Theory of Computing |
| Volume | 9 |
| DOIs | |
| State | Published - 2013 |