### A two prover one round game with strong soundness

Khot, S *(Courant Institute)*

Wednesday 30 March 2011, 15:30-16:30

Seminar Room 1, Newton Institute

#### Abstract

We show that for any large integer q, it is NP-hard to distinguish whether a two prover one round game with q^6 answers has value close to 1 or at most O(1/q). The result is obtained by combining two new 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.

As an application, we show that unless NP has quasi-polynomial time deterministic algorithms, the Quadratic Programming Problem is inapproximable within factor (\log n)^{1/6 - o(1)}.

The talk should be self-contained.

Joint work with Muli Safra