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A two prover one round game with strong soundness

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If you have a question about this talk, please contact Mustapha Amrani.

Discrete Analysis

We show that for any large integer q, it is NP-hard to distinguish whether a two prover one round game with q6 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

This talk is part of the Isaac Newton Institute Seminar Series series.

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