Testing of the long code and hardness for clique

We prove that unless NP = COR, Max Clique is hard to approximate wit hin polynomial time within a factor ni /2 ‘c for any c >0. This is done by constructing a proof system for NP w hich uses 1+6 amortized free bits for any ii >0. We build on the proof system of Bellare, Goldreich and Sudan, while seplacing their strict code-word test for the long code by a relaxed code-word test which is sufficient for the present purposes. The conclusion of this test is that if the test does not reject., then except wit h very small probability y, what the test saw is consistent with one of few possible code-words.

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