Refuting Unique Game Conjecture

Abstract

In this short note, the author shows that the gap problem of some $k$-CSPs with the support of its predicate the ground of a balanced pairwise independent distribution can be solved by a modified version of Hast's Algorithm BiLin that calls Charikar\&Wirth's SDP algorithm for two rounds in polynomial time, when $k$ is sufficiently large, the support of its predicate is combined by the grounds of three biased homogeneous distributions and the three biases satisfy certain conditions. To conclude, the author refutes Unique Game Conjecture, assuming $P\ne NP$.