%0 Journal Article
%T A Hypergraph Dictatorship Test with Perfect Completeness
%A Victor Chen
%J Mathematics
%D 2008
%I arXiv
%R 10.1007/978-3-642-03685-9_34
%X A hypergraph dictatorship test is first introduced by Samorodnitsky and Trevisan and serves as a key component in their unique games based $\PCP$ construction. Such a test has oracle access to a collection of functions and determines whether all the functions are the same dictatorship, or all their low degree influences are $o(1).$ Their test makes $q\geq3$ queries and has amortized query complexity $1+O(\frac{\log q}{q})$ but has an inherent loss of perfect completeness. In this paper we give an adaptive hypergraph dictatorship test that achieves both perfect completeness and amortized query complexity $1+O(\frac{\log q}{q})$.
%U http://arxiv.org/abs/0811.1922v3