具有完全完全性的超图独裁检验
A Hypergraph Dictatorship Test with Perfect Completeness
摘要：
超图独裁测试首先由Samorodnitsky和Trevisan引入，并作为其独特的基于游戏的$\PCP$构造的关键组件。这样的测试具有对函数集合的oracle访问，并确定所有函数是否是相同的独裁，或者所有它们的低程度影响都是$o(1).$。它们的测试进行$q\geq3$查询，并具有摊销的查询复杂性$1+O(\frac{\log q}{q})$，但具有完美完整性的固有损失。在本文中，我们给出了一个自适应超图独裁测试，实现完美的完整性和摊销的查询复杂度$1+O(\frac{\log q}{q})$。
英文摘要：
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 $1+O(\frac{\log q}{q})$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
