非确定可测超图参数的显式界
Explicit Bounds for Nondeterministically Testable Hypergraph Parameters
摘要：
本文给出了一致超图参数的可测性与不确定可测性概念等价性的一种新的有效证明方法。我们提供了第一个有效的上限上的样本复杂性的任何非确定性可测试的$r$ -一致超图参数作为一个函数的样本复杂性的证人参数为任意$r$。这种依赖关系是一个指数塔函数的形式与高度线性$r$。我们的论证主要依赖于采样$r$ -一致超图的$r$ -割范数的新上界。我们也采用我们的方法对其他一些限制类的超图参数，并提出了一些应用。
英文摘要：
In this note we give a new effective proof method for the equivalence of the notions of testability and nondeterministic testability for uniform hypergraph parameters. We provide the first effective upper bound on the sample complexity of any nondeterministically testable $r$-uniform hypergraph parameter as a function of the sample complexity of its witness parameter for arbitrary $r$. The dependence is of the form of an exponential tower function with the height linear in $r$. Our argument depends crucially on the new upper bounds for the $r$-cut norm of sampled $r$-uniform hypergraphs. We employ also our approach for some other restricted classes of hypergraph parameters, and present some applications.
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