We develop a new technique for proving distribution testing lower bounds for properties defined by inequalities involving the bin probabilities of the distribution in question. Using this technique we obtain new lower bounds for monotonicity testing over discrete cubes and tight lower bounds for log-concavity testing. Our basic technique involves constructing a pair of moment-matching families of distributions by tweaking the probabilities of pairs of bins so that one family maintains the defining inequalities while the other violates them.

翻译：我们发展了一种新技巧，用于证明由所考察分布的箱概率不等式定义的性质的分布测试下界。利用这一技巧，我们获得了离散立方体上单调性测试的新下界以及对数凹性测试的紧下界。我们的基本技巧涉及通过调整一对箱的概率来构造两个矩匹配的分布族，使得其中一个族保持定义性不等式，而另一个族违反这些不等式。