免费分发军政府测试

Zhengyang Liu, Xi Chen, R. Servedio, Ying Sheng, Jinyu Xie
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引用次数: 26

摘要

我们研究了在无分布性质检验模型中检验未知n变量布尔函数是否为k-军政府的问题,其中函数之间的距离是相对于{0,1}n上的任意未知概率分布来测量的。我们的第一个主要结果是,可以通过使用Õ(k2)/ n查询(独立于n)的自适应算法执行无分布k-军政府测试,具有单侧误差。与此相补充的是,我们的第二个主要结果是一个下界,表明任何非自适应无分布k-军政府测试算法必须进行Ω(2k/3)查询,即使测试精度为n =1/3。这些边界表明,非自适应k-军政府测试的最优查询复杂度为2Θ(k),而自适应测试的最优查询复杂度为poly(k),从而表明自适应性在测试军政府的无分布查询复杂度方面提供了指数级的改进。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Distribution-free junta testing
We study the problem of testing whether an unknown n-variable Boolean function is a k-junta in the distribution-free property testing model, where the distance between functions is measured with respect to an arbitrary and unknown probability distribution over {0,1}n. Our first main result is that distribution-free k-junta testing can be performed, with one-sided error, by an adaptive algorithm that uses Õ(k2)/є queries (independent of n). Complementing this, our second main result is a lower bound showing that any non-adaptive distribution-free k-junta testing algorithm must make Ω(2k/3) queries even to test to accuracy є=1/3. These bounds establish that while the optimal query complexity of non-adaptive k-junta testing is 2Θ(k), for adaptive testing it is poly(k), and thus show that adaptivity provides an exponential improvement in the distribution-free query complexity of testing juntas.
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