使用Õ(n^{3/4})自适应查询进行布尔一致性测试

2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS) Pub Date : 2017-10-01 DOI:10.1109/FOCS.2017.85

Xi Chen, Erik Waingarten, Jinyu Xie

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引用次数: 13

摘要

我们给出了一个自适应算法来测试未知布尔函数f: {0,1}^n -≈{0,1}是一元的(即f的每个变量要么是非递减的要么是非递增的)或者≥-远不是一元的，有单侧误差和O(n^{3/4}/≥^2)次查询。这改进了来自Baleshzar, Chakrabarty, Pallavoor, Raskhodnikova和Seshadhri的最佳自适应O(n/≥)查询算法，当1/ε

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Boolean Unateness Testing with Õ(n^{3/4}) Adaptive Queries

We give an adaptive algorithm that tests whether an unknown Boolean function f: {0,1}^n -≈ {0, 1} is unate (i.e. every variable of f is either non-decreasing or non-increasing) or ≥-far from unate with one-sided error and O(n^{3/4}/≥^2) many queries. This improves on the best adaptive O(n/≥)-query algorithm from Baleshzar, Chakrabarty, Pallavoor, Raskhodnikova and Seshadhri when 1/ε

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2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)

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