Directed Isoperimetric Theorems for Boolean Functions on the Hypergrid and an Õ(n√d) Monotonicity Tester
Directed Isoperimetric Theorems for Boolean Functions on the Hypergrid and an Õ(n√d) Monotonicity Tester
复制标题
超网格上布尔函数的有向等周定理和 Õ(n√d) 单调性测试器
DOI：
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发表时间：
2023
期刊：
影响因子：
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通讯作者：
C. Seshadhri
中科院分区：
文献类型：
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作者：
Hadley Black;Deeparnab Chakrabarty;C. Seshadhri
在超级格言上测试布尔功能的单调性，f：[n] d→{0,1}是属性测试的经典主题。 KHOT-MINZER-SAFRA（FOCS 2015）的结果给出了一个非自适应的单侧测试仪，使O（ε-2√D）的查询达到了Polylog D和ε因子。查询非自适应下限（Chen-de-servedio-tan（STOC 2015），Chen-Waingarten-XIE（STOC 2017），对于任何N> 2）。 /6） - Query上限（苏打水2020），距离本文中的超数据线相当遥远。因素从技术的角度进行非自适应的单侧单调测试仪。我们只以HyperCube而闻名。
The problem of testing monotonicity for Boolean functions on the hypergrid, f:[n]d → {0,1} is a classic topic in property testing. When n=2, the domain is the hypercube. For the hypercube case, a breakthrough result of Khot-Minzer-Safra (FOCS 2015) gave a non-adaptive, one-sided tester making O(ε−2√d) queries. Up to polylog d and ε factors, this bound matches the Ω(√d)-query non-adaptive lower bound (Chen-De-Servedio-Tan (STOC 2015), Chen-Waingarten-Xie (STOC 2017)). For any n > 2, the optimal non-adaptive complexity was unknown. A previous result of the authors achieves a O(d5/6)-query upper bound (SODA 2020), quite far from the √d bound for the hypercube. In this paper, we resolve the non-adaptive complexity of monotonicity testing for all constant n, up to poly(ε−1logd) factors. Specifically, we give a non-adaptive, one-sided monotonicity tester making O(ε−2n√d) queries. From a technical standpoint, we prove new directed isoperimetric theorems over the hypergrid [n]d. These results generalize the celebrated directed Talagrand inequalities that were only known for the hypercube.
高维分布的随机限制和子立方条件的均匀性测试
DOI：
10.5555/3458064.3458085
发表时间：
2021
期刊：
Proceedings of the 32th Annual ACM-SIAM Symposium on Discrete Algorithms
影响因子：
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作者：
Canonne, Clement;Chen, Xi;Kamath, Gautam;Levi, Amit;Waingarten, Erik
通讯作者：
Waingarten, Erik
总影响时间的自适应布尔单调性测试
DOI：
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发表时间：
2019
期刊：
ITCS 2019
影响因子：
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作者：
Chakrabarty, Deeparnab;Seshadhri, C.
通讯作者：
Seshadhri, C.