单调性检验与有向等周不等式

Circuits, Packets, and Protocols Pub Date : 1900-01-01 DOI:10.1145/3568031.3568034

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摘要

给定一个函数f:{0,1}∑{0,1}，定义函数的方差为var(f) = p(1−p)，其中p = Prx[f (x) = 1]。设Sf表示敏感边的集合，即(x, y)对的集合，使得x, y∈{0,1}n恰好在一个坐标上不同，即f (x) = 1和f (y) = 0。设If = |Sf |表示该函数的“总影响”。一个2n民俗定理指出:1

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Monotonicity Testing and Directed Isoperimetric Inequalities

2.1.1 Boolean Isoperimetric Type Theorems n Given a function f : {0, 1} ↦ {0, 1}, define the variance of the function as var(f ) = p(1 − p), where p = Prx[f (x) = 1]. Let Sf denote the set of sensitive edges, that is, the set of pairs (x, y) such that x, y ∈ {0, 1}n differ in exactly one coordinate, f (x) = 1 and f (y) = 0. Let If = |Sf | denote the “total influence” of the function. A 2n folklore theorem states:1

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Circuits, Packets, and Protocols

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