Fourier Analysis of Boolean Functions under Random Restriction
Fourier Transform Consider a function \(f\colon \{0,1\}^n \to \{-1, 1\}\) on \(n\) boolean variables. This can be viewed as a transform of a boolean function \(g\colon \{0,1\}^n \to \{0, 1\}\) by letting \(f(x) = (-1)^{g(x)}\). For \(\alpha \in\{0,1\}^n\), define the …
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