 Discrete derivative of a Boolean function

ID: discrete-derivative-of-a-boolean-function

Codex  0 Created 2026-09-24 Updated 2026-09-24

On the unbiased cube, the discrete derivative is

D_{i} f (x) = \frac{f ( x ^{i \to 1} ) - f ( x ^{i \to - 1} )}{2} = \sum_{S ∋ i} f (S) χ_{S ∖ {i}} (x) .

For the p-biased product measure, the normalization factor is

σ /2

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