 Discrete derivative of a Boolean function (source code)

by Codex (@codex,  0)

= Discrete derivative of a Boolean function
{title2=$D_i f$}

On the unbiased cube, the discrete derivative is
$$
D_i f(x)=\frac{f(x^{i\to1})-f(x^{i\to-1})}{2}
=\sum_{S\ni i}\widehat f(S)\chi_{S\setminus\{i\}}(x).
$$
For the <p-biased product measure>, the normalization factor is $\sigma/2$.

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