§3.3: Restrictions

A common operation on boolean functions $f : \{-1,1\}^n \to {\mathbb R}$ is restriction to subcubes. Suppose $[n]$ is partitioned into two sets, $J$ and $\overline{J} = [n] \setminus J$. If the inputs bits in $\overline{J}$ are fixed to constants, the result is a function $\{-1,1\}^J \to {\mathbb R}$. For example, if we [...]