Lifting theorems are used for transferring lower bounds between Boolean function complexity measures. Given a lower bound on a complexity measure $A$ for some function $f$, we compose $f$ with a carefully chosen gadget function $g$ and get essentially the same lower bound on a complexity measure $B$ for the ... more >>>

A $q$-locally correctable code (LCC) $C:\{0,1\}^k \to \{0,1\}^n$ is a code in which it is possible to correct every bit of a (not too) corrupted codeword by making at most $q$ queries to the word. The cases in which $q$ is constant are of special interest, and so are the ... more >>>

In an attempt to show that the acceptance probability of a quantum query algorithm making $q$ queries can be well-approximated almost everywhere by a classical decision tree of depth $\leq \text{poly}(q)$, Aaronson and Ambainis proposed the following conjecture: let $f: \{ \pm 1\}^n \rightarrow [0,1]$ be a degree $d$ polynomial ... more >>>