The primary goal of this paper is to define and study the interactive information complexity of functions. Let $f(x,y)$ be a function, and suppose Alice is given $x$ and Bob is given $y$. Informally, the interactive information complexity $IC(f)$ of $f$ is the least amount of information Alice and Bob ... more >>>

Let $C$ be a (fan-in $2$) Boolean circuit of size $s$ and depth $d$, and let $x$ be an input for $C$. Assume that a verifier that knows $C$ but doesn't know $x$ can access the low degree extension of $x$ at one random point. Two competing provers try to ... more >>>

We study the computability of one-way functions and pseudorandom generators
by monotone circuits, showing a substantial gap between the two:
On one hand, there exist one-way functions that are computable
by (uniform) polynomial-size monotone functions, provided (of course)
that one-way functions exist at all.
On the other hand, ... more >>>