One of the major open problems in complexity theory is proving super-logarithmic
lower bounds on the depth of circuits (i.e., $\mathbf{P}\not\subseteq\mathbf{NC}^1$). Karchmer, Raz, and Wigderson (Computational Complexity 5, 3/4) suggested to approach this problem by proving that depth complexity behaves "as expected" with respect to the composition of functions $f ... more >>>

We study the following question: Is it easier to construct a hitting-set generator for polynomials $p:\mathbb{F}^n\rightarrow\mathbb{F}$ of degree $d$ if we are guaranteed that the polynomial vanishes on at most an $\epsilon>0$ fraction of its inputs? We will specifically be interested in tiny values of $\epsilon\ll d/|\mathbb{F}|$. This question was ... more >>>

In the Minimum Circuit Size Problem (MCSP[s(m)]), we ask if there is a circuit of size s(m) computing a given truth-table of length n = 2^m. Recently, a surprising phenomenon termed as hardness magnification by [Oliveira and Santhanam, FOCS 2018] was discovered for MCSP[s(m)] and the related problem MKtP of ... more >>>