A propositional proof system is \emph{weakly automatizable} if there
is a polynomial time algorithm which separates satisfiable formulas
from formulas which have a short refutation in the system, with
respect to a given length bound. We show that if the resolution
proof system is weakly automatizable, ... more >>>

We consider arithmetic formulas consisting of alternating layers of addition $(+)$ and multiplication $(\times)$ gates such that the fanin of all the gates in any fixed layer is the same. Such a formula $\Phi$ which additionally has the property that its formal/syntactic degree is at most twice the (total) degree ... more >>>

We study lower bounds for testing membership in families of linear/affine-invariant Boolean functions over the hypercube. A family of functions $P\subseteq \{\{0,1\}^n \rightarrow \{0,1\}\}$ is linear/affine invariant if for any $f\in P$, it is the case that $f\circ L\in P$ for any linear/affine transformation $L$ of the domain. Motivated by ... more >>>