We establish a collection of new size lower bounds against fairly strong algebraic-Boolean propositional proof systems, from depth-3 semantic polynomial calculus for CNFs, up to semantic $AC^0[2]$-Frege in the regime of deep formulas, as follows:

(1) $\Sigma\Pi\Sigma$-PC: Exponential lower bound against semantic $\Sigma\Pi\Sigma$-PC over $F_2$, namely, polynomial calculus operating with ... more >>>

We investigate the derandomized version of the classical line-point low-degree test in the high-error regime in the bivariate setting and reveal some unexpected behavior. The classical line-point low-degree test takes an $m$-variate function $f$ over a finite field $\mathbb{F}_q$, queries it along a random line and accepts if the restriction ... more >>>

In this paper we give polynomial-size hitting sets for multilinear any-order read-once oblivious algebraic branching programs and for depth-$3$ set-multilinear circuits where each variable set has constant size. Our results also extend to the border of both classes and hold over fields of any characteristic.

The proof combines the ... more >>>