Kane and Williams proved average-case wire lower bounds at the $n^{5/2}/\mathrm{polylog}, n$ scale for an explicit function against depth-two linear-threshold circuits. We prove an almost-everywhere near-cubic wire lower bound for a language in $\mathrm{E}^{\mathrm{NP}}$. For every fixed $c>0$, there is one language $F_c$ and positive constants $b_{S,c}$ and $b_{T,c}$ such ... more >>>

Grochow and Pitassi (2018) introduced the algebraic proof system, the Ideal Proof System (IPS), which connects algebraic circuit complexity to propositional proof complexity. They showed that propositional proof systems such as Extended Frege (Frege) are equivalent to circuit IPS (formula IPS) if the correctness of PIT for circuits (formulas) can ... more >>>

In this paper, we investigate the low-depth circuit complexity of Group Isomorphism in the multiplication (Cayley) table model. We prove the first circuit lower bounds for Group Isomorphism: namely, we show that every family of depth-$2$ Boolean circuits deciding Group Isomorphism requires quasipolynomial-size. We complement this with upper bounds of ... more >>>