Group Isomorphism and the Polylogarithmic-Time Hierarchy: Depth-2$\frac{1}{2}$ Circuits and Lower Bounds

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 quasipoly