Modular gates are known to be immune for the random
restriction techniques of Ajtai; Furst, Saxe, Sipser; and Yao and
Hastad. We demonstrate here a random clustering technique which
overcomes this difficulty and is capable to prove generalizations of
several known modular circuit lower bounds of Barrington, Straubing,
Therien; Krause ... more >>>

We show that any Algebraic Branching Program (ABP) computing the polynomial $\sum_{i = 1}^n x_i^n$ has at least $\Omega(n^2)$ vertices. This improves upon the lower bound of $\Omega(n\log n)$, which follows from the classical result of Baur and Strassen [Str73, BS83], and extends the results by Kumar [Kum19], which showed ... more >>>