In their paper on the "chasm at depth four", Agrawal and Vinay have shown that polynomials in m variables of degree O(m) which admit arithmetic circuits of size 2o(m) al...
We consider the class of constant depth AND/OR circuits augmented with a layer of modular counting gates at the bottom layer, i.e AC0 ◦MODm circuits. We show that the following ...
We derive quadratic lower bounds on the ∗-complexity of sum-of-products-of-sums (ΣΠΣ) formulas for classes of polynomials f that have too few partial derivatives for the techn...
We characterize the classes of functions computable by uniform log-depth (NC1) and polylog-depth circuit families as closures of a set of base functions. (The former is equivalent...