A depth-4 algebraic circuit with top fan-in $k$ and bottom fan-in $2$ is a circuit $\Phi$ of the form $\Phi = \sum_{i=1}^k \prod_{j=1}^{m_i} Q_{ij}$, where the polynomials $Q_{ij} \in \mathbb{K}[x_1, \ldots, x_n]$ have degree at most $2$.
The class of all such circuits is denoted by $\Sigma^k \Pi \Sigma ... more >>>

The partial derivative method is a central tool in algebraic complexity, underlying lower bounds for multilinear formulas, bounded depth circuits, and algebraic branching programs. A key feature of this measure is its subadditivity and submultiplicativity, which are usually used to upper bound the measure. However, proving lower bounds requires bounding ... more >>>