Polynomial Identity Testing (PIT) algorithms have focused on
polynomials computed either by small alternation-depth arithmetic circuits, or by read-restricted
formulas. Read-once polynomials (ROPs) are computed by read-once
formulas (ROFs) and are the simplest of read-restricted polynomials.
Building structures above these, we show the following:
\begin{enumerate}
\item A deterministic polynomial-time non-black-box ... more >>>

We study limitations of polynomials computed by depth two circuits built over read-once polynomials (ROPs) and depth three syntactically multi-linear formulas.
We prove an exponential lower bound for the size of the $\Sigma\Pi^{[N^{1/30}]}$ arithmetic circuits built over syntactically multi-linear $\Sigma\Pi\Sigma^{[N^{8/15}]}$ arithmetic circuits computing a product of variable ... more >>>

We show nearly quadratic separations between two pairs of complexity measures:
1. We show that there is a Boolean function $f$ with $D(f)=\Omega((D^{sc}(f))^{2-o(1)})$ where $D(f)$ is the deterministic query complexity of $f$ and $D^{sc}$ is the subcube partition complexity of $f$;
2. As a consequence, we obtain that there is ... more >>>