In this work, we establish separation theorems for several subsystems of the Ideal Proof System (IPS), an algebraic proof system introduced by Grochow and Pitassi (J. ACM, 2018). Separation theorems are well-studied in the context of classical complexity theory, Boolean circuit complexity, and algebraic complexity.

In an important work ... more >>>

It is a long-standing open problem in algebraic complexity to prove lower bounds against multilinear algebraic branching programs (mABPs). The best lower bounds in this setting are still quadratic (Alon, Kumar and Volk (Combinatorica 2020)). At the same time, it remains a possibility that the “min-partition rank” method introduced by ... more >>>

In this paper, we give the first subexponential (in fact, quasi-polynomial time) reconstruction algorithm for depth-3 circuits of any constant top fan-in ($\Sigma\Pi\Sigma(k)$ circuits) over $\mathbb R$, $\mathbb C$, or any large characteristic finite field $\mathbb F$. More explicitly, we show that for any constant $k$, given black-box access to ... more >>>