We prove super-polynomial lower bounds for low-depth arithmetic circuits using the shifted partials measure [Gupta-Kamath-Kayal-Saptharishi, CCC 2013], [Kayal, ECCC 2012] and the affine projections of partials measure [Garg-Kayal-Saha, FOCS 2020], [Kayal-Nair-Saha, STACS 2016]. The recent breakthrough work of Limaye, Srinivasan and Tavenas [FOCS 2021] proved these lower bounds by proving ... more >>>

We give a deterministic white-box algorithm to estimate the expectation of a read-once branching program of length $n$ and width $w$ in space
$$\tilde{O}\left(\log n+\sqrt{\log n}\cdot\log w\right).$$
In particular, we obtain an almost optimal space $\tilde{O}(\log n)$ derandomization of programs up to width $w=2^{\sqrt{\log n}}$.
Previously, ... more >>>

Matrix powering, and more generally iterated matrix multiplication, is a fundamental linear algebraic primitive with myriad applications in computer science. Of particular interest is the problem's space complexity as it constitutes the main route towards resolving the $\mathbf{BPL}$ vs. $\mathbf{L}$ problem. The seminal work by Saks and Zhou (FOCS 1995) ... more >>>