In a recent work, Gryaznov, Pudlák and Talebanfard (CCC '22) introduced a linear variant of read-once
branching programs, with motivations from circuit and proof complexity. Such a read-once linear branching program is
a branching program where each node is allowed to make $\mathbb{F}_2$-linear queries, and are read-once in the ... more >>>

It is well-known that randomized communication protocols are more powerful than deterministic protocols. In particular the Equality function requires $\Omega(n)$ deterministic communication complexity but has efficient randomized protocols. Previous work of Chattopadhyay, Lovett and Vinyals shows that randomized communication is strictly stronger than what can be solved by deterministic protocols ... more >>>

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 >>>