The relationships between various meta-complexity problems are not well understood in the worst-case regime, including whether the search version is harder than the decision version, whether the hardness scales with the ``threshold", and how the hardness of different meta-complexity problems relate to one another, and to the task of function ... more >>>

Proving explicit lower bounds on the size of algebraic formulas is a long-standing open problem in the area of algebraic complexity theory. Recent results in the area (e.g. a lower bound against constant-depth algebraic formulas due to Limaye, Srinivasan, and Tavenas (FOCS 2021)) have indicated a way forward for attacking ... more >>>

We give simply exponential lower bounds on the probabilities of a given strongly Rayleigh distribution, depending only on its expectation. This resolves a weak version of a problem left open by Karlin-Klein-Oveis Gharan in their recent breakthrough work on metric TSP, and this resolution leads to a minor improvement of ... more >>>