The notion of control can be thought of as the process of selection of a policy to influence the dynamics of a system in order to achieve a desired objective.
Garbled circuits are a central primitive in cryptography. Intuitively, a garbled circuit enables its holder to evaluate a circuit on an input, so that the evaluator learns the output but learns nothing about the circuit or the input.
Given a graph $G$, let $\mathbb{P}_G$ denote the cone of positive semidefinite (psd) matrices, with non-negative entries, and zeros according to $G$. Which powers preserve psd-ness when applied entrywise to all matrices in $\mathbb{P}_G$?
We use exponential sums to analyze the Fourier spectrum of functions of the type MOD_m^A (with output in {-1, 1}), for any constant m, and a general accepting set A. We will then see how this yields lower bounds on the number of monomials require