We consider the algorithmic problem of finding the optimal weights and biases for a two-
layer fully connected neural network to fit a given set of data points, also known as empirical …

A continuous constraint satisfaction problem (CCSP) is a constraint satisfaction problem
(CSP) with the real numbers as domain. We engage in a systematic study to classify CCSPs …

We survey the complexity class $\exists\mathbb {R} $, which captures the complexity of
deciding the existential theory of the reals. The class $\exists\mathbb {R} $ has roots in two …

Abstract The Existential Theory of the Reals consists of true sentences of formulas of
polynomial equations and inequalities over real variables that are existentially quantified …

In this thesis, we explore a young branch of computational complexity that deals with
problems whose solutions consist of real numbers subject to a given set of polynomial …

The importance of the recently introduced complexity class∃ R has increased significantly
because of its relevance in computational geometry. The discrete real polynomial hierarchy …