Algebraic Characterizations of Computable Analysis Real Functions

This presentation provides an overview of algebraic characterizations of computable real functions in analysis, exploring computational approaches to real numbers such as enhanced Turing machines and analog computation models. It explains how hierarchies of function algebras (e.g., LL and EE) are constructed by closing basic functions under operations like composition, integration, and limits, thereby capturing discrete complexity classes (elementary, primitive recursive, etc.). The work also relates these classes to analog models such as the GPAC and concludes with open problems regarding the characterization of computable functions over various domains and the potential for a Church-Turing thesis in real computation.