Programming with (Discrete and Continuous) Ordinary Differential Equations

Nov 15 14:00 ₂₀₂₂

Abstract: Initially motivated by understanding the computational power of various continuous-time analog models of computations, several characterizations of  complexity and computability classes have been obtained recently using ordinary differential equations. Basically, each class is characterized as the class of functions containing some basic functions, and closed by composition and various natural schemas or constructions, based on ordinary differential equations.  

This means for one direction of these proofs that we can program with ordinary differential equations.

We will provide a review of some of these recent results, and some applications. We will mainly focus on their discrete counterpart, also known as discrete ordinary differential equations, or finite differences.