3 papers
cs.CC2019
Continuous Ordinary Differential Equations and Transfinite Computations
Olivier Bournez, Sabrina Ouazzani
We consider Continuous Ordinary Differential Equations (CODE) y'=f(y), where f is a continuous function. They are known to always have solutions for a given initial condition y(0)=…
cs.LO2018
Recursion schemes, discrete differential equations and characterization of polynomial time computation
Olivier Bournez, Arnaud Durand, Sabrina Ouazzani
This papers studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs). It presents a new framework using discrete ODEs as a central tool for…
cs.LO2018
Cheap Non-standard Analysis and Computability
Olivier Bournez, Sabrina Ouazzani
Non standard analysis is an area of Mathematics dealing with notions of infinitesimal and infinitely large numbers, in which many statements from classical analysis can be expresse…