A Universal Ordinary Differential Equation

Autor: Olivier Bournez, Amaury Pouly

Publikováno v: Logical Methods in Computer Science, Vol Volume 16, Issue 1 (2020)

An astonishing fact was established by Lee A. Rubel (1981): there exists a fixed non-trivial fourth-order polynomial differential algebraic equation (DAE) such that for any positive continuous function $\varphi$ on the reals, and for any positive con

Externí odkaz: https://doaj.org/article/1663ae822d1f4ecf8b8b25382a41018b

A continuous characterization of PSPACE using polynomial ordinary differential equations

Autor: Olivier Bournez, Riccardo Gozzi, Daniel S. Graça, Amaury Pouly

In this paper we provide a characterization of the complexity class PSPACE by using a purely continuous model defined with polynomial ordinary differential equations. info:eu-repo/semantics/publishedVersion

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::348625bc2b5169cfec56a89cc1ce9ff6
https://hdl.handle.net/10400.1/19387

Programming with Ordinary Differential Equations: Some First Steps Towards a Programming Language

Autor: Olivier Bournez

Publikováno v: Revolutions and Revelations in Computability ISBN: 9783031087394

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::1b54e93da3fac8439477775af498a997
https://doi.org/10.1007/978-3-031-08740-0_4

Theoretical Computer Science: Computability, Decidability and Logic

Autor: Jean-Yves Marion, Rémi Gilleron, Gilles Dowek, Serge Grigorieff, Simon Perdrix, Olivier Bournez, Sophie Tison

Publikováno v: A Guided Tour of Artificial Intelligence Research ISBN: 9783030061692
A Guided Tour of Artificial Intelligence Research-Volume III: Interfaces and Applications of Artificial Intelligence (10.1007/978-3-030-06170-8)
A Guided Tour of Artificial Intelligence Research-Volume III: Interfaces and Applications of Artificial Intelligence (10.1007/978-3-030-06170-8), Springer International Publishing, pp.1-50, 2020, ⟨10.1007/978-3-030-06170-8_1⟩

International audience; This chapter deals with a question in the very core of IA: what can be computed by a machine? An agreement has been reached on the answer brought by Alan Turing in 1936. Indeed, all other proposed approaches have led to exactl

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::714369ba9254ad8cb7b4b6e981c4955a
https://doi.org/10.1007/978-3-030-06170-8_1

On the functions generated by the general purpose analog computer

Autor: Daniel S. Graça, Olivier Bournez, Amaury Pouly

Publikováno v: Information and Computation
Repositório Científico de Acesso Aberto de Portugal
Repositório Científico de Acesso Aberto de Portugal (RCAAP)
instacron:RCAAP

We consider the General Purpose Analog Computer (GPAC), introduced by Claude Shannon in 1941 as a mathematical model of Differential Analysers, that is to say as a model of continuous-time analog (mechanical, and later one electronic) machines of tha

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b68b3eb882c170543d032af1ad499e82
https://doi.org/10.1016/j.ic.2017.09.015