Semicomputable points in Euclidean spaces - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2019

Semicomputable points in Euclidean spaces

Abstract

We introduce the notion of a semicomputable point in R^n , defined as a point having left-c.e. projections. We study the range of such a point, which is the set of directions on which its projections are left-c.e., and is a convex cone. We provide a thorough study of these notions, proving along the way new results on the computability of convex sets. We prove realization results, by identifying computability properties of convex cones that make them ranges of semicomputable points. We give two applications of the theory. The first one provides a better understanding of the Solovay derivatives. The second one is the investigation of left-c.e. quadratic polynomials. We show that this is, in fact, a particular case of the general theory of semicomputable points.
Fichier principal
Vignette du fichier
paper.pdf (487.4 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-02154825 , version 1 (13-06-2019)

Identifiers

Cite

Mathieu Hoyrup, Donald M Stull. Semicomputable points in Euclidean spaces. MFCS 2019 - 44th International Symposium on Mathematical Foundations of Computer Science, Aug 2019, Aachen, Germany. ⟨10.4230/LIPIcs.MFCS.2019.63⟩. ⟨hal-02154825⟩
47 View
24 Download

Altmetric

Share

Gmail Facebook X LinkedIn More