Layerwise Computability and Image Randomness - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Theory of Computing Systems Year : 2017

Layerwise Computability and Image Randomness

Abstract

Algorithmic randomness theory starts with a notion of an individual random object. To be reasonable, this notion should have some natural properties; in particular, an object should be random with respect to the image distribution F(P) (for some distribution P and some mapping F) if and only if it has a P-random F-preimage. This result (for computable distributions and mappings, and Martin-Löf randomness) was known for a long time (folklore); for layerwise computable mappings it was mentioned in Hoyrup and Rojas (2009, Proposition 5) (even for more general case of computable metric spaces). In this paper we provide a proof and discuss the related quantitative results and applications.
Fichier principal
Vignette du fichier
1607.04232.pdf (272.27 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01650910 , version 1 (20-04-2019)

Identifiers

Cite

Laurent Bienvenu, Mathieu Hoyrup, Alexander Shen. Layerwise Computability and Image Randomness. Theory of Computing Systems, 2017, 61 (4), pp.1353-1375. ⟨10.1007/s00224-017-9791-8⟩. ⟨hal-01650910⟩
284 View
123 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More