InforLorV4, Hal, Corpus, bibRecord, 002601

Genericity of weakly computable objects

Identifieur interne : 002601 ( Hal/Corpus ); précédent : 002600; suivant : 002602

Genericity of weakly computable objects

Auteurs : Mathieu Hoyrup

Source :

RBID : Hal:hal-01095864

English descriptors

mix :
- Computable Analysis, Generic, Irreversible function, Priority method.

Abstract

In computability theory many results state the existence of objects that in many respects lack algorithmic structure but at the same time are effective in some sense. Friedberg and Muchnik's answer to Post problem is one of the most celebrated results in this form. The main goal of the paper is to develop a general result that embodies a large number of these particular constructions, capturing the essential idea that is common to all of them, and expressing it in topological terms.To do so, we introduce the effective topological notions of irreversible function and directional genericity and provide two main results that identify situations when such constructions are possible, clarifying the role of topology in many arguments from computability theory. We apply these abstract results to particular situations, illustrating their strength and deriving new results.This paper is an extended version of a conference paper with detailed proofs and new results.

Url:

https://hal.inria.fr/hal-01095864

Links to Exploration step

Hal:hal-01095864

Le document en format XML

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Genericity of weakly computable objects

Genericity of weakly computable objects

Source :

English descriptors

Abstract

Links to Exploration step

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri