Depth as Randomness Deficiency

• Tipo: Artigo em Revista Científica Internacional
• Data: 2009

Autores

antunes, l (Autor) FCUP; matos, a (Autor) FCUP; souto, a (Autor) Outra; vitanyi, p (Autor) Outra

Revista

Título: Theory of Computing Systems

Vol. 45

Páginas: 724-739

ISSN: 1432-4350

Editora: Springer Nature

Indexação

ISI Web of Knowledge - 8 Citações

Scopus - 8 Citações

Outras Informações

ID Authenticus: P-003-EYB

DOI: 10.1007/s00224-009-9171-0

Abstract (EN): Depth of an object concerns a tradeoff between computation time and excess of program length over the shortest program length required to obtain the object. It gives an unconditional lower bound on the computation time from a given program in absence of auxiliary information. Variants known as logical depth and computational depth are expressed in Kolmogorov complexity theory. We derive quantitative relation between logical depth and computational depth and unify the different depth notions by relating them to A. Kolmogorov and L. Levin's fruitful notion of randomness deficiency. Subsequently, we revisit the computational depth of infinite strings, study the notion of super deep sequences and relate it with other approaches.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 16