Depth as Randomness Deficiency

• Type: Article in International Scientific Journal
• Date: 2009

Authors

antunes, l (Author) FCUP; matos, a (Author) FCUP; souto, a (Author) Other; vitanyi, p (Author) Other

Journal

Title: Theory of Computing Systems

Vol. 45

Pages: 724-739

ISSN: 1432-4350

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 8 Citations

Scopus - 8 Citations

Other information

Authenticus ID: 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 16