Sophistication vs Logical Depth

TitleSophistication vs Logical Depth
Publication TypeJournal Article
Year of Publication2017
AuthorsAntunes, L., Bauwens B., Souto A., & Teixeira A.
JournalTheory of Computing Systems
Volume60
Pagination280–298
Date PublishedFeb
ISSN1433-0490
Abstract

Sophistication and logical depth are two measures that express how complicated the structure in a string is. Sophistication is defined as the minimal complexity of a computable function that defines a two-part description for the string that is shortest within some precision; the second can be defined as the minimal computation time of a program that is shortest within some precision. We show that the Busy Beaver function of the sophistication of a string exceeds its logical depth with logarithmically bigger precision, and that logical depth exceeds the Busy Beaver function of sophistication with logarithmically bigger precision. We also show that sophistication is unstable in its precision: constant variations can change its value by a linear term in the length of the string.

URLhttps://doi.org/10.1007/s00224-016-9672-6
DOI10.1007/s00224-016-9672-6