Algorithmic randomness and measures of complexity

Abstract
We survey recent advances on the interface between computability theory and algorithmic randomness, with special attention on measures of relative complexity. We focus on (weak) reducibilities that measure (a) the initial segment complexity of reals and (b) the power of reals to compress strings, when they are used as oracles. The results are put into context and several connections are made with various central issues in modern algorithmic randomness and computability
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 35,457
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

Kolmogorov Complexity and Computably Enumerable Sets.George Barmpalias & Angsheng Li - 2013 - Annals of Pure and Applied Logic 164 (12):1187-1200.

Add more citations

Similar books and articles

Schnorr Randomness.Rodney G. Downey & Evan J. Griffiths - 2004 - Journal of Symbolic Logic 69 (2):533 - 554.
Chance Versus Randomness.Antony Eagle - 2010 - Stanford Encyclopedia of Philosophy.
Probabilistic Algorithmic Randomness.Sam Buss & Mia Minnes - 2013 - Journal of Symbolic Logic 78 (2):579-601.
Relative Randomness and Cardinality.George Barmpalias - 2010 - Notre Dame Journal of Formal Logic 51 (2):195-205.
A C.E. Real That Cannot Be SW-Computed by Any Ω Number.George Barmpalias & Andrew E. M. Lewis - 2006 - Notre Dame Journal of Formal Logic 47 (2):197-209.
Lowness and $\Pi _{2}^{0}$ Nullsets.Rod Downey, Andre Nies, Rebecca Weber & Liang Yu - 2006 - Journal of Symbolic Logic 71 (3):1044 - 1052.

Analytics

Added to PP index
2013-11-23

Total downloads
19 ( #318,234 of 2,285,669 )

Recent downloads (6 months)
2 ( #232,487 of 2,285,669 )

How can I increase my downloads?

Monthly downloads

My notes

Sign in to use this feature