Recursively enumerable sets and degrees
Recursively enumerable sets and degrees
Computability
An introduction to Kolmogorov complexity and its applications
An introduction to Kolmogorov complexity and its applications
A Theory of Program Size Formally Identical to Information Theory
Journal of the ACM (JACM)
Randomness and Recursive Enumerability
SIAM Journal on Computing
Recursively Enumerable Reals and Chaitin Omega Numbers
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
Visualization 2001 Conference (Acm
Visualization 2001 Conference (Acm
How powerful are integer-valued martingales?
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
Lowness for weakly 1-generic and kurtz-random
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Arithmetic complexity via effective names for random sequences
ACM Transactions on Computational Logic (TOCL)
Process and truth-table characterisations of randomness
Theoretical Computer Science
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Kurtz randomness is a notion of algorithmic randomness for real numbers. In particular a real x is called Kurtz random (or weakly random) iff it is contained in every computably enumerable set U of (Lebesgue) measure 1. We prove a number of characterizations of this notion, relating it to other notions of randomness such as the well-known notions of computable randomness, Martin-Löf randomness and Schnorr randomness. For the first time we give machine characterizations of Kurtz randomness. Whereas the Turing degree of every Martin-Löf random c.e. real is the complete degree, and the degrees of Schnorr random c.e. reals are all high, we show that Kurtz random c.e. reals occur in every non-zero c.e. degree. Additionally, we show that the sets that are low for Kurtz randomness are all hyperimmune and include those that are low for Schnorr randomness, characterized previously by Terwijn and Zambella.@ 2004 Elsevier B.V. All rights reserved.