Abstract
We now turn to lowness notions for other notions of randomness. We begin with Schnorr randomness. Since there is no universal Schnorr test, it is not clear that the notions of a set A being low for Schnorr randomness (i.e.,every Schnorr random set is Schnorr random relative to A) and being low for Schnorr tests (i.e., every Schnorr test relative to A can be covered by an unrelativized Schnorr test1) should be the same. In fact, this was an open question in Ambos-Spies and Kučera [9]. As we will see, it was solved by Kjos-Hanssen, Nies, and Stephan [207].
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Downey, R.G., Hirschfeldt, D.R. (2010). Lowness and Triviality for Other Randomness Notions. In: Algorithmic Randomness and Complexity. Theory and Applications of Computability. Springer, New York, NY. https://doi.org/10.1007/978-0-387-68441-3_12
Download citation
DOI: https://doi.org/10.1007/978-0-387-68441-3_12
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-95567-4
Online ISBN: 978-0-387-68441-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)