Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 55, Number 1 (2014), 63-73.
Lowness for Difference Tests
We show that being low for difference tests is the same as being computable and therefore lowness for difference tests is not the same as lowness for difference randomness. This is the first known example of a randomness notion where lowness for the randomness notion and lowness for the test notion do not coincide. Additionally, we show that for every incomputable set , there is a difference test relative to which cannot even be covered by finitely many unrelativized difference tests.
Notre Dame J. Formal Logic, Volume 55, Number 1 (2014), 63-73.
First available in Project Euclid: 20 January 2014
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 03D32: Algorithmic randomness and dimension [See also 68Q30]
Diamondstone, David; Franklin, Johanna N. Y. Lowness for Difference Tests. Notre Dame J. Formal Logic 55 (2014), no. 1, 63--73. doi:10.1215/00294527-2377878. https://projecteuclid.org/euclid.ndjfl/1390246438