Notre Dame Journal of Formal Logic

Lowness for Difference Tests

David Diamondstone and Johanna N. Y. Franklin

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Abstract

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 A, there is a difference test TA relative to A which cannot even be covered by finitely many unrelativized difference tests.

Article information

Source
Notre Dame J. Formal Logic, Volume 55, Number 1 (2014), 63-73.

Dates
First available in Project Euclid: 20 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1390246438

Digital Object Identifier
doi:10.1215/00294527-2377878

Mathematical Reviews number (MathSciNet)
MR3161412

Zentralblatt MATH identifier
1330.03078

Subjects
Primary: 03D32: Algorithmic randomness and dimension [See also 68Q30]

Keywords
algorithmic randomness difference randomness difference tests lowness

Citation

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


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