Notre Dame Journal of Formal Logic

Lowness for Difference Tests

David Diamondstone and Johanna N. Y. Franklin

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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.

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

First available in Project Euclid: 20 January 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

algorithmic randomness difference randomness difference tests lowness


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.

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