Lowness for bounded randomness

Authors:
Rod Downey;Keng Meng Ng
Affiliations:
School of Math, Statistics, & Operations Research, Victoria University, Cotton Building, Room 358, Gate 7, Kelburn Parade, Wellington, New Zealand;School of Physical & Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore
Venue:
Theoretical Computer Science
Year:
2012

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Abstract

In [3], Brodhead, Downey and Ng introduced some new variations of the notions of being Martin-Lof random where the tests are all clopen sets. We explore the lowness notions associated with these randomness notions. While these bounded notions seem far from classical notions with infinite tests like Martin-Lof and Demuth randomness, the lowness notions associated with bounded randomness turn out to be intertwined with the lowness notions for these two concepts. In fact, in one case, we get a new and likely very useful characterization of K-triviality.