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Bounded Randomness ⋆
"... Abstract. We introduce some new variations of the notions of being MartinLöf random where the tests are all clopen sets. We explore how these randomness notions relate to classical randomness notions and to degrees of unsolvability. 1 ..."
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Abstract. We introduce some new variations of the notions of being MartinLöf random where the tests are all clopen sets. We explore how these randomness notions relate to classical randomness notions and to degrees of unsolvability. 1
CHARACTERIZING THE STRONGLY JUMPTRACEABLE SETS VIA RANDOMNESS
"... Abstract. We show that if a set A is computable from every superlow 1random set, then A is strongly jumptraceable. Together with a result from [9], this theorem shows that the computably enumerable jumptraceable sets are exactly the computably enumerable sets computable from every superlow 1rand ..."
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Abstract. We show that if a set A is computable from every superlow 1random set, then A is strongly jumptraceable. Together with a result from [9], this theorem shows that the computably enumerable jumptraceable sets are exactly the computably enumerable sets computable from every superlow 1random set. We also prove the analogous result for superhighness: a c.e. set is strongly jumptraceable if and only if it is computable from any superhigh random set. Finally, we show that for each cost function c with the limit condition there is a random ∆ 0 2 set Y such that each c.e. set A �T Y obeys c. 1.
LOWNESS FOR BOUNDED RANDOMNESS
"... In [3], Brodhead, Downey and Ng introduced some new variations of the notions of being MartinLöf 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 ..."
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In [3], Brodhead, Downey and Ng introduced some new variations of the notions of being MartinLöf 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 MartinLöf 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 Ktriviality