منابع مشابه
Constructive Dimension and Weak Truth-Table Degrees
This paper examines the constructive Hausdorff and packing dimensions of weak truth-table degrees. The main result is that every infinite sequence S with constructive Hausdorff dimension dimH(S) and constructive packing dimension dimP(S) is weak truth-table equivalent to a sequence R with dimH(R) ≥ dimH(S)/dimP(S)− ǫ, for arbitrary ǫ > 0. Furthermore, if dimP(S) > 0, then dimP(R) ≥ 1− ǫ. The re...
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A relatively longstanding question in algorithmic randomness is Jan Reimann’s question whether there is a Turing cone of broken dimension. That is, is there a real A such that {B : B ≤T A} contains no 1-random real, yet contains elements of nonzero effective Hausdorff Dimension? We show that the answer is affirmative if Hausdorff dimension is replaced by its inner analogue packing dimension. We...
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A relatively longstanding question in algorithmic randomness is Jan Reimann’s question whether there is a Turing cone of broken dimension. That is, is there a real A such that {B : B ≤T A} contains no 1-random real, yet contains elements of nonzero effective Hausdorff Dimension? We show that the answer is affirmative if Hausdorff dimension is replaced by its inner analogue packing dimension. We...
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ژورنال
عنوان ژورنال: Theory of Computing Systems
سال: 2009
ISSN: 1432-4350,1433-0490
DOI: 10.1007/s00224-009-9170-1