Every sequence is reducible to a random one
Information and Control
Recursively enumerable sets and degrees
Recursively enumerable sets and degrees
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
A Theory of Program Size Formally Identical to Information Theory
Journal of the ACM (JACM)
A Kolmogorov complexity characterization of constructive Hausdorff dimension
Information Processing Letters
Gales suffice for constructive dimension
Information Processing Letters
Dimension in Complexity Classes
COCO '00 Proceedings of the 15th Annual IEEE Conference on Computational Complexity
The dimensions of individual strings and sequences
Information and Computation
Effective Strong Dimension in Algorithmic Information and Computational Complexity
SIAM Journal on Computing
Theoretical Computer Science
Constructive Dimension and Weak Truth-Table Degrees
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
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Kučera and Gács independently showed that every infinite sequence is Turing reducible to a Martin-Löf random sequence. We extend this result to show that every infinite sequence S is Turing reducible to a Martin-Löf random sequence R such that the asymptotic number of bits of R needed to compute n bits of S, divided by n, is precisely the constructive dimension of S. We show that this is the optimal ratio of query bits to computed bits achievable with Turing reductions. As an application of this result, we give a new characterization of constructive dimension in terms of Turing reduction compression ratios.