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 Kolmogorov complexity characterization of constructive Hausdorff dimension
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SIAM Journal on Computing
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Information and Computation
Effective Strong Dimension in Algorithmic Information and Computational Complexity
SIAM Journal on Computing
Dimension Extractors and Optimal Decompression
Theory of Computing Systems
Every sequence is decompressible from a random one
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Extracting kolmogorov complexity with applications to dimension zero-one laws
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Algorithmically Independent Sequences
DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
Extracting Kolmogorov complexity with applications to dimension zero-one laws
Information and Computation
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This paper examines the constructive Hausdorff and packingdimensions of weak truth-table degrees. The main result is thatevery infinite sequence Swith constructive Hausdorffdimension dimH(S) and constructive packingdimension dimP(S) is weak truth-tableequivalent to a sequence Rwith ${\rm dim_H}({\it R}) \geq{\rm dim_H}(S) / {\rm dim_P}(S) - \epsilon$, for arbitraryε 0. Furthermore, ifdimP(S) 0, thendimP(R) ≥ 1 - ε. Thereduction thus serves as a randomness extractorthatincreases the algorithmic randomness of S, as measured byconstructive dimension.A number of applications of this result shed new light on theconstructive dimensions of wtt degrees (and, by extension, Turingdegrees). A lower bound of dimH(S) /dimP(S) is shown to hold for the wtt degree ofany sequence S. A new proof is given of a previously-knownzero-one law for the constructive packing dimension of wtt degrees.It is also shown that, for any regularsequence S(that is, dimH(S) =dimP(S)) such that dimH(S) 0, the wtt degree of Shas constructive Hausdorff andpacking dimension equal to 1.Finally, it is shown that no single Turing reduction can be auniversalconstructive Hausdorff dimension extractor.