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Scaled Dimension and the Kolmogorov Complexity of Turing-Hard Sets

✍ Scribed by John M. Hitchcock; María López-Valdés; Elvira Mayordomo


Publisher
Springer
Year
2007
Tongue
English
Weight
503 KB
Volume
43
Category
Article
ISSN
1433-0490

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On hausdorff and topological dimensions
✍ Jin-yi Cai; Juris Hartmanis 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 767 KB

We investigate the Kolmogorov complexity of real numbers. Let K be the Kolmogorov complexity function; we determine the Hausdorff dimension and the topological dimension of the graph of K. Since these dimensions are different, the graph of the Kolmogorov complexity function of the real line forms a