On the computability of fractal dimensions and Hausdorff measure

DOI10.1016/S0168-0072(97)00060-2zbMath0926.03049MaRDI QIDQ1295381

Ker-I. Ko

Publication date: 24 June 1999

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

zbMATH Keywords

Julia setsHausdorff dimensionHausdorff measurecomputable functionsrecursive real numbersrecursively approximable setspolynomial-time computable real functionscomputable curve

Mathematics Subject Classification ID

Constructive and recursive analysis (03F60) Fractals (28A80) Complexity of computation (including implicit computational complexity) (03D15) Complexity classes (hierarchies, relations among complexity classes, etc.) (68Q15) Applications of computability and recursion theory (03D80)

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Cites Work

• A polynomial-time computable curve whose interior has a nonrecursive measure
• On Hausdorff and topological dimensions of the Kolmogorov complexity of the real line
• Recursive analysis
• Fractals, dimension, and formal languages
• On a theory of computation and complexity over the real numbers: 𝑁𝑃- completeness, recursive functions and universal machines
• Computational Complexity of Two-Dimensional Regions
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