Regular Article: On hausdorff and topological dimensions of the kolmogorov complexity of the real line

Proceedings of the 30th IEEE symposium on Foundations of computer science, pp. 605-619, 1994.

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Keywords:
hausdorff dimensionopen problemreal numbertopological dimensionkolmogorov complexity functionMore(3+)

Abstract:

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 fractal in the sense of Mandelbrot. We a...More

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