On the Kolmogorov complexity of continuous real functions
โ Scribed by Farjudian, Amin
- Book ID
- 120516410
- Publisher
- Elsevier Science
- Year
- 2013
- Tongue
- English
- Weight
- 239 KB
- Volume
- 164
- Category
- Article
- ISSN
- 0168-0072
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๐ SIMILAR VOLUMES
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
A reasonable computational complexity theory for real functions is obtained by using the modified infinite binary representation with digits 0, 1, and -1 for the real numbers and Turing machines which transform with one-way output modified binary input sequences into modified binary output sequences
The notion of Kolmogorov program-size complexity (or algorithmic information) is defined here for arbitrary objects. Using a special form of recursive topological spaces, called partition spaces, we define a recursive topology which uses a level of partition for approximation of arbitrary objects in