An introduction to Kolmogorov complexity and its applications
An introduction to Kolmogorov complexity and its applications
Proceedings of the 30th IEEE symposium on Foundations of computer science
Complexity
Information and Randomness: An Algorithmic Perspective
Information and Randomness: An Algorithmic Perspective
Information, Randomness and Incompleteness
Information, Randomness and Incompleteness
Randomness as an Invariant for Number Representations
Proceedings of the Colloquium in Honor of Arto Salomaa on Results and Trends in Theoretical Computer Science
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Kolmogorov Complexity and Hausdorff Dimension
FCT '89 Proceedings of the International Conference on Fundamentals of Computation Theory
The extent and density of sequences within the minimal-program complexity hierarchies
Journal of Computer and System Sciences
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We consider for a real number ff the Kolmogorov complexities of its expansions with respect to different bases. In the paper it is shown that, for usual and self-delimiting Kolmogorov complexity, the complexity of the prefixes of their expansions with respect to different bases r and b are related in a way which depends only on the relative information of one base with respect to the other. More precisely, we show that the complexity of the length l. logr b prefix of the base r expansion of ff is the same (up to an additive constant) as the logr b-fold complexity of the length l prefix of the base b expansion of α. Then we use this fact to derive complexity theoretic proofs for the base independence of the randomness of real numbers and for some properties of Liouville numbers.