An introduction to Kolmogorov complexity and its applications
An introduction to Kolmogorov complexity and its applications
Kolmogorov complexity and Hausdorff dimension
Information and Computation
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
Constructive dimension equals Kolmogorov complexity
Information Processing Letters
Natural halting probabilities, partial randomness, and zeta functions
Information and Computation
Randomness with Respect to the Signed-Digit Representation
Fundamenta Informaticae
Constructive dimension equals Kolmogorov complexity
Information Processing Letters
On the Kolmogorov complexity of continuous real functions
CiE'11 Proceedings of the 7th conference on Models of computation in context: computability in Europe
Randomness with Respect to the Signed-Digit Representation
Fundamenta Informaticae
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We consider for a real number α 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 that 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 - logrb prefix of the base r expansion of α is the same (up to an additive constant) as the logrb-fold complexity of the length l prefix of the base b expansion of αThen we consider the classes of reals of maximum and minimum complexity. For maximally complex reals we use our result to derive a further complexity theoretic proof for the base independence of the randomness of real numbers.Finally, we consider Liouville numbers as a natural class of low complex real numbers.