The Kolmogorov complexity of real numbers
We consider for a real number alpha the Kohnogorov 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 . log(r)b prefix of the base r expansion of alpha is the same (up to an additive constant) as the log(r)b-fold complexity of the length l prefix of the base b expansion of alpha.
kolmogorov complexity base r expansion omega-words liouville numbers disjunctive omega-words