Kolmogorov’s Complexity Conception of Probability
Kolmogorov's goal in proposing his complexity conception of probability was to provide a better foundation for the applications of probability (as opposed to the theory of probability; he believed that his 1933 axioms were suucient for the theory of probability). The complexity conception was a natural development of Kolmogorov's earlier frequentist conception combined with (a) his conviction that only nite data sequences are of any interest in the applications of probability, and (b) Turing's discovery of the universal computing device. Besides the complexity conception itself , its developments by Martin-LL of, Levin et al will be brieey discussed; I will also list some advantages and limitations of Kolmogorov's complexity conception and the algorithmic theory of randomness in general.