Kolmogorov's algorithmic complexity and its probability interpretation in quantum gravity

Quantum gravity has great difficulties in the application of the notion of probability. We analyse this problem according to the algorithmic viewpoint. According to Kolmogorov, the probability notion can be connected to the algorithmic complexity of a given object. We propose an interpretation of quantum gravity, according to which the appearance of something corresponds to its Kolmogorov algorithmic complexity. From this viewpoint the following questions are considered: a quantum transition with supplementary coordinates splitting off, the estimation of the algorithmic complexity of the Schwarzschild black hole, the redefinition of the Feynman path integral and the quantum birth of the Euclidean universe with the following change of the metric signature.