The information contained in a string x about a string y
is defined as the difference between the Kolmogorov complexity
of y and the conditional Kolmogorov complexity of y given x,
i.e., I(x:y)=\C(y)-\C(y|x). From the well-known Kolmogorov--Levin Theorem it follows that I(x:y) is symmetric up to a small ... more >>>

A fundamental notion in Algorithmic Statistics is that of a stochastic object, i.e., an object having a simple plausible explanation. Informally, a probability distribution is a plausible explanation for x if it looks likely that x was drawn at random with respect to that distribution. In this paper, we ... more >>>