This paper introduces two complexity-theoretic formulations of Bennett’s computational depth: finite-state depth and polynomial-time depth. It is shown that for both formulation...
A random set can be regarded as the result of the imprecise observation of a random variable. Following this interpretation, we study to which extent the upper and lower probabili...
A central object of study in the field of algorithmic randomness are notions of randomness for sequences, i.e., infinite sequences of zeros and ones. These notions are usually def...
: We present a formula to calculate the probability density function of the solution of the random linear transport equation in terms of the density functions of the velocity and t...