Non-algorithmic theory of randomness

Abstract

This paper proposes an alternative language for expressing results of the algorithmic theory of randomness. The language is more precise in that it does not involve unspecified additive or multiplicative constants, making mathematical results, in principle, applicable in practice. Our main testing ground for the proposed language is the problem of defining Bernoulli sequences, which was of great interest to Andrei Kolmogorov and his students.