Сorrespondence

On Computability of the Parameter in a Bernoulli Scheme

V. V. V'yugin


Abstract: We study the dependence of a priori (universal semicomputable) measure of the set of all $\Theta$-Bernoullian sequences on the value of the parameter $\Theta$. We prove that for a fixed $\Theta$, the a priori measure of the set of all $\Theta$-Bernoullian sequences equals 0 (which is equivalent to unsolvability of the problem on generating a $\Theta$-Bernoullian sequence with the use of a probabilistic machine) if and only if the parameter $\Theta$ is noncomputable; however, this measure of the set of all $\Theta$-Bernoullian sequences will be greater than 0 if q runs over a set of random (with respect to some computable measure) sequences.

UDC: 621.391.1:519.2

Received: 28.01.1982

Bibliographic databases:

•