Article collection "Mathematical Problems of Cybernetics" №10, Moscow, 2001

Authors:Kolpakov R.M.

Closed classes of Boolean random variables with rational-valued distributions

Abstract:

The paper concerns discrete transformations of Boolean random variables, i.e. random variables
which have only two values 0 and 1, with rational probabilities of values. By a discrete
transformation of Boolean random variables we mean a Boolean random variable, the value of which
is the value of an arbitrary Boolean function whose variables values are the values
of the independent initial random variables. The closure of a set of probabilities is the set
of probabilities of value 1 for all random variables obtained by discrete transformations of
Boolean random variables whose probabilities of value 1 belong to the initial set of probabilities.
A set of probabilities is closed if it coincides with its closure. In the paper all closed sets
of rational probabilities are described.

Keywords:

Boolean random variables, rational probabilities, closed class