On the possibility of constructing an arbitrary quinary fraction using induced probability functions

E. E. Trifonova


Abstract: In this paper we study transformations of independent Bernoulli random variables with rational probabilities using Boolean functions. Such transformations of random variables induce transformations of rational probabilities, hence the tasks of generating probabilities through these transformations can be considered. In the paper we study the issue of finite generation for the set of quintuple fractions. We prove that the read-once closed class 5-irreducible functions and union of 5-reducible read-once closed classes of Boolean functions are finitely generative for the set of all quintuple fractions.

Keywords: read-once closed class of Boolean functions, Bernoulli random variable, random variable transformation.