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Статья

Clone-induced approximation algebras of Bernoulli distributions

Algebra Universalis. 2019. Vol. 80. No. 1 (5). P. 1-16.

We consider the problem of approximating distributions of Bernoulli random variables by applying Boolean functions to independent random variables with distributions from a given set. For a set B of Boolean functions, the set of approximable distributions forms an algebra, named the approximation algebra of Bernoulli distributions induced by B. We provide a complete description of approximation algebras induced by most clones of Boolean functions. For remaining clones, we prove a criterion for approximation algebras and a property of algebras that are finitely generated.