Algebra universalis

, 80:5 | Cite as

Clone-induced approximation algebras of Bernoulli distributions

  • Alexey D. YashunskyEmail author


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.


Boolean function Clone Read-once term Bernoulli distribution Approximation 

Mathematics Subject Classification

08A99 60B99 



The author expresses his gratitude to O. M. Kasim-Zade for his attention to the present work.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Keldysh Institute of Applied MathematicsMoscowRussia

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