Clone-induced approximation algebras of Bernoulli distributions
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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.
KeywordsBoolean function Clone Read-once term Bernoulli distribution Approximation
Mathematics Subject Classification08A99 60B99
The author expresses his gratitude to O. M. Kasim-Zade for his attention to the present work.
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