Note on Finite-Automata Bernoulli Factories for Rational Functions

Renato Paes Leme; Jon Schneider

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arXiv · 2606.29595

Note on Finite-Automata Bernoulli Factories for Rational Functions

Renato Paes Leme·Jon Schneider

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Abstract

Mossel and Peres (2005) established a comprehensive framework for designing Bernoulli factories. Notably, they demonstrated that a single-variable function admits a finite-automata Bernoulli factory if and only if it is a rational function. Their Theorem 2.9 claims an extension of this result to multivariable functions, but it contains a subtle technical oversight in the application of P\'olya's Theorem. We provide a direct counterexample: a rational function in three variables that admits a general Bernoulli factory but cannot be implemented by a finite-automata Bernoulli factory.

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BibTeX RIS

Renato Paes Leme, Jon Schneider. 2026-06-28. Note on Finite-Automata Bernoulli Factories for Rational Functions. https://arxiv.org/abs/2606.29595

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