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Mossel-Peres Multivariable Bernoulli Factory Claim

Probability & statistics · posed by Elchanan Mossel, Yuval Peres, 2005 · disproved

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Statement

Mossel and Peres showed that a single-variable function admits a finite-automata Bernoulli factory exactly when it is rational, and their Theorem 2.9 claimed the same extension to multivariable functions. The multivariable claim is false, refuted by an explicit counterexample.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. construction · #1

    Renato Paes Leme and Jon Schneider, using Gemini 3.1 Pro (DeepThink)

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    The tool use disclosure states plainly that the authors used the DeepThink mode of Gemini 3.1 Pro to derive the counterexample, and to refine the presentation.

    the published multivariable claim fails; the single-variable theorem stands

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