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On the Algorithm Complexity of Generating Discrete Uniform Distribution from a Biased Coin
Mengqi Zhang1, Guangqiang Teng2, Xiaoyu Lei3
1School of Economics, Peking University, Beijing 100871, China.
Abstract:
Lei proposed an algorithm Algorithm A3 in 2023 to generate an exact discrete uniform distribution from an unknown biased Bernoulli source. The present paper does not claim a new extraction algorithm. Its contributions are analytical: first, we provide a Fourier-analytic proof of the uniformity mechanism based on roots of unity and coefficient extraction; second, we derive explicit acceptance-probability and expected-runtime bounds, with a rigorous treatment of composite moduli; third, we show how independent accepted A3 digits yield a continuous Uniform(0,1) limit through a base-n expansion and quantify the cost of finite-digit simulation.
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