{"paper":{"title":"Optimal linear Bernoulli factories for small mean problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DS","stat.CO"],"primary_cat":"math.PR","authors_text":"Mark Huber","submitted_at":"2015-07-03T07:56:55Z","abstract_excerpt":"Suppose a coin with unknown probability $p$ of heads can be flipped as often as desired. A Bernoulli factory for a function $f$ is an algorithm that uses flips of the coin together with auxiliary randomness to flip a single coin with probability $f(p)$ of heads. Applications include near perfect sampling from the stationary distribution of regenerative processes. When $f$ is analytic, the problem can be reduced to a Bernoulli factory of the form $f(p) = Cp$ for constant $C$. Presented here is a new algorithm where for small values of $Cp$, requires roughly only $C$ coin flips to generate a $Cp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00843","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}