Can Random Coin Flips Speed Up a Computer?

Optimal linear Bernoulli factories for small mean problems

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…

改进的硬币翻转、领导者选举和随机选择的界限

Improved Bounds for Coin Flipping, Leader Election, and Random Selection

研究改进了硬币翻转、领导者选举和随机选择在全信息模型中的界限，证明了在k轮中，每个玩家每轮发送1位时，坏玩家可以偏转协议，且提出了一种单轮随机选择协议，能够抵御更多坏玩家。