使用有偏见的硬币作为神谕
Using biased coins as oracles
摘要：
虽然众所周知，一个图灵机配备的能力，以投掷一个公平的硬币不能计算更多的一个标准的图灵机，我们表明，这是不正确的一个有偏见的硬币。实际上，任何预言集$X$可以被编码为概率$p_{X}$，使得如果图灵机被给予以概率$p_{X}$正面着陆的硬币，则它可以以任意高的概率计算在$X$中递归的任何函数。我们还展示了如何通过使用一系列越来越准确的递归偏差或通过从具有非递归均值的分布中随机选择偏差来削弱非递归偏差的假设。最后，我们简要地提到一些影响，这些方法的物理可实现性。
英文摘要：
While it is well known that a Turing machine equipped with the ability to flip a fair coin cannot compute more that a standard Turing machine, we show that this is not true for a biased coin. Indeed, any oracle set $X$ may be coded as a probability $p_{X}$ such that if a Turing machine is given a coin which lands heads with probability $p_{X}$ it can compute any function recursive in $X$ with arbitrarily high probability. We also show how the assumption of a non-recursive bias can be weakened by using a sequence of increasingly accurate recursive biases or by choosing the bias at random from a distribution with a non-recursive mean. We conclude by briefly mentioning some implications regarding the physical realisability of such methods.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
