作为随机性检验计算资源的概率分布
The probability distribution as a computational resource for randomness testing
摘要：
当根据取决于参数的概率分布测试一组数据的随机性时，对该参数的访问可以被视为计算资源。如果不允许访问此资源，我们称之为随机性测试希波克拉底。在这些条款中，我们表明，伯努利措施$μ_p$，$0\le p\le 1$和马丁-洛夫随机模型，希波克拉底随机性的一组数据是相同的普通随机性。证明的主要思想是首先表明，从希波克拉底随机数据可以图灵计算参数$p$。然而，我们发现，没有一个希波克拉底随机性测试，通过测试意味着计算$p$，特别是没有通用的希波克拉底随机性测试。
英文摘要：
When testing a set of data for randomness according to a probability distribution that depends on a parameter, access to this parameter can be considered as a computational resource. We call a randomness test Hippocratic if it is not permitted to access this resource. In these terms, we show that for Bernoulli measures $μ_p$, $0\le p\le 1$ and the Martin-Löf randomness model, Hippocratic randomness of a set of data is the same as ordinary randomness. The main idea of the proof is to first show that from Hippocrates-random data one can Turing compute the parameter $p$. However, we show that there is no single Hippocratic randomness test such that passing the test implies computing $p$, and in particular there is no universal Hippocratic randomness test.
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