Year: 2014
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Kjos-Hanssen, Bjørn
Institution: University of Hawaiʻi at Mānoa
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2952919834