David W. Jacobs, Daphna Weinshall, et al.
IEEE Transactions on Pattern Analysis and Machine Intelligence
We consider the notion of algorithmic randomness relative to an oracle. We prove that the probability β that a program for infinite computations (a program that never halts) outputs a cofinite set is random in the second jump of the halting problem. Indeed, we prove that β is exactly as random as the halting probability of a universal machine equipped with an oracle for the second jump of the halting problem, in spite of the fact that β is defined without considering oracles.
David W. Jacobs, Daphna Weinshall, et al.
IEEE Transactions on Pattern Analysis and Machine Intelligence
Mario Blaum, John L. Fan, et al.
IEEE International Symposium on Information Theory - Proceedings
Daniel J. Costello Jr., Pierre R. Chevillat, et al.
ISIT 1997
Sankar Basu
Journal of the Franklin Institute