The Probability of a Computable Output from a Random Oracle

@article{Barmpalias2017ThePO,
  title={The Probability of a Computable Output from a Random Oracle},
  author={George Barmpalias and Douglas A. Cenzer and Christopher P. Porter},
  journal={ACM Transactions on Computational Logic (TOCL)},
  year={2017},
  volume={18},
  pages={1 - 15}
}
Consider a universal oracle Turing machine that prints a finite or an infinite binary sequence, based on the answers to the binary queries that it makes during the computation. We study the probability that this output is infinite and computable when the machine is given a random (in the probabilistic sense) stream of bits as the answers to its queries during an infinitary computation. Surprisingly, we find that these probabilities are the entire class of real numbers in (0,1) that can be… 
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