Resource bounded randomness and weakly complete problems
Theoretical Computer Science
An example of a computable absolutely normal number
Theoretical Computer Science
Turing's normal numbers: towards randomness
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
A polynomial-time algorithm for computing absolutely normal numbers
Information and Computation
| Hi-index | 5.23 |
In an unpublished manuscript, Alan Turing gave a computable construction to show that absolutely normal real numbers between 0 and 1 have Lebesgue measure 1; furthermore, he gave an algorithm for computing instances in this set. We complete his manuscript by giving full proofs and correcting minor errors. While doing this, we recreate Turing's ideas as accurately as possible. One of his original lemmas remained unproved, but we have replaced it with a weaker lemma that still allows us to maintain Turing's proof idea and obtain his result.