Status of Problems from Computability and Randomness by Nies

Lectures on Effective Randomness

This class will be dealing with the intersection of randomness and computability theory, or how the tools of randomness can be applied to computability-theoretic problems. This class will not cover the history of the subject, which can be complicated and controversial, but some history can be found in the references for the course. These references are a book by Andre Nies [13] and a book by Ro...

Computability and randomness

Randomness and Computability: Open Questions

from New Zealand

0. The meeting Analysis and Randomness, http://www.cs.auckland.ac.nz/ ~nies/ARAhome.html, organised by A. Nies, was held in Auckland on 12–13 December 2011. Speakers: Laurent Bienvenu, Willem Fouche, Cameron Freer, Rupert Hölzl, A. Melnikov, Kenshi Miyabe, Jason Rute, Tom ter Elst, and Dan Turetsky. 1. The 12th Asian Logic Conference, http://msor.victoria.ac.nz/ Events/ALC2011/WebHome, was held...

Interactions of Computability and Randomness

We survey results relating the computability and randomness aspects of sets of natural numbers. Each aspect corresponds to several mathematical properties. Properties originally defined in very different ways are shown to coincide. For instance, lowness for ML-randomness is equivalent to K-triviality. We include some interactions of randomness with computable analysis. Mathematics Subject Class...