Computability Learning Seminar

Jonathan Stephenson, Department of Pure Mathematics, University of Waterloo

“Lowness Notions”

We will continue our study of the relationships between different lowness notions. Each such notion captures the idea of a real number having minimal computational power according to some criterion.

We will focus on those notions of lowness which are related to complexity and randomness, and in particular will consider lowness for K and lowness for ML-randomness. A real is low for K if it does not have sufficient computational power to reduce complexity, and is low for ML- randomness if it is unable to detect patterns in any ML-random real (and thus derandomize that real).

We will use the link between complexity and randomness to show that lowness for K implies lowness for ML-randomness, and give a characterization of lowness for ML-randomness in terms of c.e. classes.

MC 5403