Jonathan Stephenson, Department of Pure Mathematics, University of Waterloo
We will continue last week’s discussion of prefix-free Kolmogorov complexity, but will begin to focus more on infinite sequences. We will discuss what we might mean when we say that an infinite sequence looks random from an algorithmic perspective.
We will define Martin-Lf tests and discuss some of their basic properties, including how they give us a reasonable notion of algorithmic randomness. If time permits, we may discuss the relationship between Kolmogorov complexity and Martin-Lf randomness.