Las Vegas computability and algorithmic randomness

In this article we try to formalize the question “What can be computed with access to randomness?” We propose the very fine-grained Weihrauch lattice as an approach to differentiate between different types of computation with access to randomness. In particular, we show that a natural concept of Las Vegas computability on infinite objects is more powerful than mere oracle access to a Martin-Löf random object. As a concrete problem that is Las Vegas computable but not computable with access to a Martin-Löf random oracle we study the problem of finding Nash equilibria

Computable Measure Theory and Algorithmic Randomness

International audienceWe provide a survey of recent results in computable measure and probability theory, from both the perspectives of computable analysis and algorithmic randomness, and discuss the relations between them