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.
Weihrauch degrees
weak weak König's lemma
Las Vegas computability
algorithmic randomness
Nash equilibria
130-142
Regular Paper
Vasco
Brattka
Vasco Brattka
Guido
Gherardi
Guido Gherardi
Rupert
Hölzl
Rupert Hölzl
10.4230/LIPIcs.STACS.2015.130
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