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Las Vegas Computability and Algorithmic Randomness

Authors Vasco Brattka, Guido Gherardi, Rupert Hölzl

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Vasco Brattka
Guido Gherardi
Rupert Hölzl

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Vasco Brattka, Guido Gherardi, and Rupert Hölzl. Las Vegas Computability and Algorithmic Randomness. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 130-142, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
https://doi.org/10.4230/LIPIcs.STACS.2015.130

Abstract

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.
Keywords
  • Weihrauch degrees
  • weak weak König's lemma
  • Las Vegas computability
  • algorithmic randomness
  • Nash equilibria

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