License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2015.130
URN: urn:nbn:de:0030-drops-49093
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/4909/
Go to the corresponding LIPIcs Volume Portal

Brattka, Vasco ; Gherardi, Guido ; Hölzl, Rupert

Las Vegas Computability and Algorithmic Randomness

pdf-format:
9.pdf (0.6 MB)

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.

BibTeX - Entry

@InProceedings{brattka_et_al:LIPIcs:2015:4909,
  author =	{Vasco Brattka and Guido Gherardi and Rupert H{\"o}lzl},
  title =	{{Las Vegas Computability and Algorithmic Randomness}},
  booktitle =	{32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
  pages =	{130--142},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-78-1},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{30},
  editor =	{Ernst W. Mayr and Nicolas Ollinger},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/4909},
  URN =		{urn:nbn:de:0030-drops-49093},
  doi =		{10.4230/LIPIcs.STACS.2015.130},
  annote =	{Keywords: Weihrauch degrees, weak weak K{\"o}nig's lemma, Las Vegas computability, algorithmic randomness, Nash equilibria}
}

Keywords: Weihrauch degrees, weak weak König's lemma, Las Vegas computability, algorithmic randomness, Nash equilibria
Collection: 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)
Issue Date: 2015
Date of publication: 26.02.2015

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI