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.CSL.2021.22
URN: urn:nbn:de:0030-drops-134564
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/13456/
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Gaßner, Christine ; Pauly, Arno ; Steinberg, Florian

Computing Measure as a Primitive Operation in Real Number Computation

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LIPIcs-CSL-2021-22.pdf (0.6 MB)

Abstract

We study the power of BSS-machines enhanced with abilities such as computing the measure of a BSS-decidable set or computing limits of BSS-computable converging sequences. Our variations coalesce into just two equivalence classes, each of which also can be described as a lower cone in the Weihrauch degrees.
We then classify computational tasks such as computing the measure of Δ⁰₂-set of reals, integrating piece-wise continuous functions and recovering a continuous function from an L₁([0, 1])-description. All these share the Weihrauch degree lim.

BibTeX - Entry

@InProceedings{ganer_et_al:LIPIcs:2021:13456,
  author =	{Christine Ga{\ss}ner and Arno Pauly and Florian Steinberg},
  title =	{{Computing Measure as a Primitive Operation in Real Number Computation}},
  booktitle =	{29th EACSL Annual Conference on Computer Science Logic (CSL 2021)},
  pages =	{22:1--22:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-175-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{183},
  editor =	{Christel Baier and Jean Goubault-Larrecq},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/13456},
  URN =		{urn:nbn:de:0030-drops-134564},
  doi =		{10.4230/LIPIcs.CSL.2021.22},
  annote =	{Keywords: BSS-machine, Weihrauch reducibility, integrable function, Lebesgue measure, computable analysis}
}

Keywords: BSS-machine, Weihrauch reducibility, integrable function, Lebesgue measure, computable analysis
Collection: 29th EACSL Annual Conference on Computer Science Logic (CSL 2021)
Issue Date: 2021
Date of publication: 13.01.2021

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