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Computing Measure as a Primitive Operation in Real Number Computation

Authors Christine Gaßner, Arno Pauly , Florian Steinberg

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Author Details

Christine Gaßner
  • Universität Greifswald, Germany
Arno Pauly
  • Department of Computer Science, Swansea University, UK
Florian Steinberg
  • INRIA, Sophia Antipolis, France

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Christine Gaßner, Arno Pauly, and Florian Steinberg. Computing Measure as a Primitive Operation in Real Number Computation. In 29th EACSL Annual Conference on Computer Science Logic (CSL 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 183, pp. 22:1-22:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.CSL.2021.22

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Abstract machines
  • Theory of computation → Turing machines
  • Mathematics of computing → Point-set topology
  • Mathematics of computing → Integral calculus
Keywords
  • BSS-machine
  • Weihrauch reducibility
  • integrable function
  • Lebesgue measure
  • computable analysis

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