文章基本信息

标题：Computing Measure as a Primitive Operation in Real Number Computation
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作者：Gaßner, Christine ; Arno Pauly ; Florian Steinberg 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2021
卷号：183
页码：22:1-22:22
DOI：10.4230/LIPIcs.CSL.2021.22
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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 Î"â°â,,-set of reals, integrating piece-wise continuous functions and recovering a continuous function from an Lâ,([0, 1])-description. All these share the Weihrauch degree lim.
关键词：BSS-machine; Weihrauch reducibility; integrable function; Lebesgue measure; computable analysis