2026-07-25T02:44:21Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:20618 2024-08-23T05:50:29Z ddc:004 open_access

Randomness Versus Superspeedability Hölzl, Rupert Janicki, Philip Merkle, Wolfgang Stephan, Frank superspeedable numbers speedable numbers regainingly approximable numbers regular numbers left-computable numbers Speedable numbers are real numbers which are algorithmically approximable from below and whose approximations can be accelerated nonuniformly. We begin this article by answering a question of Barmpalias by separating a strict subclass that we will refer to as superspeedable from the speedable numbers; for elements of this subclass, acceleration is possible uniformly and to an even higher degree. This new type of benign left-approximation of numbers then integrates itself into a hierarchy of other such notions studied in a growing body of recent work. We add a new perspective to this study by juxtaposing this hierachy with the well-studied hierachy of algorithmic randomness notions. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Rupert Hölzl and Philip Janicki and Wolfgang Merkle and Frank Stephan 2024 Is Part Of LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.MFCS.2024.62 urn:nbn:de:0030-drops-206187 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.62 eng https://creativecommons.org/licenses/by/4.0/legalcode