Randomness versus superspeedability
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866914921173745664 |
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| author | Hölzl, Rupert Janicki, Philip Merkle, Wolfgang Stephan, Frank |
| author_facet | Hölzl, Rupert Janicki, Philip Merkle, Wolfgang Stephan, Frank |
| contents | 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-approximations 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15811 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Randomness versus superspeedability Hölzl, Rupert Janicki, Philip Merkle, Wolfgang Stephan, Frank Logic 03D32, 03D78, 03F60 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-approximations 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. |
| title | Randomness versus superspeedability |
| topic | Logic 03D32, 03D78, 03F60 |
| url | https://arxiv.org/abs/2404.15811 |