Complexity of deep computations via topology of function spaces
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910025322070016 |
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| author | Dueñez, Eduardo Iovino, José Matos-Wiederhold, Tonatiuh Salvetti, Luciano Tall, Franklin D. |
| author_facet | Dueñez, Eduardo Iovino, José Matos-Wiederhold, Tonatiuh Salvetti, Luciano Tall, Franklin D. |
| contents | We use topological methods to study complexity of deep computations and limit computations. We use topology of function spaces, specifically, the classification Rosenthal compacta, to identify new complexity classes. We use the language of model theory, specifically, the concept of \emph{independence} from Shelah's classification theory, to translate between topology and computation. We use the theory of Rosenthal compacta to characterize approximablility of deep computations, both deterministically and probabilistically. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_00528 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Complexity of deep computations via topology of function spaces Dueñez, Eduardo Iovino, José Matos-Wiederhold, Tonatiuh Salvetti, Luciano Tall, Franklin D. Logic General Topology 54H30, 68T27, 68T07, 03C98, 03D15, 05D10 We use topological methods to study complexity of deep computations and limit computations. We use topology of function spaces, specifically, the classification Rosenthal compacta, to identify new complexity classes. We use the language of model theory, specifically, the concept of \emph{independence} from Shelah's classification theory, to translate between topology and computation. We use the theory of Rosenthal compacta to characterize approximablility of deep computations, both deterministically and probabilistically. |
| title | Complexity of deep computations via topology of function spaces |
| topic | Logic General Topology 54H30, 68T27, 68T07, 03C98, 03D15, 05D10 |
| url | https://arxiv.org/abs/2601.00528 |