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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Accesso online: | https://arxiv.org/abs/2312.02863 |
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| _version_ | 1866916333971570688 |
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| author | Cardó, Carles |
| author_facet | Cardó, Carles |
| contents | The incompressibility method is a counting argument in the framework of algorithmic complexity that permits discovering properties that are satisfied by most objects of a class. This paper gives a preliminary insight into Kolmogorov's complexity of groupoids and some algebras. The incompressibility method shows that almost all the groupoids are asymmetric and simple: Only trivial or constant homomorphisms are possible. However, highly random groupoids allow subgroupoids with interesting restrictions that reveal intrinsic structural properties. We also study the issue of the algebraic varieties and wonder which equational identities allow randomness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_02863 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A look at the Kolmogorov complexity of finite groupoids and algebras Cardó, Carles Information Theory 20N02, 68Q30, 03C05 The incompressibility method is a counting argument in the framework of algorithmic complexity that permits discovering properties that are satisfied by most objects of a class. This paper gives a preliminary insight into Kolmogorov's complexity of groupoids and some algebras. The incompressibility method shows that almost all the groupoids are asymmetric and simple: Only trivial or constant homomorphisms are possible. However, highly random groupoids allow subgroupoids with interesting restrictions that reveal intrinsic structural properties. We also study the issue of the algebraic varieties and wonder which equational identities allow randomness. |
| title | A look at the Kolmogorov complexity of finite groupoids and algebras |
| topic | Information Theory 20N02, 68Q30, 03C05 |
| url | https://arxiv.org/abs/2312.02863 |