Cayley Linear-Time Computable Groups
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916198134841344 |
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| author | Kruengthomya, Prohrak Berdinsky, Dmitry |
| author_facet | Kruengthomya, Prohrak Berdinsky, Dmitry |
| contents | This paper looks at the class of groups admitting normal forms for which the right multiplication by a group element is computed in linear time on a multi-tape Turing machine. We show that the groups $\mathbb{Z}_2 \wr \mathbb{Z}^2$, $\mathbb{Z}_2 \wr \mathbb{F}_2$ and Thompson's group $F$ have normal forms for which the right multiplication by a group element is computed in linear time on a $2$-tape Turing machine. This refines the results previously established by Elder and the authors that these groups are Cayley polynomial-time computable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_20221 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cayley Linear-Time Computable Groups Kruengthomya, Prohrak Berdinsky, Dmitry Group Theory This paper looks at the class of groups admitting normal forms for which the right multiplication by a group element is computed in linear time on a multi-tape Turing machine. We show that the groups $\mathbb{Z}_2 \wr \mathbb{Z}^2$, $\mathbb{Z}_2 \wr \mathbb{F}_2$ and Thompson's group $F$ have normal forms for which the right multiplication by a group element is computed in linear time on a $2$-tape Turing machine. This refines the results previously established by Elder and the authors that these groups are Cayley polynomial-time computable. |
| title | Cayley Linear-Time Computable Groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2310.20221 |