The rotating normal form of braids is regular
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2016
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| _version_ | 1866909351717896192 |
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| author | Fromentin, Jean |
| author_facet | Fromentin, Jean |
| contents | Defined on Birman-Ko-Lee monoids, the rotating normal form has strong connections with the Dehornoy's braid ordering. It can be seen as a process for selecting between all the representative words of a Birman-Ko-Lee braid a particular one, called rotating word. In this paper we construct, for all n 2, a finite-state automaton which recognizes rotating words on n strands, proving that the rotating normal form is regular. As a consequence we obtain the regularity of a $σ$-definite normal form defined on the whole braid group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1606_08970 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | The rotating normal form of braids is regular Fromentin, Jean Group Theory Computation and Language Formal Languages and Automata Theory Defined on Birman-Ko-Lee monoids, the rotating normal form has strong connections with the Dehornoy's braid ordering. It can be seen as a process for selecting between all the representative words of a Birman-Ko-Lee braid a particular one, called rotating word. In this paper we construct, for all n 2, a finite-state automaton which recognizes rotating words on n strands, proving that the rotating normal form is regular. As a consequence we obtain the regularity of a $σ$-definite normal form defined on the whole braid group. |
| title | The rotating normal form of braids is regular |
| topic | Group Theory Computation and Language Formal Languages and Automata Theory |
| url | https://arxiv.org/abs/1606.08970 |