The rotating normal form of braids is regular
Abstract
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 $\sigma$-definite normal form defined on the whole braid group.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2016
- DOI:
- 10.48550/arXiv.1606.08970
- arXiv:
- arXiv:1606.08970
- Bibcode:
- 2016arXiv160608970F
- Keywords:
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- Mathematics - Group Theory;
- Computer Science - Formal Languages and Automata Theory