The rotating normal form of braids is regular
Résumé
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.
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