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The rotating normal form of braids is regular.

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Jean Fromentin (LMPA)

Defined on Birman-Ko-Lee monoids, the rotating normal form has strongconnections with the Dehornoy's braid ordering. It can be seen as a process forselecting between all the representative words of a Birman-Ko-Lee braid aparticular one, called rotating word. In this paper we construct, for all n 2,a finite-state automaton which recognizes rotating words on n strands, provingthat the rotating normal form is regular. As a consequence we obtain theregularity of a $\sigma$-definite normal form defined on the whole braid group.

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