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arXiv · 1507.03248

The Relaxation Normal Form of Braids is Regular

Vincent Jugé
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Abstract

Braids can be represented geometrically as laminations of punctured disks. The geometric complexity of a braid is the minimal complexity of a lamination that represents it, and tight laminations are representatives of minimal complexity. These laminations give rise to a normal form of braids, via a relaxation algorithm. We study here this relaxation algorithm and the associated normal form. We prove that this normal form is regular and prefix-closed. We provide an effective construction of a deterministic automaton that recognizes this normal form.

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Vincent Jugé. 2017-10-12. The Relaxation Normal Form of Braids is Regular. https://doi.org/10.1142/s0218196717500059

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