A new presentation of then-string braid groupBnis studied. Using it, a new solution to the word problem inBnis obtained which retains most of the desirable features of the Garside–Thurston solution, and at the same time makes possible certain computational improvements. We also give a related solution to the conjugacy problem, but the improvements in its complexity are not clear at this writing.
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Birman et al. (1998) studied this question.
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