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Feb 5, 2010 at 15:56 comment added Victor Miller You may be in luck. It turns out that finitely generated Coxeter groups are automatic: Brink and Howlett (1993). "A finiteness property and an automatic structure for Coxeter groups". Mathematische Annalen
Feb 5, 2010 at 13:10 history answered Victor Miller CC BY-SA 2.5