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May 26, 2017 at 14:12 comment added Misha @MehdiYazdi: Its complicated, see for instance "A Short course in geometric group theory" by Walter Neumann. Roughly speaking, you are looking for a regular geodesic language on your group (for some generating set).
May 26, 2017 at 1:15 comment added Mehdi Yazdi Could you explain what is the relation between 'being automatic' and 'having finitely many cone types'? Does the former imply the later? Under what conditions the former implies the later?
May 25, 2017 at 23:01 comment added Misha Igor: What Mosher proves is the existence of an automatic structure. He does not prove existence of a finite presentation which has a geodesic combing (satisfying falsification by fellow traveler property).
May 25, 2017 at 22:34 history answered Igor Rivin CC BY-SA 3.0