### Combings of Groups and the Grammar of
Reparameterization

#### Martin R. Bridson

#### Preprint 2000. To appear in Comm. Math. Helv.

A new method of constructing combings is
used to distinguish between several previously indistinguishable
classes of groups associated to the theory of automatic groups
and non-positive curvature in group theory.
We construct synchronously bounded combings for a class
of groups that are neither bicombable nor automatic.
The linguistic complexity of these combings is
analyzed: in many cases the language of words
in the combing is an indexed language.