Formal languages based on multiplication tables of finitely generated groups are investigated and used to give a linguistic characterization of word hyperbolic groups.

Automatic groups were introduced in connection with geometric problems, in particular with the study of fundamental groups of 3-manifolds. In this article the class of automatic groups is extended toâ€¦ (More)

The study of automatic and word hyperbolic groups is a prominent topic in geometric group theory. The definition of automatic groups extends naturally to semigroups [3, 8], but word hyperbolic groupsâ€¦ (More)

We prove that a finitely generated group G is virtually free if and only if there exists a generating set for G and k > 0 such that all k-locally geodesic words with respect to that generating setâ€¦ (More)

There do not exist contextâ€“free languages of intermediate growth. The function Î³ whose value at each nonâ€“negative integer n is the number of words on length n in a fixed formal language L is calledâ€¦ (More)

This article is a short introduction to generic case complexity, which is a recently developed way of measuring the difficulty of a computational problem while ignoring atypical behavior on a smallâ€¦ (More)

The notable exclusions from the family of automatic groups are those nilpotent groups which are not virtually abelian, and the fundamental groups of compact 3-manifolds based on the Nil or Solâ€¦ (More)