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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 to… (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 groups… (More)
This article presents a lemma in the spirit of the pumping lemma for indexed languages but easier to employ. Section
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 set… (More)
There do not exist context–free languages of intermediate growth. The function γ whose value at each non–negative integer n is the number of words on length n in a fixed formal language L is called… (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 small… (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 Sol… (More)
We use context free languages to analyze solution sets to one variable equations over free groups.