Author(s): Rees SE; Holt D
Abstract: We prove that for $\lambda \geq 1$ and all sufficiently large $\epsilon$, the set of \Le-quasigeodesics in an infinite word-hyperbolic group $G$ is regular if and only if $\lambda$ is rational. In fact, this set of quasigeodesics defines an asynchronous automatic structure for $G$. We also introduce the idea of an {\em exact} \Le-quasigeodesic and show that for rational $\lambda$ and appropriate $\epsilon$ the sets of exact \Le-quasigeodesics define synchronous automatic structures.
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Professor Sarah Rees
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