Star-free geodesic languages for groups

Susan Hermiller, Derek Holt and Sarah Rees

Keywords

regular languages, starfree languages, geodesics

Status

published in International Journal of Algebra and Computation 17 (2007) 329--345

Abstract

In this article we show that every group with a finite presentation satisfying one or both of the small cancellation conditions $C'(1/6)$ and $C'(1/4)-T(4)$ has the property that the set of all geodesics (over the same generating set) is a star-free regular language. Star-free regularity of the geodesic set is shown to be dependent on the generating set chosen, even for free groups. We also show that the class of groups whose geodesic sets are star-free with respect to some generating set is closed under taking graph (and hence free and direct) products, and includes all virtually abelian groups. \

The preprint is available as gzipped dvi (36 kB) and postscript (180 kB) files.

Alternatively, you can request a copy by e-mailing me.