Introduction

The purpose of this note is to give a brief description of some software that has been developed by the authors (partly in collaboration with David Epstein), and which was demonstrated by them at the Workshop at the University of Sussex. It is all written in the C language and designed for use on UNIX systems. It is available for distribution (via ftp or SUN cartridge) free of charge from either of the authors, with source code and documentation included, mainly in the form of UNIX-style manual entries. Input and output is all done using files in a specially designed format. Usually, the user only needs to create files containing group presentations prior to running the programs. There are three principal components of this package, which we shall describe individually.

Automata

This is a sequence of programs that is designed to compute the automatic structure of a short-lex automatic group. For general information on automatic groups see [ECHLPT 92], and for a detailed description of the algorithms employed in these programs see [EHR 91]. These programs were written together with David Epstein.

Let G = (X | R) be a finitely presented group, where X is ordered and closed under inversion. For each g ∈ G, let w(g) be the lexicographically least (using the given ordering of X) amongst the shortest words in X that represent g. Then G is said to be short-lex automatic (with respect to the ordered set X) if the following hold.