Automatic groups are a family of finitely generated groups whose Cayley graph satisfies a certain condition (the fellow traveller property). This condition is realised for a group G by associating with it a number of finite state automata. This makes various group operations, notably equality between words of G and word enumeration, decidable through the use of these automata.
Word hyperbolic groups are an important subclass of automatic groups. In fact the concept of an automatic group emerged from work of J. W. Cannon on the Cayley graphs of word hyperbolic groups.
In the first part of the chapter, a Magma level interface to Derek Holt's KBMAG programs, and specifically to KBMAG's automatic groups program autgroup is described. The main procedure applies the Knuth-Bendix completion procedure in an attempt to construct a confluent presentation for the group.
In the second part of the chapter an intrinsic that attempts to determine if a finitely presented group is word hyperbolic is described. The procedure was developed by Steve Linton, Max Neunhoffer, Richard Parker and Colva Roney-Dougal and implemented in Magma by Derek Holt. A separate procedure that tests whether an automatic group is word hyperbolic is also described.