52 citations · 293 across the 47 of their papers we have counts for
58 papers
On -geodetic graphs and groups
Murray Elder, Adam Piggott, Kane Townsend
We call a graph -geodetic, for some , if it is connected and between any two vertices there are at most geodesics. It is shown that any hyperbolic group with a -…
The isomorphism problem for plain groups is in
Heiko Dietrich, Murray Elder, Adam Piggott +2
Testing isomorphism of infinite groups is a classical topic, but from the complexity theory viewpoint, few results are known. S{é}nizergues and the fifth author (ICALP2018) proved…
On groups presented by inverse-closed finite convergent length-reducing rewriting systems
Murray Elder, Adam Piggott
We show that groups presented by inverse-closed finite convergent length-reducing rewriting systems are characterised by a striking geometric property: their Cayley graphs are geod…
Being Cayley automatic is closed under taking wreath product with virtually cyclic groups
Dmitry Berdinsky, Murray Elder, Jennifer Taback
We extend work of the first author and Khoussainov to show that being Cayley automatic is closed under taking the restricted wreath product with a virtually infinite cyclic group.…
Rewriting systems, plain groups, and geodetic graphs
Murray Elder, Adam Piggott
We prove that a group is presented by finite convergent length-reducing rewriting systems where each rule has left-hand side of length 3 if and only if the group is plain. Our proo…
Cayley Polynomial-Time Computable Groups
Dmitry Berdinsky, Murray Elder, Prohrak Kruengthomya
We propose a new generalisation of Cayley automatic groups, varying the time complexity of computing multiplication, and language complexity of the normal form representatives. We…