‘Automatic presentations for semigroups’
[with G. Oliver, N. Ruškuc & R. M. Thomas]
Information and Computation, 207, no. 11 (2009), pp. 1156–1168.
DOI: 10.1016/j.ic.2009.02.005. MR: 2566948. ZBL: 1192.20040.


This paper applies the concept of FA-presentable structures to semigroups. We give a complete classification of the finitely generated FA-presentable cancellative semigroups: namely, a finitely generated cancellative semigroup is FA-presentable if and only if it is a subsemigroup of a virtually abelian group. We prove that all finitely generated commutative semigroups are FA-presentable. We give a complete list of FA-presentable one-relation semigroups and compare the classes of FA-presentable semigroups and automatic semigroups.