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. © 2009 Elsevier Inc. All rights reserved.
Cain, A. J., Oliver, G., Ruškuc, N., & Thomas, R. M. (2009). Automatic presentations for semigroups. Information and Computation, 207(11), 1156–1168. https://doi.org/10.1016/j.ic.2009.02.005