Automatic presentations for semigroups

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. (C) 2009 Elsevier Inc. All rights reserved.

Citation

Cain , A J , Oliver , G , Ruskuc , N & Thomas , R M 2009 , ' Automatic presentations for semigroups ' , Information and Computation , vol. 207 , no. 11 , pp. 1156-1168 . https://doi.org/10.1016/j.ic.2009.02.005

Publication

Information and Computation

Status

Peer reviewed

DOI

https://doi.org/10.1016/j.ic.2009.02.005

ISSN

0890-5401

Type

Journal article

Rights

Description

Special Issue: 2nd International Conference on Language and Automata Theory and Applications (LATA 2008)