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Automatic presentations for semigroups

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Date
11/2009
Author
Cain, Alan James
Oliver, Graham
Ruskuc, Nik
Thomas, Richard M.
Funder
EPSRC
Grant ID
EP/C523229/1
Keywords
Automatic presentation
FA-presentable
Cancellative semigroup
Virtually abelian group
Monoids
QA Mathematics
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Abstract
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
This is an author version of this article. The published version (c) 2009 Elsevier Inc. is available at www.sciencedirect.com
Description
Special Issue: 2nd International Conference on Language and Automata Theory and Applications (LATA 2008)
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  • University of St Andrews Research
URL
http://www.scopus.com/inward/record.url?scp=70349754454&partnerID=8YFLogxK
URI
http://hdl.handle.net/10023/2147

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