Automatic presentations for semigroups

Authors:
Alan J. Cain;Graham Oliver;Nik Ruškuc;Richard M. Thomas
Affiliations:
School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, United Kingdom;Department of Computer Science, University of Leicester, University Road, Leicester LE1 7RH, United Kingdom;School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, United Kingdom;Department of Computer Science, University of Leicester, University Road, Leicester LE1 7RH, United Kingdom
Venue:
Information and Computation
Year:
2009

Citing 8
Cited 1

Commutative monoids have complete presentations by free (non-commutative) monoids

Theoretical Computer Science
Automatic semigroups

Theoretical Computer Science
Word Processing in Groups

Word Processing in Groups
Automatic Monoids Versus Monoids with Finite Convergent Presentations

RTA '98 Proceedings of the 9th International Conference on Rewriting Techniques and Applications
Automatic Presentations of Structures

LCC '94 Selected Papers from the International Workshop on Logical and Computational Complexity
On Automatic Partial Orders

LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
Automatic Structures: Richness and Limitations

LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Automatic presentations for finitely generated groups

STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science

Automaton semigroups

Theoretical Computer Science

Quantified Score

Hi-index	0.00

Visualization

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.