St Andrews Research Repository

St Andrews University Home
View Item 
  •   St Andrews Research Repository
  • University of St Andrews Research
  • University of St Andrews Research
  • University of St Andrews Research
  • View Item
  •   St Andrews Research Repository
  • University of St Andrews Research
  • University of St Andrews Research
  • University of St Andrews Research
  • View Item
  •   St Andrews Research Repository
  • University of St Andrews Research
  • University of St Andrews Research
  • University of St Andrews Research
  • View Item
  • Login
JavaScript is disabled for your browser. Some features of this site may not work without it.

Two variants of the froidure-pin algorithm for finite semigroups

Thumbnail
View/Open
Jonusas_2017_Parallel_algorithms_PM_AAM.pdf (514.0Kb)
Date
08/02/2018
Author
Jonusas, Julius
Mitchell, J. D.
Pfeiffer, M.
Keywords
Algorithms
Green's relations
Monoids
Semigroups
QA Mathematics
Mathematics(all)
DAS
Metadata
Show full item record
Abstract
In this paper, we present two algorithms based on the Froidure-Pin Algorithm for computing the structure of a finite semigroup from a generating set. As was the case with the original algorithm of Froidure and Pin, the algorithms presented here produce the left and right Cayley graphs, a confluent terminating rewriting system, and a reduced word of the rewriting system for every element of the semigroup. If U is any semigroup, and A is a subset of U, then we denote by <A> the least subsemigroup of U containing A. If B is any other subset of U, then, roughly speaking, the first algorithm we present describes how to use any information about <A>, that has been found using the Froidure-Pin Algorithm, to compute the semigroup <A∪B>. More precisely, we describe the data structure for a finite semigroup S given by Froidure and Pin, and how to obtain such a data structure for <A∪B> from that for <A>. The second algorithm is a lock-free concurrent version of the Froidure-Pin Algorithm.
Citation
Jonusas , J , Mitchell , J D & Pfeiffer , M 2018 , ' Two variants of the froidure-pin algorithm for finite semigroups ' , Portugaliae Mathematica , vol. 74 , no. 3 , pp. 173-200 . https://doi.org/10.4171/PM/2001
Publication
Portugaliae Mathematica
Status
Peer reviewed
DOI
https://doi.org/10.4171/PM/2001
ISSN
0032-5155
Type
Journal article
Rights
© 2017, Portuguese Mathematical Society. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version.
Collections
  • Centre for Interdisciplinary Research in Computational Algebra (CIRCA) Research
  • Computer Science Research
  • Pure Mathematics Research
  • University of St Andrews Research
URL
http://arxiv.org/abs/1704.04084v1
URI
http://hdl.handle.net/10023/11879

Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.

Advanced Search

Browse

All of RepositoryCommunities & CollectionsBy Issue DateNamesTitlesSubjectsClassificationTypeFunderThis CollectionBy Issue DateNamesTitlesSubjectsClassificationTypeFunder

My Account

Login

Open Access

To find out how you can benefit from open access to research, see our library web pages and Open Access blog. For open access help contact: openaccess@st-andrews.ac.uk.

Accessibility

Read our Accessibility statement.

How to submit research papers

The full text of research papers can be submitted to the repository via Pure, the University's research information system. For help see our guide: How to deposit in Pure.

Electronic thesis deposit

Help with deposit.

Repository help

For repository help contact: Digital-Repository@st-andrews.ac.uk.

Give Feedback

Cookie policy

This site may use cookies. Please see Terms and Conditions.

Usage statistics

COUNTER-compliant statistics on downloads from the repository are available from the IRUS-UK Service. Contact us for information.

© University of St Andrews Library

University of St Andrews is a charity registered in Scotland, No SC013532.

  • Facebook
  • Twitter