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dc.contributor.authorCain, Alan James
dc.contributor.authorPfeiffer, Markus Johannes
dc.identifier.citationCain , A J & Pfeiffer , M J 2016 , ' Decision problems for word-hyperbolic semigroups ' , Journal of Algebra , vol. 465 , pp. 287-321 .
dc.identifier.otherPURE: 191070636
dc.identifier.otherPURE UUID: 3804ff8d-a2a0-453b-be07-5af987c08047
dc.identifier.otherScopus: 84989918507
dc.identifier.otherORCID: /0000-0002-9881-4429/work/47136375
dc.identifier.otherWOS: 000382419500013
dc.description.abstractThis paper studies decision problems for semigroups that are word-hyperbolic in the sense of Duncan & Gilman. A fundamental investigation reveals that the natural definition of a `word-hyperbolic structure' has to be strengthened slightly in order to define a unique semigroup up to isomorphism. The isomorphism problem is proven to be undecidable for word-hyperbolic semigroups (in contrast to the situation for word-hyperbolic groups). It is proved that it is undecidable whether a word-hyperbolic semigroup is automatic, asynchronously automatic, biautomatic, or asynchronously biautomatic. (These properties do not hold in general for word-hyperbolic semigroups.) It is proved that the uniform word problem for word-hyperbolic semigroup is solvable in polynomial time (improving on the previous exponential-time algorithm). Algorithms are presented for deciding whether a word-hyperbolic semigroup is a monoid, a group, a completely simple semigroup, a Clifford semigroup, or a free semigroup.
dc.relation.ispartofJournal of Algebraen
dc.rights© 2016, Elsevier Ltd. This work is 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. The final published version of this work is available at /
dc.subjectWord-hyperbolic semigroupsen
dc.subjectDecision problemsen
dc.subjectIsomorphism problemen
dc.subjectContext-free languagesen
dc.subjectQA Mathematicsen
dc.titleDecision problems for word-hyperbolic semigroupsen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews.Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews.Centre for Interdisciplinary Research in Computational Algebraen
dc.description.statusPeer revieweden

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