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Decision problems for word-hyperbolic semigroups
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dc.contributor.author | Cain, Alan James | |
dc.contributor.author | Pfeiffer, Markus Johannes | |
dc.date.accessioned | 2017-07-22T23:32:42Z | |
dc.date.available | 2017-07-22T23:32:42Z | |
dc.date.issued | 2016-11-01 | |
dc.identifier | 191070636 | |
dc.identifier | 3804ff8d-a2a0-453b-be07-5af987c08047 | |
dc.identifier | 84989918507 | |
dc.identifier | 000382419500013 | |
dc.identifier.citation | Cain , A J & Pfeiffer , M J 2016 , ' Decision problems for word-hyperbolic semigroups ' , Journal of Algebra , vol. 465 , pp. 287-321 . https://doi.org/10.1016/j.jalgebra.2016.07.007 | en |
dc.identifier.issn | 0021-8693 | |
dc.identifier.other | ORCID: /0000-0002-9881-4429/work/47136375 | |
dc.identifier.uri | https://hdl.handle.net/10023/11263 | |
dc.description.abstract | This 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.format.extent | 458421 | |
dc.language.iso | eng | |
dc.relation.ispartof | Journal of Algebra | en |
dc.subject | Word-hyperbolic semigroups | en |
dc.subject | Decision problems | en |
dc.subject | Undecidability | en |
dc.subject | Isomorphism problem | en |
dc.subject | Context-free languages | en |
dc.subject | QA Mathematics | en |
dc.subject | NDAS | en |
dc.subject.lcc | QA | en |
dc.title | Decision problems for word-hyperbolic semigroups | en |
dc.type | Journal article | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.identifier.doi | 10.1016/j.jalgebra.2016.07.007 | |
dc.description.status | Peer reviewed | en |
dc.date.embargoedUntil | 2017-07-22 |
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