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Polynomial-time proofs that groups are hyperbolic
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dc.contributor.author | Holt, Derek | |
dc.contributor.author | Linton, Stephen | |
dc.contributor.author | Neunhoeffer, Max | |
dc.contributor.author | Parker, Richard | |
dc.contributor.author | Pfeiffer, Markus | |
dc.contributor.author | Roney-Dougal, Colva M. | |
dc.date.accessioned | 2022-02-14T00:39:31Z | |
dc.date.available | 2022-02-14T00:39:31Z | |
dc.date.issued | 2021-05 | |
dc.identifier | 269496332 | |
dc.identifier | 99aadd0b-82df-46ad-996c-61c09db74e31 | |
dc.identifier | 85090156160 | |
dc.identifier | 000598670000023 | |
dc.identifier.citation | Holt , D , Linton , S , Neunhoeffer , M , Parker , R , Pfeiffer , M & Roney-Dougal , C M 2021 , ' Polynomial-time proofs that groups are hyperbolic ' , Journal of Symbolic Computation , vol. 104 , pp. 419-475 . https://doi.org/10.1016/j.jsc.2020.08.003 | en |
dc.identifier.issn | 0747-7171 | |
dc.identifier.other | ORCID: /0000-0002-0532-3349/work/81797435 | |
dc.identifier.uri | https://hdl.handle.net/10023/24863 | |
dc.description | Funding: UK EPSRC grant number EP/I03582X/1. | en |
dc.description.abstract | It is undecidable in general whether a given finitely presented group is word hyperbolic. We use the concept of pregroups, introduced by Stallings (1971), to define a new class of van Kampen diagrams, which represent groups as quotients of virtually free groups. We then present a polynomial-time procedure that analyses these diagrams, and either returns an explicit linear Dehn function for the presentation, or returns fail, together with its reasons for failure. Furthermore, if our procedure succeeds we are often able to produce in polynomial time a word problem solver for the presentation that runs in linear time. Our algorithms have been implemented, and when successful they are many orders of magnitude faster than KBMAG, the only comparable publicly available software. | |
dc.format.extent | 626249 | |
dc.language.iso | eng | |
dc.relation.ispartof | Journal of Symbolic Computation | en |
dc.subject | Hyperbolic groups | en |
dc.subject | Word problem | en |
dc.subject | van Kampen diagrams | en |
dc.subject | Curvature | en |
dc.subject | QA75 Electronic computers. Computer science | en |
dc.subject | T-NDAS | en |
dc.subject | BDC | en |
dc.subject | R2C | en |
dc.subject | ~DC~ | en |
dc.subject.lcc | QA75 | en |
dc.title | Polynomial-time proofs that groups are hyperbolic | en |
dc.type | Journal article | en |
dc.contributor.sponsor | EPSRC | en |
dc.contributor.sponsor | EPSRC | en |
dc.contributor.institution | University of St Andrews. St Andrews GAP Centre | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.contributor.institution | University of St Andrews. School of Computer Science | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | 10.1016/j.jsc.2020.08.003 | |
dc.description.status | Peer reviewed | en |
dc.date.embargoedUntil | 2022-02-14 | |
dc.identifier.grantnumber | EP/I03582X/1 | en |
dc.identifier.grantnumber | EP/I03582X/1 | en |
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