Thompson's group F is 1-counter graph automatic

Elder, M; Taback, J

Thompson's group F is 1-counter graph automatic

Elder, M

Taback, J

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Publication Type:: Journal Article
Citation:: Groups, Complexity, Cryptology, 2016, 8 (1), pp. 21 - 33
Issue Date:: 2016-05-01

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Field	Value	Language
dc.contributor.author	Elder, M https://orcid.org/0000-0002-2438-3945	en_US
dc.contributor.author	Taback, J	en_US
dc.date.issued	2016-05-01	en_US
dc.identifier.citation	Groups, Complexity, Cryptology, 2016, 8 (1), pp. 21 - 33	en_US
dc.identifier.issn	1867-1144	en_US
dc.identifier.uri	http://hdl.handle.net/10453/94785
dc.description.abstract	© 2016 by De Gruyter. It is not known whether Thompson's group F is automatic. With the recent extensions of the notion of an automatic group to graph automatic by Kharlampovich, Khoussainov and Miasnikov and then to C-graph automatic by the authors, a compelling question is whether F is graph automatic or C-graph automatic for an appropriate language class C. The extended definitions allow the use of a symbol alphabet for the normal form language, replacing the dependence on generating set. In this paper we construct a 1-counter graph automatic structure for F based on the standard infinite normal form for group elements.	en_US
dc.relation.ispartof	Groups, Complexity, Cryptology	en_US
dc.relation.isbasedon	10.1515/gcc-2016-0001	en_US
dc.title	Thompson's group F is 1-counter graph automatic	en_US
dc.type	Journal Article
utslib.citation.volume	1	en_US
utslib.citation.volume	8	en_US
utslib.for	08 Information and Computing Sciences	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
utslib.copyright.status	open_access
pubs.issue	1	en_US
pubs.publication-status	Published	en_US
pubs.volume	8	en_US

Abstract:

© 2016 by De Gruyter. It is not known whether Thompson's group F is automatic. With the recent extensions of the notion of an automatic group to graph automatic by Kharlampovich, Khoussainov and Miasnikov and then to C-graph automatic by the authors, a compelling question is whether F is graph automatic or C-graph automatic for an appropriate language class C. The extended definitions allow the use of a symbol alphabet for the normal form language, replacing the dependence on generating set. In this paper we construct a 1-counter graph automatic structure for F based on the standard infinite normal form for group elements.

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http://hdl.handle.net/10453/94785