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Groups Complexity Cryptology

Managing Editor: Shpilrain, Vladimir / Weil, Pascal

Editorial Board: Ciobanu, Laura / Conder, Marston / Dehornoy, Patrick / Eick, Bettina / Elder, Murray / Fine, Benjamin / Gilman, Robert / Grigoriev, Dima / Ko, Ki Hyoung / Kreuzer, Martin / Mikhalev, Alexander V. / Myasnikov, Alexei / Perret, Ludovic / Roman'kov, Vitalii / Rosenberger, Gerhard / Sapir, Mark / Thomas, Rick / Tsaban, Boaz / Capell, Enric Ventura


CiteScore 2017: 0.32

SCImago Journal Rank (SJR) 2017: 0.208
Source Normalized Impact per Paper (SNIP) 2017: 0.322

Mathematical Citation Quotient (MCQ) 2017: 0.32

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1869-6104
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Thompson's group F is 1-counter graph automatic

Murray Elder / Jennifer Taback
Published Online: 2016-04-12 | DOI: https://doi.org/10.1515/gcc-2016-0001

Abstract

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 đť’ž-graph automatic by the authors, a compelling question is whether F is graph automatic or đť’ž-graph automatic for an appropriate language class đť’ž. 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.

Keywords: Thompson's group F; automatic group; graph automatic group; đť’ž-graph automatic group

MSC: 20F65; 68Q45

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About the article

Received: 2015-01-18

Published Online: 2016-04-12

Published in Print: 2016-05-01


Funding Source: Australian Research Council

Award identifier / Grant number: FT110100178

Funding Source: National Science Foundation

Award identifier / Grant number: DMS-1105407

Funding Source: Simons Foundation

Award identifier / Grant number: 31736 to Bowdoin College

The first author is supported by Australian Research Council grant FT110100178. The second author acknowledges support from National Science Foundation grant DMS-1105407 and Simons Foundation grant 31736 to Bowdoin College.


Citation Information: Groups Complexity Cryptology, Volume 8, Issue 1, Pages 21–33, ISSN (Online) 1869-6104, ISSN (Print) 1867-1144, DOI: https://doi.org/10.1515/gcc-2016-0001.

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