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Groups Complexity Cryptology

Managing Editor: Shpilrain, Vladimir / Weil, Pascal

Editorial Board: Ciobanu, Laura / Conder, Marston / 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 / Lohrey, Markus


CiteScore 2018: 0.80

SCImago Journal Rank (SJR) 2018: 0.368
Source Normalized Impact per Paper (SNIP) 2018: 1.061

Mathematical Citation Quotient (MCQ) 2018: 0.38

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1869-6104
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Tree-based language complexity of Thompson's group F

Jennifer Taback / Sharif Younes
Published Online: 2015-09-29 | DOI: https://doi.org/10.1515/gcc-2015-0009

Abstract

The definition of graph automatic groups by Kharlampovich, Khoussainov and Miasnikov and its extension to 𝒞-graph automatic by Elder and the first author raise the question of whether Thompson's group F is graph automatic. We define a language of normal forms based on the combinatorial “caret types”, which arise when elements of F are considered as pairs of finite rooted binary trees. The language is accepted by a finite state machine with two counters, and forms the basis of a 3-counter graph automatic structure for the group.

Keywords: Thompson's group F; automatic group; graph automatic group; 𝒞-graph automatic group

MSC: 20F65; 68Q45

About the article

Received: 2015-01-18

Revised: 2015-05-28

Published Online: 2015-09-29

Published in Print: 2015-11-01


Funding Source: National Science Foundation

Award identifier / Grant number: DMS-1105407

Funding Source: Simons Foundation

Award identifier / Grant number: 31736


Citation Information: Groups Complexity Cryptology, Volume 7, Issue 2, Pages 135–152, ISSN (Online) 1869-6104, ISSN (Print) 1867-1144, DOI: https://doi.org/10.1515/gcc-2015-0009.

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[1]
Murray Elder and Jennifer Taback
Journal of Algebra, 2014, Volume 413, Page 289

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