Solving the conjugacy problem in Garside groups by cyclic sliding

We present a solution to the conjugacy decision problem and the conjugacy search problem in Garside groups, which is theoretically simpler than the usual one, with no loss of efficiency. This is done by replacing the well known cycling and decycling operations by a new one, called cyclic sliding, wh...

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Detalhes bibliográficos
Autores: Gebhardt, Volker, González-Meneses López, Juan
Tipo de documento: artigo
Estado:Versión enviada para evaluación y publicación
Data de publicação:2010
País:España
Recursos:Universidad de Sevilla (US)
Repositório:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/42311
Acesso em linha:http://hdl.handle.net/11441/42311
https://doi.org/10.1016/j.jsc.2010.01.013
Access Level:Acceso aberto
Palavra-chave:Garside groups
conjugacy
conjugacy problem
cyclic sliding
sliding circuits
complexity analysis
Descrição
Resumo:We present a solution to the conjugacy decision problem and the conjugacy search problem in Garside groups, which is theoretically simpler than the usual one, with no loss of efficiency. This is done by replacing the well known cycling and decycling operations by a new one, called cyclic sliding, which appears to be a more natural choice. We give an analysis of the complexity of our algorithm in terms of fundamental operations with simple elements, so our analysis is valid for every Garside group. This paper intends to be self-contained, not requiring any previous knowledge of prior algorithms, and includes all the details for the algorithm to be implemented on a computer.