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29 March 2024
 
  » arxiv » math.GR/0203239

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Generic-case complexity, decision problems in group theory and random walks
Ilya Kapovich ; Alexei Myasnikov ; Paul Schupp ; Vladimir Shpilrain ;
Date 22 Mar 2002
Subject Group Theory; Computational Complexity MSC-class: 20F | math.GR cs.CC
AbstractWe give a precise definition of ``generic-case complexity’’ and show that for a very large class of finitely generated groups the classical decision problems of group theory - the word, conjugacy and membership problems - all have linear-time generic-case complexity. We prove such theorems by using the theory of random walks on regular graphs.
Source arXiv, math.GR/0203239
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