Generic-case complexity, decision problems in group theory and random walks
Group Theory
2007-05-23 v3 Computational Complexity
Abstract
We 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.
Cite
@article{arxiv.math/0203239,
title = {Generic-case complexity, decision problems in group theory and random walks},
author = {Ilya Kapovich and Alexei Myasnikov and Paul Schupp and Vladimir Shpilrain},
journal= {arXiv preprint arXiv:math/0203239},
year = {2007}
}
Comments
Revised version