Generic-case complexity, decision problems in group theory and random walks

Details Generic-case complexity, decision problems in group theory and random walks Generic-case complexity, decision problems in group theory and random walks

2002-03-22

arxiv.org/abs/math/0203239v3

Mathematics

Group Theory

Revised version

Scientific paper

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.

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