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

Ilya Kapovich·Alexei Myasnikov·Paul Schupp·Vladimir Shpilrain
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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.

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Ilya Kapovich, Alexei Myasnikov, Paul Schupp, Vladimir Shpilrain. 2002-06-10. Generic-case complexity, decision problems in group theory and random walks. https://arxiv.org/abs/math/0203239

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