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

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. Contents

• Type: Journal
• Year: 2002
• Where: CORR
• Authors: Ilya Kapovich, Alexei G. Myasnikov, Paul Schupp, Vladimir Shpilrain
• Keywords: Classical Decision Problems, CORR 2002, Education, Generic-case Complexity, Linear-time Generic-case Complexity