2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63638We 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.Revised versionGroup TheoryComputational Complexity20Ftext