2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64398We investigate the average-case complexity of decision problems for finitely generated groups, in particular the word and membership problems. Using our recent results on ``generic-case complexity'' we show that if a finitely generated group $G$ has the word problem solvable in subexponential time and has a subgroup of finite index which possesses a non-elementary word-hyperbolic quotient group, then the average-case complexity of the word problem for $G$ is linear time, uniformly with respect to the collection of all length-invariant measures on $G$. For example, the result applies to all braid groups $B_n$.Some misprints have been correctedGroup TheoryComputational ComplexityGeometric Topology20F36text