  We investigate partial Equality and Word Problems for finitely generated
groups. After introducing Upper Banach (UB) density on free groups, we prove
that solvability of the Equality Problem on squares of UB-generic sets implies
solvability of the whole Word Problem. In particular, we prove that solvability
of generic EP implies WP. We then exploit another definition of generic EP,
which turns out to be equivalent to generic WP. We characterize in different
ways the class of groups with unsolvable UB-generic WP, proving that it
contains that of algorithmically finite groups, and it is contained in that of
groups with unsolvable generic WP.
