  We introduce and investigate different definitions of effective amenability,
in terms of computability of F{\o}lner sets, Reiter functions, and F{\o}lner
functions. As a consequence, we prove that recursively presented amenable
groups have subrecursive F{\o}lner function, answering a question of Gromov,
for the same class of groups we prove that solvability of the Equality Problem
on a generic set (generic EP) is equivalent to solvability of the Word Problem
on the whole group (WP), thus providing the first examples of finitely
presented groups with unsolvable generic EP. In particular, we prove that for
finitely presented groups, solvability of generic WP doesn't imply solvability
of generic EP.
