  We investigate the computational complexity of various decision problems
related to conjugacy in finite inverse semigroups. We describe polynomial-time
algorithms for checking if two elements in such a semigroup are ~p conjugate
and whether an inverse monoid is factorizable. We describe a connection between
checking ~i conjugacy and checking membership in inverse semigroups. We prove
that ~o and ~c are partition covering for any countable set and that ~p, ~p* ,
and ~tr are partition covering for any finite set. Finally, we prove that
checking for nilpotency, R-triviality, and central idempotents in partial
bijection semigroups are NL-complete problems and we extend several complexity
results for partial bijection semigroups to inverse semigroups.
