We consider the extensions of modal transition systems (MTS), namely Boolean
MTS and parametric MTS and we investigate the refinement problems over both
classes. Firstly, we reduce the problem of modal refinement over both classes
to a problem solvable by a QBF solver and provide experimental results showing
our technique scales well. Secondly, we extend the algorithm for thorough
refinement of MTS providing better complexity then via reductions to previously
studied problems. Finally, we investigate the relationship between modal and
thorough refinement on the two classes and show how the thorough refinement can
be approximated by the modal refinement
