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 than 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.
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