On the Expressiveness of Tree Set Operators

In the area of program analysis, (definite) set constraints have been proven particularly useful. The set of operators on recognizable tree sets which they provide besides constructor application, union and intersection are componentwise inverses of constructors. Clearly, all formalisms which allow exactly to specify all recognizable tree sets can be considered as equally expressive. Still, different formalisms may differ significantly in the convenience of specification. To give a trivial example: instead of using set constraints, we could as well directly use finite tree automata. We clearly refrain from doing so. Instead