Joost Engelfriet, Sebastian Maneth and Helmut Seidl. Deciding equivalence of top-down XML transformations in polynomial time. J. Comput. Syst. Sci., 75(5):271--286, 2009.
Many useful XML transformations can be expressed by deterministic top–down tree transducers. A normal form is presented for such transducers (extended with the facility to inspect their input trees). A transducer in normal form has a unique canonical form which can be obtained by a minimization procedure, in polynomial time. Thus, equivalence of transducers in normal form can be decided in polynomial time. If the transducer is total, the normal form can be obtained in polynomial time as well.
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