The decidability of equivalence for three important classes of tree transducers is discussed. Each class can be obtained as a natural restriction of deterministic macro tree transducers (MTTs): (1) no context parameters, i.e., top-down tree transducers, (2) linear size increase, i.e., MSO definable tree transducers, and (3) monadic input and output ranked alphabets. For the full class of MTTs, decidability of equivalence remains a long-standing open problem.
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