  We consider the synthesis of deterministic tree transducers from automaton
definable specifications, given as binary relations, over finite trees. We
consider the case of specifications that are deterministic top-down tree
automatic, meaning the specification is recognizable by a deterministic
top-down tree automaton that reads the two given trees synchronously in
parallel. In this setting we study tree transducers that are allowed to have
either bounded delay or arbitrary delay. Delay is caused whenever the
transducer reads a symbol from the input tree but does not produce output. We
provide decision procedures for both bounded and arbitrary delay that yield
deterministic top-down tree transducers which realize the specification for
valid input trees. Similar to the case of relations over words, we use
two-player games to obtain our results.
