Decidability of functionality for compositions of attributed tree transducers

Determine whether the functionality problem for compositions of attributed tree transducers is decidable; specifically, given a finite composition C of attributed tree transducers on ranked input/output alphabets, decide whether the tree translation realized by C is a partial function (i.e., for every input tree there is at most one output tree).

Background

The paper proves that any functional composition of attributed tree transducers with look-around can be simulated by a composition of deterministic attributed tree transducers with look-around. Building on this, the authors raise the decision problem of functionality for such compositions.

They note related positive results for other formalisms (e.g., top-down tree transducers), highlighting that a corresponding decidability result for attributed tree transducers has not been established.