Deciding whether an Attributed Translation can be realized by a Top-Down Transducer

TL;DR

This paper investigates whether an attributed tree transducer with monadic output can be realized by a top-down transducer (with or without look-ahead) and provides a decidable, constructive procedure when such an equivalent device exists. The authors reduce the problem to the known two-way versus one-way definability framework, leveraging the single-path property and look-ahead preprocessing to transform the target into a form amenable to established results, and extend the approach to nondeterministic transducers with look-around. They further show that, under monadic output, the look-ahead can be incorporated and, in favorable cases, removed, yielding a deterministic top-down transducer when possible. Overall, the work delivers formal definitions, decidability results, and a constructive method with potential benefits for efficiency and closure properties in tree-translation formalisms.

Abstract

We prove that for a given partial functional attributed tree transducer with monadic output, it is decidable whether or not an equivalent top-down transducer (with or without look-ahead) exists. We present a procedure that constructs an equivalent top-down transducer (with or without look-ahead) if it exists.