Definability Results for Top-Down Tree Transducers

TL;DR

This paper establishes the decidability of whether a deterministic top-down transducer with look-ahead can be equivalently represented by a linear top-down transducer or a tree homomorphism, providing algorithms for construction.

Contribution

It introduces decidability results and algorithms for equivalence checking and construction of simpler transducers for a class of top-down tree transducers.

Findings

Decidability of definability by linear top-down transducers

Decidability of definability by tree homomorphisms

Algorithms for constructing equivalent transducers

Abstract

We prove that for a given deterministic top-down transducer with look-ahead it is decidable whether or not its translation is definable (1)~by a linear top-down tree transducer or (2)~by a tree homomorphism. We present algorithms that construct equivalent such transducers if they exist.