Attributed Tree Transducers for Partial Functions

TL;DR

This work investigates attributed tree transducers (atts) equipped with regular look-around and shows a key robustness property: when restricting to partial-function translations, every nondeterministic att with regular look-around has an equivalent deterministic att with regular look-around. The authors develop a uniformizer-based construction that reduces nondeterminism to determinism, using a nondeterministic top-down relabeling $T$ and a deterministic att $D'$ to simulate uniform translations, aided by a look-around $U$ that realizes a uniformizer. They prove that for any att with look-around, a $datt^U$ realizing a uniformizer exists, and consequently any functional composition of $n$ atts with look-around can be realized by a composition of $n$ deterministic atts with look-around, with domain recognizability and exponential complexity reflecting the inherent overhead. The results unify deterministic and nondeterministic translations under the functional constraint and open questions about decidability of functionality and uniformization for broader classes of transducers.

Abstract

Attributed tree transducers (atts) have been equipped with regular look-around (i.e., a preprocessing via an attributed relabeling) in order to obtain a more robust class of translations. Here we give further evidence of this robustness: we show that if the class of translations realized by nondeterministic atts with regular look-around is restricted to partial functions, then we obtain exactly the class of translations realized by deterministic atts with regular look-around.