Composition Closure of Linear Extended Top-down Tree Transducers

TL;DR

This paper investigates the expressive power and composition hierarchy of linear extended top-down tree transducers, revealing finite hierarchies under certain restrictions and identifying the minimal number of transducers needed for full expressiveness.

Contribution

It provides a detailed analysis of the composition hierarchy of linear extended top-down tree transducers, including the effects of restrictions like nondeletion and epsilon-freeness, and determines the minimal composition length for full expressiveness.

Findings

Finite composition hierarchy for epsilon-free variants.

Hierarchy does not collapse in most cases.

Minimal number of transducers for full expressiveness identified.

Abstract

Linear extended top-down tree transducers (or synchronous tree-substitution grammars) are popular formal models of tree transformations. The expressive power of compositions of such transducers with and without regular look-ahead is investigated. In particular, the restrictions of nondeletion, epsilon-freeness, and strictness are considered. The composition hierarchy turns out to be finite for all epsilon-free (all rules consume input) variants of these transducers except for nondeleting epsilon-free linear extended top-down tree transducers. The least number of transducers needed for the full expressive power of arbitrary compositions is presented. In all remaining cases (including nondeleting epsilon-free linear extended top-down tree transducers) the composition hierarchy does not collapse.