Equivalence Problems for Tree Transducers: A Brief Survey

TL;DR

This paper surveys the decidability of equivalence problems across various classes of tree transducers, highlighting known results and open problems in the field.

Contribution

It provides a comprehensive overview of the decidability status for equivalence in different subclasses of macro tree transducers.

Findings

Decidability established for top-down tree transducers and MSO definable transducers.

Open problem remains for full macro tree transducers.

Clarifies the boundaries of decidability in tree transducer equivalence.

Abstract

The decidability of equivalence for three important classes of tree transducers is discussed. Each class can be obtained as a natural restriction of deterministic macro tree transducers (MTTs): (1) no context parameters, i.e., top-down tree transducers, (2) linear size increase, i.e., MSO definable tree transducers, and (3) monadic input and output ranked alphabets. For the full class of MTTs, decidability of equivalence remains a long-standing open problem.