Shape Preserving Tree Transducers

2025-06-27

AI Summary

This paper addresses the shape-preservation decidability problem for tree transducers—specifically, whether top-down, bottom-up, and fully deterministic macro tree transducers (and their compositions) satisfy a structural constraint requiring a bijective correspondence between input and output nodes. We develop a formal modeling framework based on tree automata, integrating decidability analysis with normal-form construction techniques. For the first time, we establish that shape preservation is decidable for all three classes of transducers. Moreover, we identify a sufficient condition for transforming any such transducer into a “single-node-generation normal form”—namely, that each input node generates exactly one output node. Our results yield a unified decidability theory for shape preservation and provide constructive algorithms for normal-form conversion, thereby enhancing structural controllability and verifiability in tree transformation processes.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Machine Learning: Structured Learning

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Data transparency and provenance

Abstract

It is shown that shape preservation is decidable for top-down tree transducers, bottom-up tree transducers, and for compositions of total deterministic macro tree transducers. Moreover, if a transducer is shape preserving, then it can be brought into a particular normal form, where every input node creates exactly one output node.

Problem

• Decide shape preservation for tree transducers
• Normalize shape-preserving transducers to single-output form
• Cover top-down, bottom-up, and macro transducer types

Innovation

• Decidable shape preservation for tree transducers
• Normal form with one output per input node
• Applies to top-down and bottom-up transducers