Synthesis of Deterministic Top-down Tree Transducers from Automatic Tree Relations

TL;DR

This paper presents decision procedures for synthesizing deterministic top-down tree transducers from automatic tree relations, enabling automatic translation of finite trees with bounded or arbitrary delay using game-based methods.

Contribution

It introduces novel decision procedures for synthesizing deterministic top-down tree transducers from automatic specifications with delay considerations.

Findings

Decidable procedures for bounded delay transducer synthesis.

Decidable procedures for arbitrary delay transducer synthesis.

Use of two-player games to achieve synthesis results.

Abstract

We consider the synthesis of deterministic tree transducers from automaton definable specifications, given as binary relations, over finite trees. We consider the case of specifications that are deterministic top-down tree automatic, meaning the specification is recognizable by a deterministic top-down tree automaton that reads the two given trees synchronously in parallel. In this setting we study tree transducers that are allowed to have either bounded delay or arbitrary delay. Delay is caused whenever the transducer reads a symbol from the input tree but does not produce output. We provide decision procedures for both bounded and arbitrary delay that yield deterministic top-down tree transducers which realize the specification for valid input trees. Similar to the case of relations over words, we use two-player games to obtain our results.