Linking theorems for tree transducers

• Promote links of synchronous grammars to items of study.
• Investigate their properties for various tree transducers.
• Establish new proof method for expressive power of compositions of tree transducers.
• Apply the new technique to new and classic results.

Linear extended multi bottom-up tree transducers are presented in the framework of synchronous grammars, in which the input and the output tree develop in parallel by rewriting linked nonterminals (or states). These links are typically transient and disappear once the linked nonterminals are rewritten. They are promoted to primary objects here, preserved in the semantics, and carefully studied. It is demonstrated that the links computed during the derivation of an input and output tree pair are hierarchically organized and that the distance between (input and output) link targets is bounded. Based on these properties, two linking theorems are developed that postulate the existence of certain natural links in each derivation for a given input and output tree pair. These linking theorems allow easy, high-level proofs that certain tree translations cannot be implemented by (compositions of) linear extended multi bottom-up tree transducers.