Streaming Tree Transducers

• Published in: Automata, Languages, and Programming pp. 42 - 53
• Main Authors: Alur, Rajeev, D’Antoni, Loris
• Format: Book Chapter
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg
• Series: Lecture Notes in Computer Science
• Subjects: Binary Tree; Input Tree; Input Word; Regular Language; Type Check
• ISBN: 9783642315848; 3642315844
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-642-31585-5_8

Theory of tree transducers provides a foundation for understanding expressiveness and complexity of analysis problems for specification languages for transforming hierarchically structured data such as XML documents. We introduce streaming tree transducers as an analyzable, executable, and expressive model for transforming unranked ordered trees (and hedges) in a single pass. Given a linear encoding of the input tree, the transducer makes a single left-to-right pass through the input, and computes the output using a finite-state control, a visibly pushdown stack, and a finite number of variables that store output chunks that can be combined using the operations of string-concatenation and tree-insertion. We prove that the expressiveness of the model coincides with transductions definable using monadic second-order logic (MSO). We establish complexity upper bounds of ExpTime for type-checking and NExpTime for checking functional equivalence for our model. We consider variations of the basic model when inputs/outputs are restricted to strings and ranked trees, and in particular, present the model of bottom-up ranked-tree transducers, which is the first known MSO-equivalent transducer model that processes trees in a bottom-up manner.