XML Navigation and Transformation by Tree-Walking Automata and Transducers with Visible and Invisible Pebbles

TL;DR

This paper extends pebble tree automata and transducers with invisible pebbles, enhancing their recognition, validation, and transformation capabilities for tree languages and MSO definable patterns, with applications to XPath and XSLT.

Contribution

It introduces the concept of invisible pebbles in pebble automata and transducers, enabling more powerful recognition and transformation of tree languages, and improves typechecking complexity.

Findings

Recognize all regular tree languages and validate generalized DTDs.

Realize XPath-like navigation for MSO definable patterns.

Maintain decidable typechecking with enhanced expressive power.

Abstract

The pebble tree automaton and the pebble tree transducer are enhanced by additionally allowing an unbounded number of "invisible" pebbles (as opposed to the usual "visible" ones). The resulting pebble tree automata recognize the regular tree languages (i.e., can validate all generalized DTD's) and hence can find all matches of MSO definable patterns. Moreover, when viewed as a navigational device, they lead to an XPath-like formalism that has a path expression for every MSO definable binary pattern. The resulting pebble tree transducers can apply arbitrary MSO definable tests to (the observable part of) their configurations, they (still) have a decidable typechecking problem, and they can model the recursion mechanism of XSLT. The time complexity of the typechecking problem for conjunctive queries that use MSO definable patterns can often be reduced through the use of invisible pebbles.