Caterpillars, context, tree automata and tree pattern matching

We present a novel, yet simple, technique for the speciication of context in struc-tured documents that we call caterpillar expressions. Although we are primarily applying this technique in the speciication of context-dependent style sheets for HTML, SGML and XML documents, it can also be used for query speciication for structured documents, as we shall demonstrate, and for the speciication of computer program transformations. From a conceptual point of view, structured documents are trees, and one of the oldest and best-established techniques to process trees and, hence, structured documents are tree automata. We present a number of theoretical results that allow us to compare the expressive power of caterpillar expressions and caterpillar au-tomata, their companions, to the expressive power of tree automata. In particular, we demonstrate that each caterpillar expression describes a regular tree language that is, hence, recognizable by a tree automaton. Finally, we employ caterpillar expressions for tree pattern matching. We demonstrate that caterpillar automata are able to solve tree-pattern-matching problems for some, but not all, types of tree inclusion that Kilpell ainen investigated in his PhD thesis. In simulating tree pattern matching with caterpillar automata, we reprove some of Kilpell ainen's results in a uniform framework.