Frontiers of tractability for typechecking simple XML transformations

Abstract

Typechecking consists of statically verifying whether the output of an XML transformation is always conform to an output type for documents satisfying a given input type. We focus on complete algorithms which always produce the correct answer. We consider top-down XML transformations incorporating XPath expressions and abstract document types by grammars and tree automata. By restricting schema languages and transformations, we identify several practical settings for which typechecking is in polynomial time. Moreover, the resulting framework provides a rather complete picture as we show that most scenarios can not be enlarged without rendering the typechecking problem intractable. So, the present research sheds light on when to use fast complete algorithms and when to reside to sound but incomplete ones.

Transforming XML documents as schemas evolve

“…In other words, we would like to know the XML schema that defines the set of all possible output documents. In general, this problem, also known as static type checking for XSLT, is intractable [6] [7]. However, we provide an approximate solution to it.…”

Visibly Pushdown Transducers

“…They also operate in a top-down manner but a rule is always applied to all children uniformly. Their work mainly investigates the complexity of the type checking problem parameterized by several restrictions on the transformations [MN04, MN05,MN07].…”

“…Both the expressiveness of the model and the type checking problems have been extensively investigated for these models [FH07,MNG08,MN07,MSV03]. They however do not tackle the problem of efficiently performing the transformation.…”

Minimizing Tree Automata for Unranked Trees

“…In the context of XML schema languages, minimized schemas would improve the running time on document validation, or on static tests involving the schemas, such as typechecking of XML transformations [13,26]. Minimal deterministic automata for unranked tree languages play a prominent role in recent approaches to query induction for Web information extraction [3].…”