Abstract

Thèmes COM et SYM -Systèmes communicants et Systèmes symboliqueś Equipes-Projets Wam et Sardes Rapport de recherche n°6590 -Juillet 2008 -41 pagesAbstract: We present an algorithm to solve XPath decision problems under regular tree type constraints and show its use to statically type-check XPath queries. To this end, we prove the decidability of a logic with converse for finite ordered trees whose time complexity is a simple exponential of the size of a formula. The logic corresponds to the alternation free modal µ-calculus without greatest fixpoint, restricted to finite trees, and where formulas are cycle-free. Our proof method is based on two auxiliary results. First, XML regular tree types and XPath expressions have a linear translation to cycle-free formulas. Second, the least and greatest fixpoints are equivalent for finite trees, hence the logic is closed under negation.Building on these results, we describe a practical, effective system for solving the satisfiability of a formula. The system has been experimented with some decision problems such as XPath emptiness, containment, overlap, and coverage, with or without type constraints. The benefit of the approach is that our system can be effectively used in static analyzers for programming languages manipulating both XPath expressions and XML type annotations (as input and output types).Key-words: Mu-calculus, satisfiability, trees, XPath, queries, XML, types, regular tree grammars An extended abstract of this work was presented at the ACM Conference on Programming Language Design and Implementation (PLDI), 2007 [21]. Extensions included in this article notably comprise proof sketches, crucial implementation techniques for building a satisfiability-testing algorithm which performs well in practice, a detailed description of the algorithm, and formal descriptions and explanations about an important property of the logic: cycle-freeness for formulas.

We present Madeus, an authoring environment for interactive multimedia documents. Madeus 'aim can be sumed up in the following statement : high temporal expressivity must not be reached to the detriment of a user-friendly interjace editing approach. We provide the author with a declarative and hierarchic speciJication language based on an extension of Allen's algebra. Static temporal checking and dynamic scheduling are based on an extension of temporal constraint networks.