Section: New Results

Specification and verification of database driven systems

Participants : Serge Abiteboul, Pierre Bourhis, Luc Segoufin, Szymon Toruńczyk, Victor Vianu.

Modelization and verification of data centric systems.

We have intensively studied the Active XML model. It is a high-level specification language tailored to data-intensive, distributed, dynamic Web services. Active XML is based on XML documents with embedded function calls. The state of a document evolves depending on the result of internal function calls (local computations) or external ones (interactions with users or other services). Function calls return documents that may be active, so may activate new subtasks. Our first line of result is a comparison of the specification power of various workflow control mechanisms within the Active XML framework and beyond [23] .

AXML is very powerful and many static analysis problems are undecidable. We have also introduced a model of automata designed for modeling infinite runs of systems equipped with static relational databases. The automata model is equipped with finitely many variables, each of which can store values from a linearly ordered domain, such as the natural numbers. The transitions of the automata depends on a conjunctive query involving the database and the current values of the variables. For verifying infinite runs of such automata, an extension of temporal logic is considered, capable of comparing values stored in the variables and the database, at different times of the run. The main contribution of the work is the proof that automated verification of such temporal properties of the system can be carried out in PSpace. For more details, see [35] .

Static analysis of query languages.

XPath is arguably the most widely used XML query language as it is implemented in XSLT and XQuery and it is used as a constituent part of several specification and update languages. Hence in order to perform static analysis on a system manipulating XML data it is important to master the static analysis for XPath. Most of the important static analysis problems reduce to satisfiability checking: does a given query return a non-empty answer on some data. In general, in the presence of data values, the satisfiability of XPath is undecidable. We have shown that when restricted to its vertical navigational power, XPath becomes decidable [30] .