Section: New Results

Specification and verification of data-driven systems

Verification of Hierarchical Artifact Systems

Data-driven workflows, of which "business artifacts" are a prime exponent, have been successfully deployed in practice, adopted in industrial standards, and have spawned a rich body of research in academia, focused primarily on static analysis. Over the past few years, we have embarked upon a study of the verification problem for artifact systems. This is a challenging problem because of the presence of unbounded data. In order to deal with the resulting infinite-state system, we developed in earlier work a symbolic approach allowing a reduction to finite-state model checking and yielding a pspace verification algorithm for the simplest variant of the model (no database dependencies and uninterpreted data domain). Subsequently, we extended our approach to allow for database dependencies and numeric data testable by arithmetic constraints. In [19], we make significant progress on several fronts, by considering a much richer and more realistic model than in previous work, incorporating core elements of IBM's successful Guard-Stage-Milestone model. In particular, the model features task hierarchy, concurrency, and richer artifact data. It also allows database key and foreign key dependencies, as well as arithmetic constraints. The results require qualitatively novel techniques, because the reduction to finite-state model checking used in previous work is no longer possible. Instead, the richer model requires the use of a hierarchy of Vector Addition Systems with States. The arithmetic constraints are handled using quantifier elimination techniques, adapted to our setting.

Process-centric views of data-driven workflows.

We also studied the models of data Petri nets and $\nu$-Petri nets. While these models were introduced in the verification community to analyse protocols and process algebra, they can also be seen as (very limited) data-driven workflows with only unary predicates. Our results this year show that various boundedness problems (e.g. can the database grow unbounded?) are decidable in data Petri nets [22], and pinpoint the exact complexity of safety analysis in $\nu$-Petri nets [23].

Complexity in counter systems and in proof systems.

The static analysis of queries on XML trees and data streams relies in a majority of cases on decision procedures expressed in terms of formal systems like counter systems or proof systems. For instance, two-variables first-order data queries on words can be related to reachability in vector addition systems (VAS), and the same queries on trees to reachability in a branching extension of VAS [12]. We are at the forefront on the complexity analysis for such systems [15], [13], [16], [14].

We investigate in the ANR prodaq project a different angle on the static analysis of queries, relying on proof systems. Our first results on the subject [18] provide a sequent calculus for a modal data logic with an optimal proof-search algorithm.