Section: New Results

Petri Nets and their Synthesis

Participants : Eric Badouel, Philippe Darondeau.

Deciding Selective Declassification of Petri Nets

In [20] , we consider declassification, as effected by downgrading actions $D$, in the context of intransitive non-interference encountered in systems that consist of high-level (secret) actions $H$ and low-level (public) actions $L$. In a previous work, we had shown the decidability of a strong form of declassification, by which $D$ contains only a single action $d$ declassifying all $H$ actions at once. We continue this study by considering selective declassification, where each transition $d$ in $D$ can declassify a subset $H\left(d\right)$ of $H$. The decidability of this more flexible, application-prone declassification framework is proved in the context of (possibly unbounded) Petri nets with possibly infinite state spaces.

Petri Net Distributability

A Petri net is distributed if, given an allocation of transitions to (geographical) locations, no two transitions at different locations share a common input place. A system is distributable if there is some distributed Petri net implementing it. We address in [21] the question of which systems can be distributed, while respecting a given allocation. We state the problem formally and discuss several examples illuminating — to the best of our knowledge — the current status of this work.

Petri Net Reachability Graphs: Decidability Status of First Order Prioperties

We investigated in [13] the decidability and complexity status of model-checking problems on unlabelled reachability graphs of Petri nets by considering first-order, modal and pattern-based languages without labels on transitions or atomic propositions on markings. We have considered several parameters to separate decidable problems from undecidable ones. Not only were we able to provide precise borders and a systematic analysis, but we also demonstrated the robustness of our proof techniques.

$\alpha$-reconstructibility of Workflow Nets

The $\alpha$-algorithm is a process mining algorithm, introduced by van der Aalst et al, that constructs a workflow net from an event log. A class of nets, the structured workflow nets, was recognized to be reconstructible by algorithm $\alpha$ from their language (or a representative subset of it). In [14] we assessed more precisely the $\alpha$-algorithm we provided a characterization of the class of the workflow nets that are discovered by $\alpha$.