Section: New Results

Management of Large Distributed Systems

Parameterized Systems

Participants : Nathalie Bertrand, Nicolas Markey

Reconfigurable broadcast networks provide a convenient formalism for modelling and reasoning about networks of mobile agents broadcasting messages to other agents following some (evolving) communication topology. The parameterized verification of such models aims at checking whether a given property holds irrespective of the initial configuration (number of agents, initial states and initial communication topology). In [15], we focus on the synchronization property, asking whether all agents converge to a set of target states after some execution. This problem is known to be decidable in polynomial time when no constraints are imposed on the evolution of the communication topology (while it is undecidable for static broadcast networks).

During the internship of A.R. Balasubramanian, we investigated how various constraints on reconfigurations affect the decidability and complexity of the synchronization problem. In particular, we show that when bounding the number of reconfigured links between two communications steps by a constant, synchronization becomes undecidable; on the other hand, synchronization remains decidable in PTIME when the bound grows with the number of agents.

Smart Regulation for Urban Trains

Participants : Loïc Hélouët, Karim Kecir, Flavia Palmieri

We have launched a new thread of research for efficient regulation with the M2 internship of Flavia Palmieri. The objective is to use efficient planning techniques to perform regulation in metro networks. Usually, regulation algorithms are simple reactive rules, that build decisions from local measures of train delays. These algorithms are arbitrary decisions, which efficiency is only empirically proved. On the other hand, optimality of regulation decision with respect to some quality criterion could be achieved through optimization algorithms, associating an optimal execution date to next events (arrivals and departures) while fulfilling constraints on causal dependencies, track allocations, etc. However, these algorithms are NP-complete, and do not return answers fast enough to be used online as regulation tools (use usually expects a decision within a few seconds after a train's arrival). During this internship, we have started integrating optimal planning techniques to regulation schemes. The main idea is to perform optimization online for a subset of the next occurring events. Performance of this regulation scheme is currently under evaluation.

Analysis of Concurrent Systems

Participants : Éric Fabre, Loïc Hélouët, Engel Lefaucheux

Generalization of Unfolding Techniques for Petri Nets

The verification of concurrent systems relies on an adequate representation of their trajectory sets, where each trajectory is a partial order of events. Several compact structures have been proposed in the past, starting with unfoldings and event structures. While unfoldings expand both time and conflicts, they generate extremely large branching constructions. To avoid expanding conflicts where they are not meaningful, more compact structures were proposed, as merged processes and trellis processes. In [23], we examine structures that would not fully unfold time as well, thus resulting in partially unfolded nets. To do so, we proposed the notion of spread nets, (safe) Petri nets equipped with vector clocks on places and with ticking functions on transitions, and such that vector clocks are consistent with the ticking of transitions. Such nets allow one to generalize previous constructions as unfoldings and merged processes, and can be fully paremeterized to display or hide some behaviors of the net, and thus facilitate its analysis.

Hyper Partial Order Logic

In [21], we define HyPOL, a local hyper logic for partial order models, expressing properties of sets of runs. These properties depict shapes of causal dependencies in sets of partially ordered executions, with similarity relations defined as isomorphisms of past observations. This type of logics is tailored to address security properties of concurrent systems. Unsurprisingly, since comparison of projections are included, satisfiability of this logic is undecidable. We then address model checking of HyPOL and show that, already for safe Petri nets, the problem is undecidable. Fortunately, sensible restrictions of observations and nets allow us to bring back model checking of HyPOL to a decidable problem, namely model checking of MSO on graphs of bounded treewidth.

Diagnosability Analysis for Concurrent Systems

Petri nets have been proposed as a fundamental model for discrete-event systems in a wide variety of applications and have been an asset to reduce the computational complexity involved in solving a series of problems, such as control, state estimation, fault diagnosis, etc. Many of those problems require an analysis of the reachability graph of the Petri net. The basis reachability graph is a condensed version of the reachability graph that was introduced to efficiently solve problems linked to partial observation. It was in particular used for diagnosis which consists in deciding whether some fault events occurred or not in the system, given partial observations on the run of the system. However this method is, with very specific exceptions, limited to bounded Petri nets. In [28], we introduce the notion of basis coverability graph to remove this requirement. We then establish the relationship between the coverability graph and the basis coverability graph. Finally, we focus on the diagnosability problem: we show how the basis coverability graph can be used to get an efficient algorithm.