Section: New Results

Model expressivity and quantitative verification

Diagnosis from scenarios

Participants : Loïc Hélouët, Blaise Genest, Hervé Marchand.

Diagnosis of a system consists in providing explanations to a supervisor from a partial observation of the system and a model of possible executions. This year, we have extended results on diagnosis algorithm from scenarios. Systems are modeled using High-level Message Sequence Charts (HMSCs), and the diagnosis is given as a new HMSC, which behaviors are all explanations of the partial observation. The results published this year are first an offline centralized diagnosis algorithm (a single process in a network collects an observation, and emits a diagnosis) that has then been extended to a decentralized version of this algorithm. This allows us to give a complete diagnosis framework for infinite state systems, with a strong emphasis on concurrency and causal ordering in behaviors. HMSC-based diagnosis showed nice properties w.r.t. compositionality. We have also considered solutions for online diagnosis from scenarios, but came to the conclusion that online solutions are memory consuming, and need too many restrictions to run with finite memory.

The last contribution of this work is an application of diagnosis techniques to anomaly detection, that is a comparison of observation of the system with a model of usual behaviors to detect security attacks. This work is already available online in [25] , and will soon be published.

Probabilistic model checking

Participants : Nathalie Bertrand, Blaise Genest, Paulin Fournier.

In [20] , we considered the verification of Markov chains against properties talking about distributions of probabilities. Even though a Markov chain is a very simple formalism, by discretizing in a finite number of classes the space of distributions through some symbolics, we proved that the language of trajectories of distribution (one for each initial distribution) is not regular in general, even with 3 states. We then proposed a parametrized algorithm which approximate what happens to infinity, such that each symbolic block in the approximate language is at most $ϵ$ away from the concrete distribution.

With the objective of model checking infinite state probabilistic systems, we proved a general finite-time convergence theorem for fixpoint expressions over a well-quasi-ordered set [22] . This has immediate applications for the verification of well-structured systems, where a main issue is the computability of fixpoint expressions, and in particular for game-theoretical properties and probabilistic systems where nesting and alternation of least and greatest fixpoints are common [35] .

Parameterized verification aims at validating a system's model irrespective of the value of a parameter. In [34] we introduced a model for networks of an arbitrary number of probabilistic timed processes, communicating by broadcasting. This model is suitable for distributed protocols, and can be applied to wireless sensor networks or peer-to-peer applications. The number of processes is unknown and either is constant (static case), or evolves over time through random disappearances and creations (dynamic case). On the one hand, most parameterized verification problems turn out to be undecidable in the static case (even for untimed processes). On the other hand, we prove their decidability in the dynamic case.

Distributed timed systems

Participants : Nathalie Bertrand, Amélie Stainer.

We study the reachability problem for communicating timed processes, both in discrete and dense time. Our model comprises automata with local timing constraints communicating over unbounded FIFO channels. Each automaton can only access its set of local clocks; all clocks evolve at the same rate. Our main contribution is a complete characterization of decidable and undecidable communication topologies, for both discrete and dense time. We also obtain complexity results, by showing that communicating timed processes are at least as hard as Petri nets; in the discrete time, we also show equivalence with Petri nets. Our results follow from mutual topology-preserving reductions between timed automata and (untimed) counter automata. To account for urgency of receptions, we also investigate the case where processes can test emptiness of channels. This resut is published in [39] and is a part of Amélie Stainer's PhD manuscript [18] . It also constitutes a contribution to ANR VACSIM.

We also studied a model for distributed systems composed of stochastic and timed processes that interact via broadcasting. For these networks of stochastic timed automata (NSTA), we provided a precise performance evaluation algorithm, without resorting to simulation techniques. The idea is to characterize the general state space Markov chain through transient stochastic state classes that represent the system's state after each action. This yields an algorithmic approach to the transient analysis of NSTA models, with fairly general termination conditions [32] .