## Section: New Results

### Verification

#### Analysis of partially observed recursive discrete-event systems

Participants : Sébastien Chédor, Thierry Jéron, Hervé Marchand, Christophe Morvan.

Monitoring of recursive discrete-event systems under partial observation is an important issue with major applications such as the diagnosability of faulty behaviors and the detection of information flow. We consider regular discrete-event systems, that is recursive discrete-event systems definable by deterministic graph grammars. This setting is expressive enough to capture classical models of recursive systems such as the pushdown systems. Hence they are infinite-state in general and standard powerset constructions for monitoring do not apply anymore. We exhibit computable conditions on these grammars together with non-trivial transformations of graph grammars that enable us to construct a monitor. This construction is applied to diagnose faulty behaviors, to detect information flow in regular discrete-event systems, and to generate tests.

#### Analysis of timed systems

##### Approximate determinization of timed automata

Participants : Nathalie Bertrand, Thierry Jéron, Amélie Stainer.

Timed automata are frequently used to model real-time systems. Their
determinization is a key issue for several validation
problems. However, not all timed automata can be determinized, and
determinizability itself is
undecidable. In [18] , we propose a
game-based algorithm which, given a timed automaton, tries to produce
a language-equivalent deterministic timed automaton, otherwise a
deterministic over-approximation. Our method subsumes two recent
contributions: it is at once more general than an existing (non
terminating) determinization procedure by Baier *et al.* (2009)
and more precise than the approximation algorithm of Krichen and
Tripakis (2009). Moreover, an extension of the method allows to deal
with invariants and $\u03f5$-transitions, and to consider other
useful approximations: under approximation, and combination of under-
and over-approximations which are particularly useful in testing (see
6.2.1 ).

##### Frequency analysis for timed automata

Participants : Nathalie Bertrand, Amélie Stainer.

The languages of infinite timed words accepted by timed automata are traditionally defined using Büchi-like conditions. These acceptance conditions focus on the set of locations visited infinitely often along a run, but completely ignore quantitative timing aspects. In [15] we propose a natural quantitative semantics for timed automata based on the so-called frequency, which measures the proportion of time spent in the accepting states. We study various properties of timed languages accepted with positive frequency, and in particular the emptiness and universality problems.

#### Petri nets reachability graphs

Participant : Christophe Morvan.

Petri nets are a general model for concurrency, the structure of their reachability graph is mostly unknown. In [19] we have investigated 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 consider several parameters to separate decidable problems from undecidable ones. These results illustrate the intrinsic complexity of the structure of these graphs.