## Section: New Results

### Fundamentals and algorithms: communication with messages and Scenarios

Participants : Loïc Hélouët, Blaise Genest.

In this paragraph, we collect our fundamental results regarding the models and algorithms we use for communicating systems, and in particular, scenarios.

A major challenge with models communicating with messages (e.g.: scenarios) is to *exhibit good classes of models*
allowing users to *specify easily complex distributed systems* while *preserving the decidability* of some key problems, such as diagnosis, equality and intersection.
Furthermore, when these problems are decidable for the designed
models, the second challenge is to design algorithms to keep the *complexity low enough* to allow *implementation in real cases* .

For the last three years, we have developped a new model of scenarios, namely Causal HMSCs [13] , in order to specify complex telecommunication protocols, such as sliding windows protocols. The main novelty of the approach is to allow for an independance alphabet on each process, instead of the rigid total order of HMSCs. Interestingly, many problems on this model remain decidable without requiring (existential) bounds on the message queues. The decidable questions we have considered are diagnosis and comparison (equality, intersection) with other Causal HMSCs, and we gave the optimal associated algorithms. However, when comparing Causal HMSCs with other models (logics, communicating automata, or even Causal HMSCs built with different independence alphabets), the problems turn out to be undecidable, unless there is an (existential) bounds on the number of messages present in any channel at a given time. We thus consider the problem to know whether a given system is existentially bounded, modeled as communicating automata [11] . We proved that this problem is undecidable. However, we give algorithms to solve the problem in a non trivial subclass.

Our last work in the topic of algorithms for Scenarios was to consider basic test on languages of scenarios, depicted as graphs, to be included in our tool SOFAT. The problem is that a graph of scenarios might exhibit counterintuitive behaviors, as an event appearing much further than a given event in the graph can happen at the same time or even before this event. We call such a case disorder [12] , we give quantification of this disorder, and give an efficient algorithm to compute the worst disorder, that is to display its “most counterintuitive” behavior.

We have also considered an extension of coregions in HMSCs. A coregion is a part of a process description in which the ordering of events is relaxed. Usually, the ordering of events on a single process is a total order. The Z.120 standard [44] also allows for general orderings, that is a replacement of the total ordering imposed on a process by a partial ordering. However, coregions are limited to a finite set of events. We have extended the orginal formalism to allow for infinite coregions containing partial orderings. Within this context, we also have provided algorithms to detect discrepancies between the visual ordering of events and their actual ordering imposed by the semantics (this notion is usually called “race condition”). This work was done during a collaboration with Masaryk University (Czech Republic).