LIPN, CNRS UMR 7030, Université Paris 13, Institut Galilée, salle B107.

**Abstract : **
Model checking is a successful method for checking properties on the state space of concurrent, reactive systems. Since it is based on exhaustive search, scaling the method to industrial systems has been a challenge since its conception. Research has focused on clever data structures and algorithms, to reduce the size of the state space or its representation; smart search heuristics, to reveal potential bugs and counterexamples early; and high-performance computing, to deploy the brute force processing power of clusters of compute-servers.
The main challenge is to combine a brute force approach with clever algorithms: brute force alone (when implemented carefully) can bring a linear speedup in the number of processors. This is great, since it reduces model-checking times from days to minutes. On the other hand, proper algorithms and data structures can lead to exponential gains. Therefore, the parallelization bonus is only real if we manage to speedup clever algorithms.
There are some obstacles: many linear-time graph algorithms depend on a depth-first exploration order, which is hard to parallelize. Examples include the detection of strongly connected components (SCC), and the nested depth-first-search (NDFS) algorithm. Both are used in model checking LTL properties. Symbolic representations, like binary decision diagrams (BDDs), reduce model checking to "pointer-chasing", leading to irregular memory-access patterns. This poses severe challenges on achieving actual speedup in (clusters of) modern multi-core computer architectures.
This talk will present some of the solutions found over the last 10 years, leading to the high-performance model checker LTSmin. These include parallel NDFS (based on the PhD thesis of Alfons Laarman), the parallel detection of SCCs with concurrent Union-Find (based on the PhD thesis of Vincent Bloemen), and concurrent BDDs and other decision diagrams (based on the PhD thesis of Tom van Dijk). This functionality is provided in a specification-language agnostic manner, while exploiting the locality typical for a-synchronous distributed systems (based on the PhD thesis of Jeroen Meijer).
Finally, I will sketch a perspective on moving forward from high-performance model checking to high-performance synthesis algorithms. Examples include parameter synthesis for stochastic and timed systems, and strategy synthesis for (stochastic and timed) games.
The focus of the talk will be on a parallel algorithm for SCC decomposition

**Abstract : **
The next generation of space systems will have to achieve more and more complex missions. In order to master the development cost and duration of such systems, an alternative to a manual design is to automatically synthesize the main parameters of the system. In this work, we present an approach on the specific case of the scheduling of the flight control of a space launcher. The approach requires two successive steps: (1) the formalization of the problem to be solved in a parametric formal model and (2) the synthesis of the model parameters with a tool in an optimal way. We first describe the problematic of the scheduling of a launcher flight control, then we show how this problematic can be formalized with parametric stopwatch automata; we then present the results computed by IMITATOR. We compare the results to the ones obtained by other tools classically used in scheduling.