Analyse de systèmes modulaires à l'aide de techniques d'abstractions hiérarchiques.

Abstract : In this thesis, we are interested in limiting the combinatorial explosion that happens when modelchecking modular systems. We use hierarchical abstraction techniques, which allow one to build an abstraction of a modular system by composing abstractions of his parts, while ensuring that this operation does not change the temporal properties we are interested in. At first, we define the modular regulation networks formalism in order to apply hierarchical abstraction techniques to the study of biological systems. We then use this approach to find the reachable stable states of a multi-cellular model involved in the development of the fruit fly embryo. For this, we use the abstraction called SAFETY which reduces a system while keeping all of its reachable stable states. This is a classical reduction which is quite general in the sens that it also preserves all the safety properties of the model. After this, we define two new reduction operations, which are dependent on the μ-calculus formula we seek to verify on the global system. We also assume that we know the initial state of the module or sub-system to be reduced. Since these reductions must only preserve the value of one formula over the global system, they should be able to return smaller systems than the general ones. While computing these reductions on one module or sub-system, we use partial analysis techniques to test if it contains enough information to conclude about the truth value of the formula on the global system. If it is the case, we can stop the incremental analysis right away; otherwise, this step is still useful for the computation of the reduced subsystem. Finally, we use a prototype to test the first one of our reduction operations on some simple examples. This enables us to observe how big the reductions are as well as getting data in order to tackle the problem of the order of analysis in the future. It is a difficult question and an important one since the hierarchical order in which we build the abstraction has a huge weight on the efficiency of these methods.
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Yves-Stan Le Cornec. Analyse de systèmes modulaires à l'aide de techniques d'abstractions hiérarchiques.. Calcul formel [cs.SC]. Université Paris-Saclay; Université d'Evry-Val-d'Essonne, 2016. Français. ⟨NNT : 2016SACLE019⟩. ⟨tel-01778406⟩

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