Thèse de doctorat
Résumé : In the field of formal verification of real-time systems, major developments have been recorded in the last fifteen years. It is about logics, automata, process algebra, programming languages, etc. From the beginning, a formalism has played an important role: timed automata and their natural extension,hybrid automata. Those models allow the definition of real-time constraints using real-valued clocks, or more generally analog variables whose evolution is governed by differential equations. They generalize finite automata in that their semantics defines timed words where each symbol is associated with an occurrence timestamp.

The decidability and algorithmic analysis of timed and hybrid automata have been intensively studied in the literature. The central result for timed automata is that they are positively decidable. This is not the case for hybrid automata, but semi-algorithmic methods are known when the dynamics is relatively simple, namely a linear relation between the derivatives of the variables.

With the increasing complexity of nowadays systems, those models are however limited in their classical semantics, for modelling realistic implementations or dynamical systems.

In this thesis, we study the algorithmics of complex semantics for timed and hybrid automata.

On the one hand, we propose implementable semantics for timed automata and we study their computational properties: by contrast with other works, we identify a semantics that is implementable and that has decidable properties.

On the other hand, we give new algorithmic approaches to the analysis of hybrid automata whose dynamics is given by an affine function of its variables.