Compositional verification of component-based real-time systems and applications. (Vérification compositionnelle des systèmes temps-réel à base de composants et applications)

ion-Based Techniques In [BPG08], the Assume-guarantee-Abstraction Refinement method is proposed for the automation of this compositional reasoning paradigm and applied for Rule 2.1. It is mainly inspired by the CEGAR approach and iteratively finds assumptions that represent the abstraction of the behavior of component B0 which concerns its interaction with component B. Therefore, in each iteration, the assumption A satisfies the first premise of the rule and is verified for the second premise. The generated counterexamples are analyzed and those which are spurious serve to strengthen iteratively the overapproximation made by the abstraction. 2.1.2 Assume-guarantee Reasoning for Timed Systems The above-mentioned research works are focused on the untimed systems. The proposals to handle real-time systems are more limited. In [GJL04, GJP06, GJL10], the authors extended the learning techniques which were first proposed by Angluin for finite automata to the setting of real-time systems. In the field of timed automata, one major obstacle for learning assumptions is that the set of clocks is not known in advance. Regarding this difficulty, the authors restricted their methods for event-recording-automata (ERA) [AFH99] where the last occurrence of each action is registered. The three developed algorithms focus on ERA with canonical shapes and which can be perceived as finite automata over a symbolic alphabet. Another method for learning timed systems was proposed in [VDWW06]. It deals with timed automata containing one clock reset at every transition. There, the generalization to automata with multiple clocks is difficult. In [LAL+14], another method for learning the non circular rule of assume-guarantee method is proposed for the verification of timed systems, focusing also on ERA. It consists in a twosteps flow: first, an untimed assumption is generated in order to ensure the events sequence is correct, then these assumptions are refined so that timing constraints are satisfied. 2.2. Contract-Based Reasoning and Interface Theories 19 In [FHK04], an assume-guarantee reasoning approach is proposed for hybrid I/O-automata [LSV03] where a novel rule is proposed on the basis of simulation relations. One advantage of this approach is that circularity is countered by a state-based non blocking condition that can be checked during the computation of the simulation relations.