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This article is concerned with the verification of closed-loop asynchronous reactive systems. Such systems, specified for instance with the industrial SDL (Specification and Description Language) language, communicate with their environment through buffers which memorize occurrences of events. Such a communication mechanism is quite interesting for specifying systems connected to several asynchronous external actors. However, it leads to a verification model possibly composed of a huge number of states (due to the state-space of the buffers). This article shows how this combinatorial explosion could be reduced by specifying the environment of the system to be verified, and by using partial-orders methods both on the system and its environment. After presenting the formal modeling languages SDL (for the reactive system) and CDL Context Description Language (for its environment), the main points of our work are two-fold: (1) we define an independence relation between input events for a given specification C, S, ϕ where S is the specification of the system (in SDL), C is the behavior of its external environment (in CDL), and ϕ the property to verify. The key point is that this independence relation is separately computed on S, C and ϕ, without building the global synchronization product of the system; (2) we apply the Mazurkiewicz theory for defining the set of scenarios (sequences of input events) which exactly covers the environment C and which is sufficient for verifying ϕ on S. We finally show on two industrial case-studies that this approach leads to an interesting reduction in verification time.