interpretation is a general methodology for building static analyses of programs. It was introduced by P. and R. Cousot in \cite{cc}. We present, in this paper, an application of a generic abstract interpretation to domain of model-checking. Dynamic checking are usually easier to use, because the concept are establishe d and wide well know. But they are usually limited to systems whose states space is finite. In an other part, certain faults cannot be detected dynamically, even by keeping track of the history of the states space.Indeed, the classical problem of finding the right test cases is far from trivial and limit the abilities of dynamic checkers further. Static checking have the advantage that they work on a more abstract level than dynamic checker and can verify system properties for all inputs. Problem, it is hard to guarantee that a violation of a modeled property corresponds to a fault in the concrete system. We propose an approach, in which we generate counter-examples dynamically using the abstract interpretation techniques.