How to compute the refinement relation for parameterized systems

In this paper, we present a refinement verification for a class of parameterized systems. These systems are composed of an arbitrary number of similar processes. As in (Abdulla et al., 199) we represent the states by regular languages and the transitions by transducers over regular languages. If we can compute a symbolic model by acceleration of the actions, then we can also verify a refinement relation R between the symbolic models. We show that, under some conditions, if R is verified between two symbolic models, then refinement is verified between concrete parameterized systems. Then, we can take advantage of the property (safety and PLTL properties) preservation by refinement for their verification.