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In this paper we survey abstraction and refinement in model checking. We restrict the discussion to existential abstraction which over-approximates the behaviors of the concrete model. The logics preserved under this abstraction are the universal fragments of branching-time temporal logics as well as linear-time temporal logics. For simplicity of presentation, we also restrict the discussion to abstraction functions, rather then abstraction relations. Thus, every concrete state is represented by exactly one abstract state. An abstract state then represents a set of concrete states, which is disjoint from the sets represented by other abstract states.