We propose a method based on program specialization, which improves the effectiveness of the backward and forward reachability analyses.  ...  We consider infinite state reactive systems specified by using linear constraints over the integers, and we address the problem of verifying safety properties of these systems by applying reachability  ...  Thanks to Laurent Fribourg and John Gallagher for many stimulating conversations about the topics of this paper. Many thanks to the anonymous referees for constructive comments.  ...