Abstract: We start by giving a simple and efficient method to prove safety properties for parameterized systems with linear topologies. A process in the system is a finite-state automaton, where the transitions are guarded by both local and global conditions. The method derives an over-approximation of the induced transition system, which allows the use of a simple class of regular expressions as a symbolic representation (upward closed sets). We explain how this work can be extended to the case of parameterized systems where each process manipulates integer variables.