We use downward closed languages for representing sets of states when performing forward reachability analysis on infinite-state systems. Downward closed languages are often more succinct than exact representations of the set of reachable states. We introduce a formalism for representing downward closed languages, called downward closed language generators (dlgs). We show that standard set operations needed for performing symbolic reachability analysis are computable for dlgs. Using a class of hierarchically defined dlgs, we have implemented a prototype for analysing timed Petri nets and used it to analyze a parameterized version of Fischer's protocol. We also show how dlgs can be used for uniform representation of formalisms previously presented for models such as Petri nets and lossy channel systems.
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