A Case Study in Verification Based on Trace Abstractions

In 14], we proposed a framework for the automatic veriica-tion of reactive systems. Our main tool is a decision procedure, Mona, for Monadic Second-order Logic (M2L) on nite strings. Mona translates a formula in M2L into a nite-state automaton. We show in 14] how traces, i.e. nite executions, and their abstractions can be described behaviorally. These state-less descriptions can be formulated in terms of customized temporal logic operators or idioms. In the present paper, we give a self-contained, introductory account of our method applied to the RPC-memory speciication problem of the 1994 Dagstuhl Seminar on Speciication and Reenement of Reactive Systems. The purely behavioral descriptions that we formulate from the informal speciications are formulas that may span 10 pages or more. Such descriptions are a couple of magnitudes larger than usual temporal logic formulas found in the literature on veriication. To securely write these formulas, we use Fido 16] as a reactive system description language. Fido is designed as a high-level symbolic language for expressing regular properties about recursive data structures. All of our descriptions have been veriied automatically by Mona from M2L formulas generated by Fido. Our work shows that complex behaviors of reactive systems can be formulated and reasoned about without explicit state-based programming. With Fido, we can state temporal properties succinctly while enjoying automated analysis and veriication.