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In [14], we proposed a framework for the automatic verification of reactive systems. Our main tool is a decision procedure, Mona, for Monadic Second-order Logic (M2L) on finite strings. Mona translates a formula in M2L into a finite-state automaton. We show in [14] how traces, i.e. finite 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 specification problem of the 1994 Dagstuhl Seminar on Specification and Refinement of Reactive Systems. The purely behavioral descriptions that we formulate from the informal specifications 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 verification. To securely write these formulas, we introduce 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 verified 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 verification.

A Case Study in Automated Verification Based on Trace Abstractions