Temporal logic in finite-state verification

In finite-state verification, model checkers examine finite-state machines representing concurrent software systems looking for errors in design. Errors are defined as violations of requirements expressed as properties of the system. In the event that the finite-state machine fails to satisfy the property, a model checker is in some cases capable of producing a counterexample – an execution of the system demonstrating how the error occurs.

Property specifications are often written as Linear Temporal Logic (LTL) expressions. Once a requirement is expressed as an LTL formula, a model checker can automatically verify this property against the model.

Example

One example of such a system requirement: Between the time an elevator is called at a floor and the time it opens its doors at that floor, the elevator can arrive at that floor at most twice. The authors of "Patterns in Property Specification for Finite-State Verification" translate this requirement into the following LTL formula:^[1]

$\begin{align}\Box((call \lor \Diamond open) \to & ((\lnot atfloor \lor \lnot open) ~\mathcal{U} \\ & (open \lor ((atfloor \land \lnot open) ~\mathcal{U}\\ & (open \lor ((\lnot atfloor \land \lnot open) ~\mathcal{U} \\ & (open \lor ((atfloor \land \lnot open) ~\mathcal{U} \\ & (open \lor (\lnot atfloor ~\mathcal{U}~ open)))))))))))\end{align}$

See also

• Finite-state machines
• Formal methods
• Formal verification
• Kripke structure
• Linear temporal logic
• Model checking
• Temporal logic

References

1. Dwyer, M.; Avruin, G.; Corbett, J. (March 1998). Ardis, M., ed. Patterns in Property Specification for Finite-State Verification (PDF). Proceedings of the Second Workshop on Formal Methods in Software Practice. pp. 7–15.

Bibliography

1. Z. Manna and Amir Pnueli, The Temporal Logic of Reactive and Concurrent Systems: Specification, Springer-Verlag, New York, 1991.
2. Amir Pnueli, The Temporal Logic of Programs. In Proceedings of the 18th IEEE Symposium on Foundations of Computer Science (FOCS 1977), pages 46–57, 1977.