Borel subgroup

Template:Mergeto Template:Essay 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:

$\begin{array}{rl}◻((call\vee ◊open)\to & ((\mathrm{\neg }atfloor\vee \mathrm{\neg }open)\mathcal{𝒰}\\ & (open\vee ((atfloor\wedge \mathrm{\neg }open)\mathcal{𝒰}\\ & (open\vee ((\mathrm{\neg }atfloor\wedge \mathrm{\neg }open)\mathcal{𝒰}\\ & (open\vee ((atfloor\wedge \mathrm{\neg }open)\mathcal{𝒰}\\ & (open\vee (\mathrm{\neg }atfloor\mathcal{𝒰}open)))))))))))\end{array}$

See also

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

References

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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.