Abstract
Runtime Verification is a branch of formal methods concerned with analysis of execution traces for the purpose of determining the state or general quality of the executing system. The field covers numerous approaches, one of which is specification-based runtime verification, where execution traces are checked against formal specifications. The paper presents syntax, semantics, and monitoring algorithms for respectively propositional and first-order temporal logics. In propositional logics the observed events in the execution trace are represented using atomic propositions, while first-order logic allows universal and existential quantification over data occurring as arguments in events. Monitoring of the first-order case is drastically more challenging than the propositional case, and we present a solution for this problem based on BDDs. We furthermore discuss monitorability of temporal properties by dividing them into different classes representing different degrees of monitorability.
The research performed by the first author was carried out at Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. The research performed by the second author was partially funded by Israeli Science Foundation grant 2239/15: “Runtime Measuring and Checking of Cyber Physical Systems”.
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Notes
- 1.
RV can be understood more broadly to mean: any processing of execution traces for the purpose of evaluating a system state or quality. Some approaches do not involve specifications but rather use pre-programmed algorithms as monitors.
- 2.
This definition is equivalent to the traditional definition \(\xi , {i} \models ( \varphi \ \mathcal {S}\ \psi )\) iff for some \(0 < j \le i\), \(\xi , {j} \models \psi \), and for all \(j < k \le i\) it holds that \(\xi , {k} \models \varphi \), but is more intuitive for the forthcoming presentation of the RV algorithm.
- 3.
There are examples of safety properties that are much more compact when expressed with the past temporal operators [21], and for symmetrical considerations also vice versa.
- 4.
To show that a property is not monitorable, one needs to guess a state of \(\mathcal{B}_\varphi \times \mathcal{B}_{\lnot \varphi }\) and check that (1) it is reachable, and (2) one cannot reach from it an empty component, both for \(\mathcal{B}_\varphi \) and for \(\mathcal{B}_{\lnot \varphi }\). (There is no need to construct \(\mathcal{C}_\varphi \) or \(\mathcal{C}_{\lnot \varphi }\).).
- 5.
Proving that liveness was PSPACE-hard was shown in [3].
- 6.
All examples of safety properties henceforth will omit the implied
operator. - 7.
For dealing with finite domains see [12].
- 8.
is the overriding of \(\gamma \) with the binding 
. - 9.
An additional 600+ lines of property independent boilerplate code is generated.
- 10.
Traces accepted by the tool are concretely in CSV format. For example the first event is a single line of the form: open,input,read.
operator.
is the overriding of 
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Havelund, K., Peled, D. (2018). Runtime Verification: From Propositional to First-Order Temporal Logic. In: Colombo, C., Leucker, M. (eds) Runtime Verification. RV 2018. Lecture Notes in Computer Science(), vol 11237. Springer, Cham. https://doi.org/10.1007/978-3-030-03769-7_7
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