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On monitoring linear temporal properties

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Abstract

Runtime verification facilitates monitoring the executions of a system against temporal properties, commonly to detect violations. Not every temporal property is fully monitorable however: in some cases, a positive or negative verdict on the monitored execution does not depend on any finite prefix of it. We study the problem of monitoring properties written in linear temporal logic. We provide a complete classification of the temporal properties based on the ability to provide positive and/or negative verdicts in finite time.

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Notes

  1. This was done without a proof, hence, for completeness we detail the proof here.

  2. 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 \(\mathcal{C}_{\lnot \varphi }\).)

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Acknowledgements

The authors would like to thank Moran Omer for useful comments on the manuscript. The research performed by Klaus Havelund 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 Doron Peled was partially funded by Israeli Science Foundation grant 1464/18: “Efficient Runtime Verification for Systems with Lots of Data and its Applications”.

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Authors and Affiliations

  1. Laboratory for Reliable Software, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, 91109, USA

    Klaus Havelund

  2. Department of Computer Science, Bar Ilan University, 5290002, Ramat Gan, Israel

    Doron Peled

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  1. Klaus Havelund
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  2. Doron Peled
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Correspondence to Doron Peled.

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Havelund, K., Peled, D. On monitoring linear temporal properties. Form Methods Syst Des 60, 405–425 (2022). https://doi.org/10.1007/s10703-023-00429-8

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