Abstract
We address the specification and verification of spatio-temporal behaviours of complex systems, extending Signal Spatio-Temporal Logic (SSTL) with a spatial operator capable of specifying topological properties in a discrete space. The latter is modelled as a weighted graph, and provided with a boolean and a quantitative semantics. Furthermore, we define efficient monitoring algorithms for both the boolean and the quantitative semantics. These are implemented in a Java tool available online. We illustrate the expressiveness of SSTL and the effectiveness of the monitoring procedures on the formation of patterns in a Turing reaction-diffusion system.
Work partially funded by the EU-FET project QUANTICOL (nr. 600708), by the German Research Council (DFG) as part of the Cluster of Excellence on Multimodal Computing and Interaction at Saarland University and the IT MIUR project CINA. We thank Diego Latella and Ezio Bartocci for the discussions and EB for sharing the code to generate traces of the example.
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Notes
- 1.
Due to lack of space all proofs are omitted. The interested reader may refer to [17].
- 2.
Time bounds can be restricted to rational numbers, hence there always exists an \(h>0\) satisfying all assumptions.
- 3.
The assumption of Lipschitz continuity holds whenever the primary signal is the solution of an ODE with a locally Lipschitz vector field, as usually is the case.
- 4.
jSSTL is available on-line at https://bitbucket.org/LauraNenzi/jsstl.
- 5.
- 6.
For simplicity, here we fix \(\delta =1\). Note that using a non-uniform mesh the weights of the edges of the resulting graph will not be uniform.
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Nenzi, L., Bortolussi, L., Ciancia, V., Loreti, M., Massink, M. (2015). Qualitative and Quantitative Monitoring of Spatio-Temporal Properties. In: Bartocci, E., Majumdar, R. (eds) Runtime Verification. Lecture Notes in Computer Science(), vol 9333. Springer, Cham. https://doi.org/10.1007/978-3-319-23820-3_2
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