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L. Bortolussi, G. Maria Gallo, J. Křetínský, L. Nenzi:
"Learning Model Checking and the Kernel Trick for Signal Temporal Logic on Stochastic Processes";
accepted as talk for: Proc. of TACAS 2022: the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, Munich, Germany; 2022-04-02 - 2022-04-07; in: "Proc. of TACAS 2022: the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems", Proc. of TACAS 2022: the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, (2022), 1 - 20.

We introduce a similarity function on formulae of signal temporal logic (STL). It comes in the form of a kernel function, well known
in machine learning as a conceptually and computationally efficient tool.
The corresponding kernel trick allows us to circumvent the complicated
process of feature extraction, i.e. the (typically manual) effort to identify the decisive properties of formulae so that learning can be applied. We demonstrate this consequence and its advantages on the task of predicting (quantitative) satisfaction of STL formulae on stochastic processes:

Using our kernel and the kernel trick, we learn (i) computationally efficiently (ii) a practically precise predictor of satisfaction, (iii) avoiding the difficult task of finding a way to explicitly turn formulae into vectors of numbers in a sensible way. We back the high precision we have achieved in the experiments by a theoretically sound PAC guarantee, ensuring our procedure efficiently delivers a close-to-optimal predictor.