Abstract
We present a technique for learning explainable timed automata from passive observations of a black-box function, such as an artificial intelligence system. Our method accepts a single, long, timed word with mixed input and output actions and learns a Mealy machine with one timer. The primary advantage of our approach is that it constructs a symbolic observation tree from a concrete timed word. This symbolic tree is then transformed into a human comprehensible automaton. We provide a prototype implementation and evaluate it by learning the controllers of two systems: a brick-sorter conveyor belt trained with reinforcement learning and a real-world derived smart traffic light controller. We compare different model generators using our symbolic observation tree as their input and achieve the best results using k-tails. In our experiments, we learn smaller and simpler automata than existing passive timed learners while maintaining accuracy.
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Notes
- 1.
Note that the approach also works with more than one word.
- 2.
A note on the experiment design: since the symbolic abstraction is not learned (i.e., does not extrapolate beyond certain knowledge), we do not evaluate its performance but focus on the utility in model learning. We fix adequate initial conditions for computing the trace databases.
- 3.
A problem with applying TkT to the intersection’s logs is that an unbounded number of inputs can occur before a relevant output (i.e., cars being detected before the signal switches). As a result, no k can be chosen that would avoid overfitting.
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Acknowledgements
This work was supported by the S40S Villum Investigator Grant (37819) from VILLUM FONDEN, the ERC Advanced Grant LASSO, DIREC, and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – 495857894 (STING).
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Dierl, S. et al. (2023). Learning Symbolic Timed Models from Concrete Timed Data. In: Rozier, K.Y., Chaudhuri, S. (eds) NASA Formal Methods. NFM 2023. Lecture Notes in Computer Science, vol 13903. Springer, Cham. https://doi.org/10.1007/978-3-031-33170-1_7
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