Abstract
Active inference algorithms that are used to extract behavioural models of software systems usually assume that the System Under Inference (SUI) can be reset. Two approaches have been proposed to infer systems that cannot be reset. Rivest and Schapire proposed an adaptation of the \(L^*\) algorithm that relies on having a homing sequence for the SUI. We detail here another approach that is based on characterization sequences. More precisely, we assume classical testing hypotheses, namely that we are given a bound n on the number of states and a set W of characterizing sequences to distinguish states. Contrary to \(L^*\), it does not require an external oracle to decide on equivalence. The length of the test sequence is polynomial in n and the exponent depends on the cardinality |W| of the characterization set. For systems where resetting is impossible or expensive, this approach can be a viable alternative to classical learning methods.
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Notes
- 1.
The round trip time for a local network is usually between 0.1 and 1 ms. Resetting a virtual machine may depend on the type of virtualization and the speed of the underlying processor, but starting a Linux or Windows machine usually takes several tens of seconds.
- 2.
The size of the output set does not play a role in this bound. The number of transitions is solely determined by the number of states and the number of inputs. In practice, a higher number of different outputs increases distinguishability and therefore can reduce the length and the number of separating sequences. The worst case in practice is for \(|O|=2\).
- 3.
Since we have a bound on the number of states, another method for searching counterexamples could be used: enumerating sequences of increasing length up to the given bound. This would be an exponential search, but with a low bound it could be viable. However, this would still be longer than the shortest counterexamples to which we compared for reference.
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The authors acknowledge the work of Nicolas Bremond, master student from Enseirb-Matmeca who implemented the algorithms.
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Groz, R., Simao, A., Petrenko, A., Oriat, C. (2018). Inferring FSM Models of Systems Without Reset. In: Bennaceur, A., Hähnle, R., Meinke, K. (eds) Machine Learning for Dynamic Software Analysis: Potentials and Limits. Lecture Notes in Computer Science(), vol 11026. Springer, Cham. https://doi.org/10.1007/978-3-319-96562-8_7
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