Learning Mealy Machines with Timers

Bengt Jonsson and Frits Vaandrager. Learning Mealy Machines with Timers January 2018.


We introduce a new model of Mealy machines with timers (MMTs), which is able to describe the timing behavior of a broad class of practical systems, and sufficiently restricted for active learning algorithms. We present a natural extension of Angluin's active learning algorithm, which employs sequences of inputs with precise timing. Our algorithm is based on three key results: (i) an untimed semantics for MMTs, which is equivalent to the natural timed one (ii) a Nerode congruence based on the untimed semantics, and (iii) an active automata learning algorithm which is based on approximating this Nerode congruence. This algorithm allows to learn MMTs using a number of membership and equivalence queries, which is polynomial in the number of states of the resulting MMT, and doubly exponential in the maximal number of simultaneously active timers.

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