Active Learning of Nondeterministic Finite State Machines

Abstract EN

We consider the problem of learning nondeterministic finite state machines (NFSMs) from systems where their internal structures are implicit and nondeterministic.

Recently, an algorithm for inferring observable NFSMs (ONFSMs), which are the potentially learnable subclass of NFSMs, has been proposed based on the hypothesis that the complete testing assumption is satisfied.

According to this assumption, with an input sequence (query), the complete set of all possible output sequences is given by the so-called Teacher, so the number of times for asking the same query is not taken into account in the algorithm.

In this paper, we propose LNM*, a refined ONFSM learning algorithm that considers the amount for repeating the same query as one parameter.

Unlike the previous work, our approach does not require all possible output sequences in one answer.

Instead, it tries to observe the possible output sequences by asking the same query many times to the Teacher.

We have proved that LNM* can infer the corresponding ONFSMs of the unknown systems when the number of tries for the same query is adequate to guarantee the complete testing assumption.

Moreover, the proof shows that our algorithm will eventually terminate no matter whether the assumption is fulfilled or not.

We also present the theoretical time complexity analysis of LNM*.

In addition, experimental results demonstrate the practical efficiency of our approach.