Active Learning of Nondeterministic Finite State Machines

Abstract

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 proposeLNM*, 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 thatLNM*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 ofLNM*. In addition, experimental results demonstrate the practical efficiency of our approach.

Learning Abstracted Non-deterministic Finite State Machines

“…Tackling the problem that systems behave non-deterministic due to various reasons, e.g. ignoring timed behavior, L * -based learning algorithms [7,16,11] for ONFSMs were proposed. The algorithms for ONFSMs follow the idea of the Mealy machine learning algorithms, but instead of considering just one possible output for an input, all possible outputs are saved in the observation table.…”

“…We weaken the all-weather assumption [13] for the observation of outputs, and assume like other learning algorithms for non-deterministic systems [16,11,26] that all outputs are observable after performing a query n times. Regarding the challenge that not all outputs are observable at once, we discuss three technical aspects of our implementation: (1) repeated execution of output queries, (2) stopping criterion for output queries, and (3) shrinking of the observation table.…”

“…Our proposed learning algorithm for ONFSM is based on Angluin's L * [4]. In the literature, the majority of learning algorithms for non-deterministic systems [6,7,16,11,25,26] also follows the same principle. Bollig et al [6] introduced a learning algorithm for residual finite-state automata, which are a subclass of nondeterministic finite automata.…”

“…All Angluin-based algorithms for ONFSMs [7,16,11] basically follow the approach that was first proposed by El-Fakih et al [7]. Their algorithm is based on the all-weather assumption, i.e.…”

“…In the literature, several work on learning-based testing [23,8,3] stress the problem of observing non-deterministic behavior during learning. However, we already find learning algorithms [7,16,11] for observable non-deterministic reactive systems. To make them applicable, we have to provide an input and output alphabet that establishes observable non-determinism, i.e.…”