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Mathematical Problems in Engineering
Volume 2013, Article ID 373265, 11 pages
Research Article

Active Learning of Nondeterministic Finite State Machines

1Department of Computer Engineering, Chulalongkorn University, Bangkok 10330, Thailand
2School of Information Science, Japan Advanced Institute of Science and Technology, Ishikawa 923-1292, Japan
3Department of Mathematics, Chulalongkorn University, Bangkok 10330, Thailand

Received 27 June 2013; Revised 12 October 2013; Accepted 12 October 2013

Academic Editor: Yang Tang

Copyright © 2013 Warawoot Pacharoen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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