Identification of biRFSA languages

Authors:
Michel Latteux;Aurélien Lemay;Yves Roos;Alain Terlutte
Affiliations:
Laboratoire d'Informatique Fondamentale de Lille, Université de Lille, Villeneuve d'Ascq Cedex, France;Équipe Grappa-EA, Université de Lille, Domaine universitaire du "Pont de bois", Villeneuve d'Ascq Cedex, France;Laboratoire d'Informatique Fondamentale de Lille, Université de Lille, Villeneuve d'Ascq Cedex, France;Équipe Grappa-EA, Université de Lille, Domaine universitaire du "Pont de bois", Villeneuve d'Ascq Cedex, France
Venue:
Theoretical Computer Science - In honour of Professor Christian Choffrut on the occasion of his 60th birthday
Year:
2006

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Abstract

The task of identifying a language from a set of its words is not an easy one. For instance, it is not feasible to identify regular languages in the general case. Therefore, looking for subclasses of regular languages that can be identified in this framework is an interesting problem. One of the most classical identifiable classes is the class of reversible languages, introduced by D. Angluin, also called bideterministic languages as they can be represented by deterministic automata (DFA) whose reverse is also deterministic. Residual finite state automata (RFSA) on the other hand is a class of non-deterministic automata that shares some properties with DFA. In particular, DFA are RFSA and RFSA can be much smaller. We study here learnability of the class of languages that can be represented by biRFSA: RFSA whose reverse are RFSA. We prove that this class is not identifiable in general but we present two subclasses that are learnable, the second one being identifiable in polynomial time.