Polynomial-time learning of very simple grammars from positive data

This paper concerns a subclass of simple deterministic grammars, called very simple grammars , and studies the problem of identifying the subclass in the limit from positive data. The class of very simple languages forms a proper subclass of simple deterministic languages and is incomparable to the class of regular languages. After providing some characterization results for very simple languages, we show that the class of very simple grammars is polynomial-time identifiable in the limit from positive data in the sense of Pitt. That is, there is an algorithm that, given the targeted very simple grammar G * , identifies a very simple grammar G equivalent to G * in the limit from positive data, satisfying the property that the time for updating a conjecture is bounded by a polynomial in m , and the total number of prediction errors made by the algorithm is bounded by the cardinality k of the terminal alphabet involved in G * , where m is the maximum of k and the total lengths of all positive data provided.