Identiflability of subspaces and homomorphic images of zero-reversible languages

Abstract

In this paper, we study two operations of taking subspaces and homomorphic images of identifiable concept classes from positive data. We give sufficient conditions for the identifiable classes to be identifiable from positive data after the applications of those two operations. As one of the examples to show the effectiveness of the obtained theorems, we will apply them to the class of zero-reversible languages, and obtain some interesting identifiable language classes related to reversible languages. Further, we will show a connection of those theories to the theory of approximate identification in the limit from positive data([Kob96]). Another important contribution of this paper is am algebraic extension of Angluin's theorem in [Ang80] based on am algebraic characterization of zero-reversible languages given by [Pin87]. This generalized theorem tells us the importaace of Pin's chazacterization of zero-reversible languages using finitely generated groups in the context of identification in the limit from positive data.