Learning balls of strings with correction queries

Abstract

During the 80's, Angluin introduced an active learning paradigm, using an Oracle, capable of answering both membership and equivalence queries. However, practical evidence tends to show that if the former are often available, this is usually not the case of the latter. We propose new queries, called correction queries, which we study in the framework of Grammatical Inference. When a string is submitted to the Oracle, either she validates it if it belongs to the target language, or she proposes a correction, i.e., a string of the language close to the query with respect to the edit distance. We also introduce a non-standard class of languages: The topological balls of strings. We show that this class is not learnable in Angluin's MAT model, but is with a linear number of correction queries. We conduct several experiments with an Oracle simulating a human Expert, and show that our algorithm is resistant to approximate answers. © Springer-Verlag Berlin Heidelberg 2007.