Formal language identification: query learning vs. Gold-style learning

Abstract

A natural approach towards powerful machine learning systems is to enable options for additional machine/user interactions, for instance by allowing the system to ask queries about the concept to be learned. This motivates the development and analysis of adequate formal learning models. In the present paper, we investigate two different types of query learning models in the context of learning indexable classes of recursive languages: Angluin's original model and a relaxation thereof, called learning with extra queries. In the original model the learner is restricted to query languages belonging to the target class, while in the new model it is allowed to query other languages, too. As usual, the following standard types of queries are considered: superset, subset, equivalence, and membership queries. The learning capabilities of the resulting query learning models are compared to one another and to different versions of Gold-style language learning from only positive data and from positive and negative data (including finite learning, conservative inference, and learning in the limit). A complete picture of the relation of all these models has been elaborated. A couple of interesting differences and similarities between query learning and Gold-style learning have been observed. In particular, query learning with extra superset queries coincides with conservative inference from only positive data. This result documents the naturalness of the new query model.