Learnability of automatic classes

The present work initiates the study of the learnability of automatic indexable classes which are classes of regular languages of a certain form. Angluinʼs tell-tale condition characterises when these classes are explanatorily learnable. Therefore, the more interesting question is when learnability holds for learners with complexity bounds, formulated in the automata–theoretic setting. The learners in question work iteratively, in some cases with an additional long-term memory, where the update function of the learner mapping old hypothesis, old memory and current datum to new hypothesis and new memory is automatic. Furthermore, the dependence of the learnability on the indexing is also investigated. This work brings together the fields of inductive inference and automatic structures.

► This paper brings together the fields of automatic structures and learning theory.
► The paper first considers automatic families and formalises when they are learnable.
► In particular, it introduces the notion of automatic learners and establishes first results.
► It explores how bounds on the long-term memory of an automatic learner relate to learnability.
► It contains detailed results on additional constraints on learning (consistency, conservativeness, …).