Robust Learning of Automatic Classes of Languages

This paper adapts and investigates the paradigm of robust learning, originally defined in the inductive inference literature for classes of recursive functions, to learning languages from positive data. Robustness is a very desirable property, as it captures a form of invariance of learnability under admissible transformations on the object of study. The classes of languages of interest are automatic — a formal concept that captures the notion of being recognisable by a finite automaton. A class of first-order definable operators — called translators — is introduced as natural transformations that preserve automaticity of languages in a given class and the inclusion relations between languages in the class. For many learning criteria, we characterise the classes of languages all of whose translations are learnable under that criterion. The learning criteria have been chosen from the literature on both explanatory learning from positive data and query learning, and include consistent and conservative learning, strong-monotonic learning, strong-monotonic consistent learning, finite learning, learning from subset queries, learning from superset queries, and learning from membership queries.