Learning Context Free Grammars in the Limit Aided by the Sample Distribution

We present an algorithm for learning context free grammars from positive structural examples (unlabeled parse trees). The algorithm receives a parameter in the form of a finite set of structures and the class of languages learnable by the algorithm depends on this parameter. Every context free language belongs to many such learnable classes. A second part of the algorithm is then used to determine this parameter (based on the language sample). By Gold’s theorem, without introducing additional assumptions, there is no way to ensure that, for every language, the parameter chosen by the learner will make the language learnable. However, we show that determining the parameter based on the sample distribution is often reasonable, given some weak assumptions on this distribution. Among other things, repeated learning, where one learner learns the language the previous learner converged to, is guaranteed to produce a learnable language after a finite number of steps. This set of limit languages then forms a natural class of learnable languages.