Learning Balls of Strings: A Horizontal Analysis

There are a number of established paradigms to study the learnability of classes of functions or languages: Query learning, Identification in the limit, Probably Approximately Correct learning. Comparison between these paradigms is hard. Moreover, when to the question of converging one adds computational constraints, the picture becomes even less clear. We concentrate here on just one class of languages, that of topological balls of strings (for the edit distance), and visit the different learning paradigms in this context. Between the results, we show that surprisingly it is technically easier to learn from text than from an informant.