Partially distribution-free learning of regular languages from positive samples

Regular languages are widely used in NLP today in spite of their shortcomings. Efficient algorithms that can reliably learn these languages, and which must in realistic applications only use positive samples, are necessary. These languages are not learnable under traditional distribution free criteria. We claim that an appropriate learning framework is PAC learning where the distributions are constrained to be generated by a class of stochastic automata with support equal to the target concept. We discuss how this is related to other learning paradigms. We then present a simple learning algorithm for regular languages, and a self-contained proof that it learns according to this partially distribution free criterion.