Feasible Learnability of Formal Grammars and The Theory of Natural Language Acquisition

We propose to apply a complexity theoretic notion of feasible learnability called "polynomial learnability" to the evaluation of grammatical formalisms for linguistic description. Polynomial learnability was originally defined by Valiant in the context of boolean concept learning and subsequently generalized by Blumer et al. to infinitary domains. We give a clear, intuitive exposition of this notion of learnability and what characteristics of a collection of languages may or many not help feasible learn ability under this paradigm. In particular, we present a novel, nontrivial constraint on the degree of "locality" of grammars which allows a rich class of mildly context sensitive languages to be feasibly learnable. We discuss possible implications of this observation to the theory of natural language acquisition.