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 may not help feasible learnability 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. Comments University of Pennsylvania Department of Computer and Information Science Technical Report No. MSCIS-88-50. This technical report is available at ScholarlyCommons: http://repository.upenn.edu/cis_reports/674 FEASIBLE LEARNABILITY OF FORMAL GRAMMARS AND THE THEORY OF NATURAL LANGUAGE ACQUlSTlON Naoki Abe MS-CIS-88-50 LlNC LAB 120 Department of Computer and Information Science School of Engineering and Applied Science University of Pennsylvania Philadelphia, PA 191 04 July 1988 Acknowledgements: This research was supported in part by an IBM graduate fellowship, DARPA grant NO001 4-85-K-0018, NSF grants MCS-8219196-CER, IR184-10413-A02 and U.S. Army grants DAA29-84-K-0061, DAA29-84-9-0027. Feasible Learnability of Formal Grammars and the Theory of Natural Language Acquisition Naoki Abe Department of Computer and Information Science, University of Pennsylvania, Philadelphia, PA1 9 104.