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

Polynomial Learnability and Locality of Formal Grammars

We apply a complexity theoretic notion of feasible learnability called polynomial learnability to the evaluation of grammatical formalisms for linguistic description. We show that a novel, nontrivial constraint on the degree of locality of grammars allows not only context free languages but also a rich class of mildly context sensitive languages to be polynomially learnable. We discuss possible implications of this result to the theory of natural language acquisition

The Tree-Generative Capacity of Combinatory Categorial Grammars

The generative capacity of combinatory categorial grammars as acceptors of tree languages is investigated. It is demonstrated that the such obtained tree languages can also be generated by simple monadic context-free tree grammars. However, the subclass of pure combinatory categorial grammars cannot even accept all regular tree languages. Additionally, the tree languages accepted by combinatory categorial grammars with limited rule degrees are characterized: If only application rules are allowed, then they can accept only a proper subset of the regular tree languages, whereas they can accept exactly the regular tree languages once first degree composition rules are permitted

On the complexity of bounded second-order unification and stratified context unification

Bounded Second-Order Unification is a decidable variant of undecidable Second-Order Unification. Stratified Context Unification is a decidable restriction of Context Unification, whose decidability is a long-standing open problem. This paper is a join of two separate previous, preliminary papers on NP-completeness of Bounded Second-Order Unification and Stratified Context Unification. It clarifies some omissions in these papers, joins the algorithmic parts that construct a minimal solution, and gives a clear account of a method of using singleton tree grammars for compression that may have potential usage for other algorithmic questions in related areas. © The Author 2010. Published by Oxford University Press. All rights reserved.This research has been partially supported by the research projects Mulog-2 (TIN2007-68005-C04-01) and SuRoS TIN2008-04547) funded by the CICyTPeer Reviewe

Equivalence Problems for Tree Transducers: A Brief Survey

The decidability of equivalence for three important classes of tree transducers is discussed. Each class can be obtained as a natural restriction of deterministic macro tree transducers (MTTs): (1) no context parameters, i.e., top-down tree transducers, (2) linear size increase, i.e., MSO definable tree transducers, and (3) monadic input and output ranked alphabets. For the full class of MTTs, decidability of equivalence remains a long-standing open problem.Comment: In Proceedings AFL 2014, arXiv:1405.527