An Alternative Conception of Tree-Adjoining Derivation

The precise formulation of derivation for tree-adjoining grammars has important ramifications for a wide variety of uses of the formalism, from syntactic analysis to semantic interpretation and statistical language modeling. We argue that the definition of tree-adjoining derivation must be reformulated in order to manifest the proper linguistic dependencies in derivations. The particular proposal is both precisely characterizable through a definition of TAG derivations as equivalence classes of ordered derivation trees, and computationally operational, by virtue of a compilation to linear indexed grammars together with an efficient algorithm for recognition and parsing according to the compiled grammar.Comment: 33 page

Probabilistic parsing

Postprin

Analytic aspects of the shuffle product

There exist very lucid explanations of the combinatorial origins of rational and algebraic functions, in particular with respect to regular and context free languages. In the search to understand how to extend these natural correspondences, we find that the shuffle product models many key aspects of D-finite generating functions, a class which contains algebraic. We consider several different takes on the shuffle product, shuffle closure, and shuffle grammars, and give explicit generating function consequences. In the process, we define a grammar class that models D-finite generating functions