Parsing CFGs and PCFGs with a Chomsky-Schützenberger Representation

We present a parsing algorithm for arbitrary context-free and probabilistic context-free grammars based on a representation of such grammars as a combination of a regular grammar and a grammar of balanced parentheses, similar to the representation used in the Chomsky-Schützenberger theorem. The basic algorithm has the same worst-case complexity as the popular CKY and Earley parsing algorithms frequently employed in natural language processing tasks. As natural languages rarely take advantage of the crucial distinguishing feature between regular and context-free languages, that of center embedding, we also investigate methods to speed up parsing at the cost of some overgeneration by forgoing the enforcement of proper nesting of constituents in the algorithm.