TAL Recognition inO(M(n2)) Time

摘要

We propose anO(M(n2)) time algorithm for the recognition of tree adjoining languages (TALs), wherenis the size of the input string andM(k) is the time needed to multiply twok×kboolean matrices. Tree adjoining grammars are formalisms suitable for natural language processing and have received enormous attention in the past among not only natural language processing researchers but also algorithms designers. The first polynomial time algorithm for TAL parsing was proposed in 1986 and had a run time ofO(n6). Quite recently, anO(n3M(n)) algorithm has been proposed. The algorithm presented in this paper improves the run time of the recent result using an entirely different approach.