We propose an O(M(n2)) time algorithm for the recognition of Tree Adjoining Languages (TALs), where n is the size of the input string and M(k) is the time needed to multiply two k x k boolean matrices. Tree Adjoining Grammars (TAGs) 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 of O(n6). has been proposed. .
