TAL RECOGNITION IN O(M(N(2))) TIME

We propose an O(M(n(2))) time algorithm for the recognition of tree ad joining languages (TALs), where n is the sire of the input string and M(k) is the time needed to multiply two kxk boolean matrices. Tree adj oining grammars are formalisms suitable for natural language processin g and have received enormous attention in the past among not only natu ral 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(n(6)). Quite recently. an O(n(3)/M(n)) algorit hm has been proposed. The algorithm presented in this paper improves t he run time of the recent result using an entirely different approach. (C) 1998 Academic Press.