An E cient Recognition Algorithm for Multiple Context - Free

Valiant proposed an O(n 2) time algorithm which reduces the recognition problem for context-free languages (CFLs) to the boolean matrices multiplication problem. By this algorithm, the recognition problem for CFLs can be solved in O(maxfn 2 ; M(n)g) time where n is the length of an input string and M(k) is the time needed for multiplying two k k boolean matrices. The best known value for M(k) is O(k 2:376). Multiple context-free grammars (MCFGs) were introduced to denote the syntax of natural languages. By the known fastest algorithm, the recognition problem for multiple context-free languages (MCFLs) can be solved in O(n e) time where e is a constant which depends only on a given MCFG G, called the degree of G. In this paper, we propose an algorithm which reduces the recognition problem for MCFLs to the boolean matrices multiplication problem. By this algorithm, the recognition problem for MCFLs can be solved in O(n e 0 ?3i 0 +1 M(n i 0)) time where e 0 and i 0 are constants which depend only on a given MCFG (e 0 e; i 0 1). The time complexity of this algorithm is less than that of the forementioned algorithm unless e 0 = e and i 0 = 1.