Extracting Synchronous Grammar Rules From Word-Level Alignments in Linear Time

We generalize Uno and Yagiura's algorithm for finding all common intervals of two permutations to the setting of two sequences with many-to-many alignment links across the two sides. We show how to maximally decompose a word-aligned sentence pair in linear time, which can be used to generate all possible phrase pairs or a Synchronous Context-Free Grammar (SCFG) with the simplest rules possible. We also use the algorithm to precisely analyze the maximum SCFG rule length needed to cover hand-aligned data from various language pairs.