For CLA word alignment, if we use the same association score, direct and inverse CLA word alignments should be exactly the same.
we use different functions to compute the surface similarities, such as using maximum common subsequence (MCS) to compute inverse word alignment, and using longest matched prefix (LMP) for computing direct word alignment, as in Equation 4  2) When two word alignments are ready, we start from the intersection of the two word alignments, and then continuously add new links between backbone and hypothesis if and only if both of the two words of the new link are unaligned and this link exists in the union of two word alignments.