Operators of length four like 2, 4, 1, 3 (Wu, 1997) are presumably more complex than 2, 1 , whereas operators longer than four signify even more complex order difference.
we devise possible branching feature functions over the operator length for the nodes in PETs: • factor 2 -with two features: ∆ [ ] and ∆ <> (there are no nodes with factor 3 (Wu, 1997)) • factor 4 -feature ∆ =4 • factor bigger than 4 -feature ∆ >4 Consider permutations 2, 1, 4, 3 and 4, 3, 2, 1 , none of which has exactly matching ngrams beyond unigrams.